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CARMA-Sponsored Seminar Series: Colloquia, Seminars and More.

Last updated Wednesday, 23 Sep, 2015


[Note: events are listed by descending date.]
  • CARMA SEMINAR
  • Speaker: Ernst Stephan, Institute for Applied Mathematics, Leibniz University Hannover
  • Title: Adaptive and higher-order time domain boundary elements for the wave equation
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Tue, 21st Nov 2017
  • Abstract:
    We present $h$ and $p$-versions of the time domain boundary element method for boundary and screen problems for the wave equation in $\mathbb{R}^3$. First, graded meshes are shown to recover optimal approximation rates for solution in the presence of edge and corner singularities on screens. Then an a posteriori error estimate is presented for general discretizations, and it gives rise to adaptive mesh refinement procedures. We also discuss preliminary results for $p$ and $hp$-versions of the time domain boundary element method. Numerical experiments illustrate the theory. Joint with H. Gimperlein and D. Stark, Heriot-Watt University, Edinburgh.
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  • CARMA SEMINAR
  • Speaker: Dr Davor Dragicevic, University of NSW
  • Title: Lyapunov functions for hyperbolic behaviour
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Tue, 19th Sep 2017
  • Abstract:
    I will present a brief survey of some recent results that deal with the characterization of hyperbolic dynamics in terms of the existence of appropriate Lyapunov functions. The main novelty of these results lies in the fact that they consider noninvertible and infinite-dimensional dynamics. This is a joint work with L. Barreira, C. Preda and C. Valls.
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  • CARMA SEMINAR
  • Speaker: Dr Bishnu Lamichhane, CARMA, The University of Newcastle
  • Title: My recent journey into mixed finite element methods
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Tue, 8th Aug 2017
  • Abstract:
    In this talk I will briefly introduce the mixed finite element method and show their applications. I consider Poisson, elasticity, Stokes and biharmonic equations for the applications of the mixed finite element method. The mixed finite element method also arises naturally in Stokes flow, multi-physics problems as well as when we consider non-conforming discretisation techniques. I will also present my recent works on the mixed finite element method for biharmonic and Reissner-Mindlin plate equations.
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  • CARMA SEMINAR
  • Speaker: A/Prof Chris Kellett, School of Electrical Engineering and Computer Science, The University of Newcastle
  • Title: Back and Forth in Lyapunov's Second Method - Non-uniform Subtleties
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Tue, 13th Jun 2017
  • Abstract:

    Lyapunov's second or direct method provides an easy-to-check sufficient condition for stability properties of equilibria. The converse question - given a stability property, does there exist an appropriate Lyapunov function? - has been fundamental in differentiating and classifying different stability properties, particularly with regards to "uniform" stability.

    In this talk, I will review the usual textbook definitions for Lyapunov functions for time-varying systems and describe where they are deficient. Some interesting new sufficient (and probably necessary) conditions pop up along the way.

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  • CARMA SEMINAR
  • Speaker: Prof. André Nies, Department of Computer Science, The University of Auckland
  • Title: The complexity of the isomorphism problem for t.d.l.c. and other types of groups
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 1st Jun 2017
  • Abstract:

    We determine the Borel complexity of the topological isomorphism problem for profinite, t.d.l.c., and Roelcke precompact non-Archimedean groups, by showing it is equivalent to graph isomorphism.

    For oligomorphic groups we merely establish this as an upper bound.

    Joint work with Kechris and Tent.

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  • CARMA SEMINAR
  • Speaker: Dr Philipp Braun, School of Electrical Engineering and Computer Science, The University of Newcastle
  • Title: (Nonsmooth) Control Lyapunov Functions: Stabilization and Destabilization of Nonlinear Systems
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Tue, 23rd May 2017
  • Abstract:
    Control Lyapunov functions (CLFs) for the control of dynamical systems have faded from the spotlight over the last years even though their full potential has not been explored yet. To reactivate research on CLFs we review existing results on Lyapunov functions and (nonsmooth) CLFs in the context of stability and stabilization of nonlinear dynamical systems. Moreover, we highlight open problems and results on CLFs for destabilization. The talk concludes with ideas on Complete CLFs, which combine the concepts of stability and instability. The results presented in the talk are illustrated and motivated on the examples of a nonholonomic integrator and Artstein's circles.
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  • CARMA SEMINAR
  • Speaker: Prof Wadim Zudilin, CARMA, The University of Newcastle
  • Title: Hypergeometric heritage of W.N. Bailey
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Tue, 16th May 2017
  • Abstract:
    Part of my 2016 SSP included completion of a semi-historical review on the mathematics of W.N. Bailey, a familiar name in some combinatorics circles in relation with the "Bailey lemma" and "Bailey pairs." My personal encounters with the mathematician from the first half of the 20th century were somewhat different and more related to applications of special functions to number theory—the subject Bailey had never dealt with himself. One motivation for my writing was the place where I spent my SSP—details to be revealed in the talk. There will be some formulas displayed, sometimes scary, but they will serve as a background to historical achievements. Broad audience is welcome.
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  • CARMA SEMINAR
  • Speaker: Dr Matt Tam, Institute for Numerical and Applied Mathematics, University of Goettingen
  • Title: Symbolic convex analysis
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 11th May 2017
  • Abstract:
    In this talk we consider a class of monotone operators which are appropriate for symbolic representation and manipulation within a computer algebra system. Various structural properties of the class (e.g., closure under taking inverses, resolvents) are investigated as well as the role played by maximal monotonicity within the class. In particular, we show that there is a natural correspondence between our class of monotone operators and the subdifferentials of convex functions belonging to a class of convex functions deemed suitable for symbolic computation of Fenchel conjugates which were previously studied by Bauschke & von Mohrenschildt and by Borwein & Hamilton. A number of illustrative computational examples utilising the introduced class of operators will be provided including computation of proximity operators, recovery of a convex penalty function associated with the hard thresholding operator, and computation of superexpectations, superdistributions and superquantiles with specialization to risk measures.
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  • CARMA SEMINAR
  • Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
  • Title: Honeycomb Toroidal Graphs: A Drama in Three Acts
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Tue, 9th May 2017
  • Abstract:
    I am going to look at three unsolved graph theory problems for which the same family of graphs presents a barrier to either solving or making substantial progress on the problems. The graphs in this family are called honeycomb toroidal graphs. The three problems are not closely related.
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  • CARMA SEMINAR
  • Speaker: Nicolai Stammeier, The University of Oslo
  • Title: The internal structure of Zappa-Szép products of right LCM semigroups
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 23rd Mar 2017
  • Abstract:
    In recent joint work on equilibrium states on semigroup C*-algebras with Afsar, Brownlowe, and Larsen, we discovered that the structure of equilibrium states admits an elegant description in terms of substructures of the original semigroup. More precisely, we consider two almost contrary subsemigroups and related features to obtain a unifying picture for a number of predating case studies. Somewhat surprisingly, all the examples from the case studies satisfy a list of four abstract properties (and are then called admissible). The nature and presence of these properties is yet to be fully understood. In this talk, I will focus on a class of examples arising as Zappa-Szép products of right LCM semigroups which showcases some interesting features. No prerequisites in operator algebras are required to follow this talk.
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  • CARMA SEMINAR
  • Speaker: Dr Jeff Hogan, CARMA, The University of Newcastle
  • Title: A Guided Tour of Harmonic Analysis
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Tue, 14th Mar 2017
  • Abstract:
    This talk gives an outline of (mostly unfinished) work done collaboratively while on sabbatical in semester 2 last year. Join me as we travel through the USA, Germany, Belgium and Austria. Your guide will share off-the-beaten-track highlights such as quaternionic splines, prolate shift systems, higher-dimensional Hardy, Paley-Wiener and Bernstein spaces, the Clifford Fourier transform, multidimensional prolates, and a Jon Borwein-inspired optimization-based approach to the construction of multidimensional wavelets. Breakfast not included.
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  • CARMA SEMINAR
  • Speaker: Duc Tran, The University of Newcastle
  • Title: Incremental Stability Properties for Discrete-Time Systems
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Dates: Wed, 30th Nov 2016 - Wed, 30th Nov 2016
  • Abstract:
    Incremental stability describes the asymptotic behavior between any two trajectories of dynamical systems. Such properties are of interest, for example, in the study of observers or synchronization of chaos. In this paper, we develop the notions of incremental stability and incremental input-to-state stability (ISS) for discrete-time systems. We derive Lyapunov function characterizations for these properties as well as a useful summation-to-summation formulation of the incremental stability property.
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  • CARMA SEMINAR
  • Speaker: Andrew Goh, The University of Newcastle
  • Title: Solving free group equations on a computer
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Dates: Wed, 30th Nov 2016 - Wed, 30th Nov 2016
  • Abstract:
    I will discuss how to solve free group equations using a practical computer program. Ciobanu, Diekert and Elder recently gave a theoretical algorithm which runs in nondeterministic space $n\log n$, but implementing their method as an actual computer program presents many challenges, which I will describe.
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  • CARMA SEMINAR
  • Speaker: George Havas, The University of Queensland
  • Title: Commutator identities as products of powers
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 11:00 am, Mon, 28th Nov 2016
  • Abstract:
    Some Engel words and also commutators of commutators can be expressed as products of powers. I discuss recent work of Colin Ramsay in this area, using PEACE (Proof Extraction After Coset Enumeration), and in particular provide expressions for commutators of commutators as short products of cubes.
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  • CARMA SEMINAR
  • Speaker: James Rout, University of Wollongong
  • Title: Structure and classification of generalised Bunce-Deddens algebras
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 3rd Nov 2016
  • Abstract:
    In this talk I will present a class of C*-algebras known as "generalised Bunce-Deddens algebras" which were constructed by Kribs and Solel in 2007 from directed graphs and sequences of natural numbers. I will present answers to questions asked by Kribs and Solel about the simplicity and the classification of these C*-algebras. These results are from my PhD thesis supervised by Dave Robertson and Aidan Sims.
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  • CARMA SEMINAR
  • Speaker: Dr David Simmons, University of York
  • Title: Unconventional height functions in Diophantine approximation
  • Location: Room V108, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 28th Jul 2016
  • Abstract:

    The standard height function $H(\mathbf p/q) = q$ of simultaneous approximation can be calculated by taking the LCM (least common multiple) of the denominators of the coordinates of the rational points: $H(p_1/q_1,\ldots,p_d/q_d) = \mathrm{lcm}(q_1,\ldots,q_m)$. If the LCM operator is replaced by another operator such as the maximum, minimum, or product, then a different height function and thus a different theory of simultaneous approximation will result. In this talk I will discuss some basic results regarding approximation by these nonstandard height functions, as well as mentioning their connection with intrinsic approximation on Segre manifolds using standard height functions. This work is joint with Lior Fishman.

    Dr Simmons is a visitor of Dr Mumtaz Hussain.

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  • CARMA SEMINAR
  • Speaker: Dr Faustin Adiceam, University of York
  • Title: On the minimum of a positive definite quadratic form over non-zero lattice points. Theory and applications.
  • Location: Room V108, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Thu, 28th Jul 2016
  • Abstract:

    Let $\Sigma_d^{++}(\R)$ be the set of positive definite matrices with determinant 1 in dimension $d\ge 2$. Identifying two $SL_d(\Z)$-congruent elements in $\Sigma_d^{++}(\R)$ gives rise to the space of reduced quadratic forms of determinant one, which in turn can be identified with the locally symmetric space $X_d:=SL_d(\Z)\backslash SL_d(\R)\slash SO_d(\R)$. Equip the latter space with its natural probability measure coming from the Haar measure on $SL_d(\R)$. In 1998, Kleinbock and Margulis established very sharp estimates for the probability that an element of $X_d$ takes a value less than a given real number $\delta>0$ over the non-zero lattice points $\Z^d\backslash\{ \bm{0} \}$.

    This talk will be concerned with extensions of such estimates to a large class of probability measures arising either from the spectral or the Cholesky decomposition of an element of $\Sigma_d^{++}(\R)$. The sharpness of the bounds thus obtained are also established for a subclass of these measures.

    This theory has been developed with a view towards application to Information Theory. Time permitting, we will briefly introduce this topic and show how the estimates previously obtained play a crucial role in the analysis of the perfomance of communication networks.

    This is work joint with Evgeniy Zorin (University of York). Dr Adiceam is a visitor of Dr Mumtaz Hussain.

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  • CARMA SEMINAR
  • Speaker: Milutin Brankovic, unknown or leave blank,
  • Title: Lehmer's Question and the Newton Polytope
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 28th Apr 2016
  • Abstract:

    Lehmer's famous question concerns the existence of monic integer coefficient polynomials with Mahler measure smaller than a certain constant. Despite significant partial progress, the problem has not been fully resolved since its formulation in 1933. A powerful result independently proven by Lawton and Boyd in the 1980s establishes a connection between the classical Mahler measure of single variable polynomials and the generalized Mahler measure of multivariate polynomials. This led to speculation that it may be possible to answer Lehmer's question in the affirmative with a multivariate polynomial although the general consensus among researchers today is that no such polynomial exists. We show that each possible candidate among two variable polynomials corresponding to curves of genus 1 can be bi-rationally mapped onto a polynomial with Mahler measure greater than Lehmer's constant. Such bi-rational maps are expected to preserve the Mahler measure for large values of a certain parameter.

    Milutin is a completing Honours Student of Wadim Zudilin.

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  • CARMA SEMINAR
  • Speaker: Mark Kayll, University of Montana
  • Title: Adventures with Burn-off Chip-firing Games
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 7th Apr 2016
  • Abstract:
    Start by placing piles of indistinguishable chips on the vertices of a graph. A vertex can fire if it's supercritical; i.e., if its chip count exceeds its valency. When this happens, it sends one chip to each neighbour and annihilates one chip. Initialize a game by firing all possible vertices until no supercriticals remain. Then drop chips one-by-one on randomly selected vertices, at each step firing any supercritical ones. Perhaps surprisingly, this seemingly haphazard process admits analysis. And besides having diverse applications (e.g., in modelling avalanches, earthquakes, traffic jams, and brain activity), chip-firing reaches into numerous mathematical crevices. The latter include, alphabetically, algebraic combinatorics, discrepancy theory, enumeration, graph theory, stochastic processes, and the list could go on (to zonotopes). I'll share some joint work—with Dave Perkins—that touches on a few items from this list. The talk'll be accessible to non-specialists. Promise!
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  • CARMA SEMINAR
  • Speaker: Roberto Costas-Santos, Universidad de Alcalá
  • Title: Basic hypergeometric orthogonal polynomials
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Tue, 16th Feb 2016
  • Abstract:
    We will review the (now classical) scheme of basic ($q$-) hypergeometric orthogonal polynomials. It contains more than twenty families; for each family there exists at least one positive weight with respect to which the polynomials are orthogonal provided the parameter $q$ is real and lies between 0 and 1. In the talk we will describe how to reduce the scheme allowing the parameters in the families to be complex. The construction leads to new orthogonality properties or to generalization of known ones to the complex plane.
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  • CARMA SEMINAR
  • Speaker: Jim Cooper, President & CEO, Maplesoft
  • Title: The Future of Education
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 2:30 pm, Wed, 10th Feb 2016
  • Abstract:

    In this presentation we address the issues and challenges for Future of Education and how Maplesoft is committed to offers Tools such as Möbius™ to handle these challenges. Möbius is a comprehensive online courseware environment that focuses on science, technology, engineering, and mathematics (STEM). It is built on the notion that people learn by doing. With Möbius, your students can explore important concepts using engaging, interactive applications, visualize problems and solutions, and test their understanding by answering questions that are graded instantly. Throughout the entire lesson, students remain actively engaged with the material and receive constant feedback that solidifies their understanding.

    When you use Möbiusto develop and deliver your online offerings, you remain in full control of your content and the learning experience.

    • Bring your online vision to life, including online courses, open-access courses, formative testing, placement and remediation programs, independent learning, outreach programs, and flipped or blended classrooms.
    • Provide exactly the content you want, from individual lessons and textbook supplements, to full courses, remedial materials, enrichment content, and more.
    • Choose the learning experience by allowing students open access to your course material or guiding them along a specific learning path.
    • Stay in control of your content, creating and customizing materials as you wish to suit your needs.
    • Save your students money by dropping a traditional textbook, while simultaneously improving the learning experience.

    For more information on Möbiusplease visit http://maplesoft.com/products/Mobius/.

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  • CARMA SEMINAR
  • Speaker: Ernst Stephan, Insitut fur Angewandte Mathematik (IfAM), Leibniz Universitat Hannover
  • Title: hp-adaptive Interior Penalty FEM for Elliptic Obstacle Problems DG for Laplace, $C^0$ for bi-Laplace
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Tue, 24th Nov 2015
  • Abstract:

    Firstly, from [1] we consider a mixed formulation for an elliptic obstacle problem for a 2nd order operator and present an hp-FE interior penalty discontinous Galerkin (IPDG) method. The primal variable is approximated by a linear combination of Gauss-Lobatto-Lagrange(GLL)-basis functions, whereas the discrete Lagrangian multiplier is a linear combination of biorthogonal basis functions. A residual based a posteriori error estimate is derived. For its construction the approximation error is split into a discretization error of a linear variational equality problem and additional consistency and obstacle condition terms.

    Secondly, an hp-adaptive $C^0$-interior penalty method for the bi-Laplace obstacle problem is presented from [2]. Again we take a mixed formulation using GLL-basis functions for the primal variable and biorthogonal basis functions for the Lagrangian multiplier and present also a residual a posteriori error estimate. For both cases (2nd and 4th order obstacle problems) our numerical experiments clearly demonstrate the superior convergence of the hp-adaptive schemes compared with uniform and h-adaptive schemes.

    References
    [1] L.Banz, E.P.Stephan, A posteriori error estimates of hp-adaptive IPDG-FEM for elliptic obstacle problems, Applied Numerical Mathematics 76,(2014) 76-92
    [2] L.Banz, B.P.Lamichhane, E.P.Stephan, An hp-adaptive $C^0$-interior penalty method for the obstacle problem of clamped Kirchhoff plates, preprint (2015)

    (Joint work with Lothar Banz, University Salzburg, Austria)

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  • CARMA SEMINAR
  • Speaker: Vladimir Peller, Michigan State University
  • Title: Functions of noncommuting self-adjoint operators under perturbation
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 5th Nov 2015
  • Abstract:
    I am going to discuss a construction of functional calculus $$f\mapsto f(A,B),$$ where $A$ and $B$ are noncommuting self-adjoint operators. I am going to discuss the problem of estimating the norms $\|f(A_1,B_1)-f(A_2,B_2)\|$, where the pair $(A_2,B_2)$ is a perturbation of the pair $(A_1,B_1)$.
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  • CARMA SEMINAR
  • Speaker: Prof Richard Brent, CARMA, The University of Newcastle
  • Title: Some Identities involving Products of Gamma Functions: a Case Study in Experimental Mathematics
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 2:00 pm, Tue, 27th Oct 2015
  • Abstract:

    We consider identities satisfied by discrete analogues of Mehta-like integrals. The integrals are related to Selberg’s integral and the Macdonald conjectures. Our discrete analogues have the form

    $$S_{\alpha,\beta,\delta} (r,n) := \sum_{k_1,...,k_r\in\mathbb{Z}} \prod_{1\leq i < j\leq r} |k_i^\alpha - k_j^\alpha|^\beta \prod_{j=1}^r |k_j|^\delta \binom{2n}{n+k_j},$$

    where $\alpha,\beta,\delta,r,n$ are non-negative integers subject to certain restrictions.

    In the cases that we consider, it is possible to express $S_{\alpha,\beta,\delta} (r,n)$ as a product of Gamma functions and simple functions such as powers of two. For example, if $1 \leq r \leq n$, then $$S_{2,2,3} (r,n) = \prod_{j=1}^r \frac{(2n)!j!^2}{(n-j)!^2}.$$

    The emphasis of the talk will be on how such identities can be obtained, with a high degree of certainty, using numerical computation. In other cases the existence of such identities can be ruled out, again with a high degree of certainty. We shall not give any proofs in detail, but will outline the ideas behind some of our proofs. These involve $q$-series identities and arguments based on non-intersecting lattice paths.

    This is joint work with Christian Krattenthaler and Ole Warnaar.

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  • CARMA SEMINAR
  • Speaker: Michael Schönlein, Universität Würzburg
  • Title: Asymptotic stability and Lyapunov functions for a class of abstract positive systems
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Fri, 23rd Oct 2015
  • Abstract:
    We consider the stability of a class of abstract positive systems originating from the recurrence analysis of stochastic systems, such as multiclass queueing networks and semimartingale reflected Brownian motions. We outline that this class of systems can also be described by differential inclusions in a natural way. We will point out that because of the positivity of the systems the set-valued map defining the differential inclusion is not upper semicontinuous in general and, thus, well-known characterizations of asymptotic stability in terms of the existence of a (smooth) Lyapunov function cannot be applied to this class of positive systems. Following an abstract approach, based on common properties of the positive systems under consideration, we show that asymptotic stability is equivalent to the existence of a Lyapunov function. Moreover, we examine the existence of smooth Lyapunov functions. Putting an assumption on the trajectories of the positive systems which demands for any trajectory the existence of a neighboring trajectory such that their difference grows linearly in time and distance of the starting points, we prove the existence of a $C^\infty$-smooth Lyapunov function. Looking at this hypothesis from the differential inclusions perspective it turns out that differential inclusions defined by Lipschitz continuous set-valued maps taking nonempty, compact and convex values have this property.
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  • CARMA SEMINAR
  • Speaker: Dr Björn Rüffer, CARMA, The University of Newcastle
  • Title: Separable Lyapunov functions for monotone systems
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 24th Sep 2015
  • Abstract:

    We consider monotone systems defined by ODEs on the positive orthant in $\mathbb{R}^n$. These systems appear in various areas of application, and we will discuss in some level of detail one of these applications related to large-scale systems stability analysis.

    Lyapunov functions are frequently used in stability analysis of dynamical systems. For monotone systems so called sum- and max-separable Lyapunov functions have proven very successful. One can be written as a sum, the other as a maximum of functions of scalar arguments.

    We will discuss several constructive existence results for both types of Lyapunov function. To some degree, these functions can be associated with left- and right eigenvectors of an appropriate mapping. However, and perhaps surprisingly, examples will demonstrate that stable systems may admit only one or even neither type of separable Lyapunov function.

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  • CARMA SEMINAR
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 1:00 pm, Thu, 24th Sep 2015
  • Practice talks for the 2015 AustMS Meeting.


  • Speaker: Mr Matthew Tam, School of Mathematical and Physical Sciences, The University of Newcastle
  • Title: Reconstruction Algorithms for Blind Ptychographic Imaging
  • Abstract for Reconstruction Algorithms for Blind Ptychographic Imaging:
         In scanning ptychography, an unknown specimen is illuminated by a localised illumination function resulting in an exit-wave whose intensity is observed in the far-field. A ptychography dataset is a series of these observations, each of which is obtained by shifting the illumination function to a different position relative to the specimen with neighbouring illumination regions overlapping. Given a ptychographic data set, the blind ptychography problem is to simultaneously reconstruct the specimen, illumination function, and relative phase of the exit-wave. In this talk I will discuss an optimisation framework which reveals current state-of-the-art reconstruction methods in ptychography as (non-convex) alternating minimization-type algorithms. Within this framework, we provide a proof of global convergence to critical points using the Kurdyka-Łojasiewicz property.

  • Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle
  • Title: Using random walks to detect amenability in finitely generated groups
  • Abstract for Using random walks to detect amenability in finitely generated groups:
         We use random walks to experimentally compute the first few terms of the cogrowth series for a finitely presented group. We propose candidates for the amenable radical of any non-amenable group, and a Følner sequence for any amenable group, based on convergence properties of random walks.

  • Speaker: David Franklin, School of Mathematical and Physical Sciences, The University of Newcastle
  • Title: Hardy Spaces and Paley-Wiener Spaces for Clifford-valued functions
  • Abstract for Hardy Spaces and Paley-Wiener Spaces for Clifford-valued functions:
         The Hardy and Paley-Wiener Spaces are defined due to important structural theorems relating the support of a function's Fourier transform to the growth rate of the analytic extension of a function. In this talk we show that analogues of these spaces exist for Clifford-valued functions in n dimensions, using the Clifford-Fourier Transform of Brackx et al and the monogenic ($n+1$ dimensional) extension of these functions.
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  • CARMA SEMINAR
  • Speaker: George Havas, The University of Queensland
  • Title: Group theoretic proofs by coset enumeration
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Wed, 23rd Sep 2015
  • Abstract:
    Given a finite presentation of a group, proving properties of the group can be difficult. Indeed, many questions about finitely presented groups are unsolvable in general. Algorithms exist for answering some questions while for other questions algorithms exist for verifying the truth of positive answers. An important tool in this regard is the Todd-Coxeter coset enumeration procedure. It is possible to extract formal proofs from the internal working of coset enumerations. We give examples of how this works, and show how the proofs produced can be mechanically verified and how they can be converted to alternative forms. We discuss these automatically produced proofs in terms of their size and the insights they offer. We compare them to hand proofs and to the simplest possible proofs. We point out that this technique has been used to help solve a longstanding conjecture about an infinite class of finitely presented groups.
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  • CARMA SEMINAR
  • Speaker: Mourad Ismail, unknown or leave blank,
  • Title: A class of 2D orthogonal polynomials
  • Location: Room VG01, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 1:00 pm, Tue, 22nd Sep 2015
  • Abstract:
    We survey the literature on orthogonal polynomials in several variables starting from Hermite's work in the late 19th century to the works of Zernike (1920's) and Ito (1950's). We explore combinatorial and analytic properties of the Ito polynomials and offer a general class in 2 dimensions which as interesting structural properties. Connections with certain PDE's will be mentioned.
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  • CARMA SEMINAR
  • Speaker: Prof Levent Tunçel, University of Waterloo
  • Title: Superlinear Convergence of polynomial-time interior-point methods for convex optimization
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 17th Sep 2015
  • Abstract:

    We propose new path-following predictor-corrector algorithms for solving convex optimization problems in conic form. The main structural properties used in our design and analysis of the algorithms hinge on some key properties of a special class of very smooth, strictly convex barrier functions. Even though our analysis has primal and dual components, our algorithms work with the dual iterates only, in the dual space. Our algorithms converge globally at the same worst-case rate as the current best polynomial-time interior-point methods. In addition, our algorithm have the local superlinear convergence property under some mild assumptions. The algorithms are based on an easily computable gradient proximity measure, which ensures an automatic transformation of the global linear rate of convergence to the locally superlinear one under some mild assumptions. Our step-size procedure for the predictor step is related to the maximum step size (the one that takes us to the boundary).

    This talk is based on joint work with Yu. Nesterov.

  • [Permanent event link]

  • CARMA AND AMSI LECTURE SERIES
  • Speaker: Prof Michael Shelley, New York University
  • Title: Boundary integral methods for flows interacting with moving and flexible structures
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 2:00 pm, Wed, 12th Aug 2015
  • Abstract:
    In either the inviscid limit of the Euler equations, or the viscously dominated limit of the Stokes equations, the determination of fluid flows can be reduced to solving singular integral equations on immersed structures and bounding surfaces. Further dimensional reduction is achieved using asymptotics when these structures are sheets or slender fibers. These reductions in dimension, and the convolutional second-kind structure of the integral equations, allows for very efficient and accurate simulations of complex fluid-structure interaction problems using solvers based on the Fast Multipole or related methods. These representations also give a natural setting for developing implicit time-stepping methods for the stiff dynamics of elastic structures moving in fluids. I'll discuss these integral formulations, their numerical treatment, and application to simulating structures moving in high-speed flows (flapping flags and flyers), and for resolving the complex interactions of many, possibly flexible, bodies moving in microscopic biological flows.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Hendrik de Bie, Ghent University
  • Title: A powerful new technique for the Clifford-Fourier transform
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 23rd Jul 2015
  • Abstract:

    In recent years, there has been quite a bit of interest in generalized Fourier transforms in Clifford analysis and in particular for the so-called Clifford-Fourier transform.

    In the first part of the talk I will provide some motivation for the study of this transform. In the second part we will develop a new technique to find a closed formula for its integral kernel, based on the familiar Laplace transform. As a bonus, this yields a compact and elegant formula for the generating function of all even dimensional kernels.

  • [Permanent event link]

  • CARMA AND AMSI LECTURE SERIES
  • Mathematical Logic and Philosophy
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Fri, 22nd May 2015
  • Download: Lecture Tour Flyer (424 KB)
  • Four lectures by Professor Jeremy Avigad (Department of Philosophy and the Department of Mathematical Sciences, Carnegie Mellon University). This is the fourth lecture.
  • Abstract

    Computers are changing the way we do mathematics, as well as introducing new research agendas. Computational methods in mathematics, including symbolic and numerical computation and simulation, are by now familiar. These lectures will explore the way that "formal methods," based on formal languages and logic, can contribute to mathematics as well.

    In the 19th century, George Boole argued that if we take mathematics to be the science of calculation, then symbolic logic should be viewed as a branch of mathematics: just as number theory and analysis provide means to calculate with numbers, logic provides means to calculate with propositions. Computers are, indeed, good at calculating with propositions, and there are at least two ways that this can be mathematically useful: first, in the discovery of new proofs, and, second, in verifying the correctness of existing ones.

    The first goal generally falls under the ambit of "automated theorem proving" and the second falls under the ambit of "interactive theorem proving." There is no sharp distinction between these two fields, however, and the line between them is becoming increasingly blurry. In these lectures, I will provide an overview of both fields and the interactions between them, and speculate as to the roles they can play in mainstream mathematics.

    I will aim to make the lectures accessible to a broad audience. The first lecture will provide a self-contained overview. The remaining lectures are for the most part independent of one another, and will not rely on the first lecture.

  • [Permanent event link]

  • CARMA AND AMSI LECTURE SERIES
  • Mathematical Logic and Philosophy
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Fri, 15th May 2015
  • Download: Lecture Tour Flyer (424 KB)
  • Four lectures by Professor Jeremy Avigad (Department of Philosophy and the Department of Mathematical Sciences, Carnegie Mellon University). This is the third lecture.
  • Abstract

    Computers are changing the way we do mathematics, as well as introducing new research agendas. Computational methods in mathematics, including symbolic and numerical computation and simulation, are by now familiar. These lectures will explore the way that "formal methods," based on formal languages and logic, can contribute to mathematics as well.

    In the 19th century, George Boole argued that if we take mathematics to be the science of calculation, then symbolic logic should be viewed as a branch of mathematics: just as number theory and analysis provide means to calculate with numbers, logic provides means to calculate with propositions. Computers are, indeed, good at calculating with propositions, and there are at least two ways that this can be mathematically useful: first, in the discovery of new proofs, and, second, in verifying the correctness of existing ones.

    The first goal generally falls under the ambit of "automated theorem proving" and the second falls under the ambit of "interactive theorem proving." There is no sharp distinction between these two fields, however, and the line between them is becoming increasingly blurry. In these lectures, I will provide an overview of both fields and the interactions between them, and speculate as to the roles they can play in mainstream mathematics.

    I will aim to make the lectures accessible to a broad audience. The first lecture will provide a self-contained overview. The remaining lectures are for the most part independent of one another, and will not rely on the first lecture.

  • [Permanent event link]

  • CARMA AND AMSI LECTURE SERIES
  • Mathematical Logic and Philosophy
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Dates: Fri, 8th May 2015 - Fri, 8th May 2015
  • Download: Lecture Tour Flyer (424 KB)
  • Four lectures by Professor Jeremy Avigad (Department of Philosophy and the Department of Mathematical Sciences, Carnegie Mellon University). This session includes two of the four lectures.
  • Abstract

    Computers are changing the way we do mathematics, as well as introducing new research agendas. Computational methods in mathematics, including symbolic and numerical computation and simulation, are by now familiar. These lectures will explore the way that "formal methods," based on formal languages and logic, can contribute to mathematics as well.

    In the 19th century, George Boole argued that if we take mathematics to be the science of calculation, then symbolic logic should be viewed as a branch of mathematics: just as number theory and analysis provide means to calculate with numbers, logic provides means to calculate with propositions. Computers are, indeed, good at calculating with propositions, and there are at least two ways that this can be mathematically useful: first, in the discovery of new proofs, and, second, in verifying the correctness of existing ones.

    The first goal generally falls under the ambit of "automated theorem proving" and the second falls under the ambit of "interactive theorem proving." There is no sharp distinction between these two fields, however, and the line between them is becoming increasingly blurry. In these lectures, I will provide an overview of both fields and the interactions between them, and speculate as to the roles they can play in mainstream mathematics.

    I will aim to make the lectures accessible to a broad audience. The first lecture will provide a self-contained overview. The remaining lectures are for the most part independent of one another, and will not rely on the first lecture.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Alexander Fish, School of Mathematics and Statistics, The University of Sydney
  • Title: Ergodic theorems for amenable groups
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 23rd Apr 2015
  • Abstract:

    We will talk on the validity of the mean ergodic theorem along left Følner sequences in a countable amenable group G. Although the weak ergodic theorem always holds along any left Følner sequence in G, we will provide examples where the mean ergodic theorem fails in quite dramatic ways. On the other hand, if G does not admit any ICC quotients, e.g. if G is virtually nilpotent, then we will prove that the mean ergodic theorem does indeed hold along any left Følner sequence.

    Based on the joint work with M. Bjorklund (Chalmers).

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Ernst Stephan, Insitut fur Angewandte Mathematik (IfAM), Leibniz Universitat Hannover
  • Title: hp-BEM for frictional contact problems in linear elasticity
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Tue, 17th Mar 2015
  • Abstract:

    A mixed formulation for a Tresca frictional contact problem in linear elasticity is considered in the context of boundary integral equations, which is later extended to Coulomb friction. The discrete Lagrange multiplier, an approximation of the surface traction on the contact boundary part, is a linear combination of biorthogonal basis functions. The biorthogonality allows to rewrite the variational inequality constraints as a simple set of complementary problems. Thus, enabling an efficient application of a semi-smooth Newton solver for the discrete mixed problems. Typically, the solution of frictional contact problems is of reduced regularity at the interface between contact to non-contact and from stick to slip. To identify the a priori unknown locations of these interfaces a posteriori error estimations of residual and hierarchical type are introduced. For a stabilized version of our mixed formulation (with the Poincare- Steklov operator) we present also a priori estimates for the solution. Numerical results show the applicability of the error estimators and the superiority of hp-adaptivity compared to low order uniform and adaptive approaches.

    Ernst Stephan is a visitor of Bishnu Lamichhane.

  • [Permanent event link]


  • CARMA SEMINAR
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Dates: Thu, 4th Dec 2014 - Thu, 4th Dec 2014
  • Talks by RHD students who will be presenting at the AustMS conference in Melbourne the following week.



  • Speaker: Cameron Rogers, School of Mathematical and Physical Sciences, The University of Newcastle
  • Title: Using Random walks to estimate the shape of Folner Sets
  • Abstract for Using Random walks to estimate the shape of Folner Sets:
         (Groups & Dynamics Special Session)

  • Speaker: Ben Carter, The University of Newcastle
  • Title: Adaptive assessment for differing maths backgrounds?
  • Abstract for Adaptive assessment for differing maths backgrounds?:
         (Maths Education Special Session)

  • Speaker: Ohad Giladi, CARMA, The University of Newcastle
  • Title: Small ball estimates for quasi norms
  • Abstract for Small ball estimates for quasi norms:
         (Operator Algebra/ Functional Analysis Special Session)
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Nathan Clisby, The University of Melbourne
  • Title: Monte Carlo simulation of self-avoiding walks
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 23rd Oct 2014
  • Abstract:

    Self-avoiding walks are a widely studied model of polymers, which are defined as walks on a lattice where each successive step visits a neighbouring site, provided the site has not already been visited. Despite the apparent simplicity of the model, it has been of much interest to statistical mechanicians and probabilists for over 60 years, and many important questions about it remain open.

    One of the most powerful methods to study self-avoiding walks is Monte Carlo simulation. I'll give an overview of the historical developments in this field, and will explain what ingredients are needed for a good Monte Carlo algorithm. I'll then describe how recent progress has allowed for the efficient simulation of truly long walks with many millions of steps. Finally, I'll discuss whether lessons we've learned from simulating self-avoiding walks may be applicable to a wide range of Markov chain Monte Carlo simulations.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Paul Vrbik, School of Mathematical and Physical Sciences, The University of Newcastle
  • Title: Computer Algebra : A Retrospective
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 16th Oct 2014
  • Abstract:

    We discuss the genesis of symbolic computation, its deployment into computer algebra systems, and the applications of these systems in the modern era.

    We will pay special attention to polynomial system solvers and highlight the problems that arise when considering non-linear problems. For instance, forgetting about actually solving, how does one even represent infinite solution sets?

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Prof George Willis, CARMA, The University of Newcastle
  • Title: Operators on the p-adic analogue of Hilbert space
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 21st Aug 2014
  • Abstract:

    The restricted product over $X$ of copies of the $p$-adic numbers $\mathbb{Q}_p$, denoted $\mathbb{Q}_p(X)$, is self-dual and is the natural $p$-adic analogue of Hilbert space. The additive group of this space is locally compact and the continuous endomorphisms of the group are precisely the continuous linear operators on $\mathbb{Q}_p(X)$.

    Attempts to develop a spectral theory for continuous linear operators on $\mathbb{Q}_p(X)$ will be described at an elementary level. The Berkovich spectral theory over non-Archimedean fields will be summarised and the spectrum of the linear operator $T$ compared with the scale of $T$ as an endomorphism of $(\mathbb{Q}_p(X),+)$.

    The original motivation for this work, which is joint with Andreas Thom (Leipzig), will also be briefly discussed. A certain result that holds for representations of any group on a Hilbert space, proved by operator theoretic methods, can only be proved for representations of sofic groups on $\mathbb{Q}_p(X)$ and it is thought that the difficulty might lie with the lack of understanding of linear operators on $\mathbb{Q}_p(X)$ rather than with non-sofic groups.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Laura Ciobanu, University of Neuchatel
  • Title: Equations in groups
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 7th Aug 2014
  • Abstract:

    The Diophantine Problem in group theory can be stated as: is it algorithmically decidable whether an equation whose coefficients are elements of a given group has at least one solution in that group?

    The talk will be a survey on this topic, with emphasis on what is known about solving equations in free groups. I will also present some of the algebraic geometry over groups developed in the last 20 years, and the connections to logic and geometry. I will conclude with results concerning the asymptotic behavior of satisfiable homogeneous equations in surface groups.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Simon Smith, University of Western Australia
  • Title: Infinite discrete primitive permutation groups
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 17th Jul 2014
  • Abstract:

    Usually, when we want to study permutation groups, we look first at the primitive permutation groups (transitive groups in which point stabilizers are maximal); in the finite case these groups are the basic building blocks from which all finite permutation groups are comprised. Thanks to the seminal O'Nan—Scott Theorem and the Classification of the Finite Simple Groups, the structure of finite primitive permutation groups is broadly known.

    In this talk I'll describe a new theorem of mine which extends the O'Nan—Scott Theorem to a classification of all primitive permutation groups with finite point stabilizers. This theorem describes the structure of these groups in terms of finitely generated simple groups.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Prof. Sarah Rees, Mathematics and Statistics, Newcastle University
  • Title: When Artin groups are sufficiently large...
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Access Grid Venue: TBC
  • Time and Date: 1:30 pm, Mon, 14th Jul 2014
  • Abstract:
    (see PDF)
  • Download: Seminar abstract (74 KB)
  • Via AGR from UWS
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle
  • Title: An algebraic generating function for permutations generated by a stack of depth 2 and infinite stack in series
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Wed, 14th May 2014
  • Abstract:

    This is joint work with Geoffrey Lee.

    The set of permutations generated by a passing an ordered sequence through a stack of depth 2 followed by an infinite stack in series was shown to be finitely based by Elder in 2005. In this new work we obtain an algebraic generating function for this class, by showing it is in bijection with an unambiguous context-free grammar.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Mr Chris Banks, CARMA, The University of Newcastle
  • Title: On simple groups acting on trees
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Wed, 23rd Apr 2014
  • Abstract:
    In this talk I will present a general method of finding simple groups acting on trees. This process, beginning with any group $G$ acting on a tree, produces more groups known as the $k$-closures of $G$. I will use several examples to highlight the versatility of this method, and I will discuss the properties of the $k$-closures that allow us to find abstractly simple groups.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Victoria Stodden, Department of Statistics, Columbia University
  • Title: Reproducibility in Experimental Mathematics
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Fri, 28th Mar 2014
  • Abstract:

    New questions regarding the reliability and verifiability of scientific findings are emerging as computational methods are being increasingly used in research. In this talk I will present a framework for incorporating computational research into the scientific method, namely standards for carrying out and disseminating research to facilitate reproducibility. I will present some recent empirical results on data and code publication; the pilot project http://ResearchCompendia.org for linking data and codes to published results and validating findings; and the "Reproducible Research Standard" for ensuring the distribution of legally usable data and code. If time permits, I will present preliminary work on assessing the reproducibility of published computational findings based on the 2012 ICERM workshop on Reproducibility in Computational and Experimental Mathematics report [1]. Some of this research is described in my forthcoming co-edited books "Implementing Reproducible Research" and "Privacy, Big Data, and the Public Good."

    [1] D. H. Bailey, J. M. Borwein, Victoria Stodden "Set the Default to 'Open'," Notices of the AMS, June/July 2013.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Xian'an Jin, School of Mathematics, Xiamen University
  • Title: DNA and protein polyhedral links
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Mon, 10th Feb 2014
  • Abstract:
    Polyhedral links, interlinked and interlocked architectures, have been proposed for the description and characterization of DNA and protein polyhedra. Chirality is a very important feature for biomacromolecules. In this talk, we discuss the topological chirality of a type of DNA polyhedral links constructed by the strategy of "n-point stars and a type of protein polyhedral links constructed by "three-cross curves" covering. We shall ignore DNA sequence and use the orientation of the 2 backbone strands of the dsDNA to orient DNA polyhedral links, thus consider DNA polyhedral links as oriented links with antiparallel orientations. We shall ignore protein sequence and view protein polyhedral links as unoriented ones. It is well known that there is a correspondence between alternating links and plane graphs. We prove that links corresponding to bipartite plane graphs have antiparallel orientations, and under these orientations, their writhes are not zero. As a result, the type of right-handed double crossover 4-turn DNA polyhedral links are topologically chiral. We also prove that the unoriented link corresponding to a connected, even, bipartite plane graph has self-writhe 0 and using the Jones polynomial we present a criterion for chirality of unoriented alternating links with self-writhe 0. By applying this criterion we obtain that 3-regular protein polyhedral links are also topologically chiral. Topological chirality always implies chemical chirality, hence the corresponding DNA and protein polyhedra are all chemically chiral. Our chiral criteria may be used to detect the topological chirality of more complicated DNA and protein polyhedral links to be synthesized by chemists and biologists in the future.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Liangjin Yao, CARMA, The University of Newcastle
  • Title: Characterizations of ultramaximally monotone operators
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:30 pm, Mon, 2nd Dec 2013
  • Abstract:

    In this talk, we provide some characterizations of ultramaximally monotone operators. We establish the Brezis--Haraux condition in the setting of a general Banach space. We also present some characterizations of reflexivity of a Banach space by a linear continuous ultramaximally monotone operator.

    Joint work with Jon Borwein.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle
  • Title: A Metropolis Markov Chain algorithm to sample trivial words and compute cogrowth in finitely generated groups; or -- F is not amenable.
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 21st Nov 2013
  • Abstract:
    In this talk I will describe an algorithm to do a random walk in the space of all words equal to the identity in a finitely presented group. We prove that the algorithm samples from a well defined distribution, and using the distribution we can find the expected value for the mean length of a trivial word. We then use this information to estimate the cogrowth of the group. We ran the algorithm on several examples -- where the cogrowth series in known exactly our results are in agreement with the exact results. Running the algorithm on Thompson's group $F$, we see behaviour consistent with the hypothesis that $F$ is not amenable.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Alexander Fish, School of Mathematics and Statistics, The University of Sydney
  • Title: Product set phenomena for countable groups
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 7th Nov 2013
  • Abstract:

    We analyse local combinatorial structure in product sets of two subsets of a countable group which are "large" with respect to certain classes (not necessarily invariant) means on the group. As an example of such phenomenon, we can mention the result by Bergelson, Furstenberg and Weiss which says that the sumset of two sets of positive density in integers contains locally an almost-periodic set. In this theorem, large sets are the sets of positive density, and a combinatorial structure is an almost periodic set.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Hanna Kokko, unknown or leave blank,
  • Title: Is Mother Nature shortsighted?
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 24th Oct 2013
  • Abstract:
    Popular accounts of evolution typically create an expectation that populations become ever better adapted over time, and some formal treatments of evolutionary processes suggest this too. However, such analyses do not highlight the fact that competition with conspecics has negative population-level consequences too, particularly when individuals invest in success in zero-sum games. My own work is at the interface of theoretical biology and empirical data, and I will discuss several examples where an adaptive evolutionary process leads to something that appears silly from the population point of view, including a heightened risk of extinction in the Gouldian finch, reduced productivity of species in which males do not participate in parental care, and deterministic extinction of local populations in systems that feature sexual parasitism.
  • [Permanent event link]


  • CARMA SEMINAR
  • Speaker: Kieran Larkin, Nontrivialzeros Research
  • Title: Phase in Imaging
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:30 pm, Mon, 26th Aug 2013
  • Abstract:

    Image processing research is dominated, to a considerable degree, by linear-additive models of images. For example, wavelet decompositions are very popular both with experimentalists and theoreticians primarily because of their neatly convergent properties. Fourier and orthogonal series decompositions are also popular in applications, as well as playing an important part in the analysis of wavelet methods.

    Multiplicative decomposition, on the other hand, has had very little use in image processing. In 1-D signal processing and communication theory it has played a vital part (amplitude, phase, and frequency modulations of communications theory especially).

    In many cases 2-D multiplicative decompositions have just been too hard to formulate or expand. Insurmountable problems (divergences) often occur as the subtle consequences of unconscious errors in the choice of mathematical structure. In my work over the last 17 years I've seen how to overcome some of the problems in 2-D, and the concept of phase is a central, recurring theme. But there is still so much more to be done in 2-D and higher dimensions.

    This talk will be a whirlwind tour of some main ideas and applications of phase in imaging.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: , CARMA, The University of Newcastle
  • Title: Douglas-Rachford Brainstorm
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 1:00 pm, Tue, 20th Aug 2013
  • Abstract:
    The aim of this Douglas-Rachford brainstorming session to discuss:
    -New applications and large scale experiments
    -Diagnosing and profiling successful non-convex applications
    -New conjectures
    -Anything else you may think is relevant
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Dongxi (Lawrence) Ye , Massey University
  • Title: Level 13 modular functions
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 10:00 am, Tue, 20th Aug 2013
  • Abstract:
    The talk will be about new results on modular forms obtained by the speaker in collaboration with Shaun Cooper.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Edward Saff, Vanderbilt University
  • Title: Minimal Energy and Maximal Polarization
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 25th Jul 2013
  • Abstract:

    This talk deals with problems that are asymptotically related to best-packing and best-covering. In particular, we discuss how to efficiently generate N points on a d-dimensional manifold that have the desirable qualities of well-separation and optimal order covering radius, while asymptotically having a prescribed distribution. Even for certain small numbers of points like N=5, optimal arrangements with regard to energy and polarization can be a challenging problem.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Dr Bishnu Lamichhane, CARMA, The University of Newcastle
  • Title: Efficient Finite Element Methods for Reissner-Mindlin, Biharmonic and Thin Plate Equations
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 18th Jul 2013
  • Abstract:

    The finite element method has become the most powerful approach in approximating solutions of partial differential equations arising in modern engineering and physical applications. We present some efficient finite element methods for Reissner-Mindlin, biharmonic and thin plate equations.

    In the first part of the talk I present some applied partial differential equations, and introduce the finite element method using the biharmonic equation. In the second part of the talk I will discuss about the finite element method for Reissner-Mindlin, biharmonic and thin plate spline equations in a unified framework.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Prof George Willis, CARMA, The University of Newcastle
  • Title: The 21st birthday of the Factoring Lemma
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 20th Jun 2013
  • Abstract:

    You are invited to a celebration of the 21st anniversary of the Factoring Lemma. This lemma was the key to solving some long-standing open problems, and was the starting point of an investigation of totally disconnected, locally compact groups that has ensued over the last 20 years. In this talk, the life of the lemma will described from its conception through to a very recent strengthening of it. It will be described at a technical level, as well as viewed through its relationships with topology, geometry, combinatorics, algebra, linear algebra and research grants.

    A birthday cake will be served afterwards.

    Please make donations to the Mathematics Prize Fund in lieu of gifts.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle
  • Title: C-graph automatic groups
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 16th May 2013
  • Abstract:

    Graph automatic groups are an extension of the notion of an automatic group, introduced by Kharlampovich, Khoussainov and Miasnikov in 2011, with the intention to capture a wider class of groups while preserving computational properties such as having quadratic time word problem. We extend the notion further by replacing regular with more general language classes. We prove that nonsolvable Baumslag-Solitar groups are (context free)-graph automatic, (context sensitive)-graph automatic implies a context-sensitive word problem and conversely groups with context sensitive word problem are (context sensitive)-automatic. Finally an obstruction to (context sensitive)-graph automatic implying polynomial time word problem is given.

    This is joint work with Jennifer Taback, Bowdoin College.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Dr Jeff Hogan, CARMA, The University of Newcastle
  • Title: Prolate spheroidal wavefunctions II
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 2nd May 2013
  • Abstract:
    The classical prolate spheroidal wavefunctions (prolates) arise when solving the Helmholtz equation by separation of variables in prolate spheroidal coordinates. They interpolate between Legendre polynomials and Hermite functions. In a beautiful series of papers published in the Bell Labs Technical Journal in the 1960's, they were rediscovered by Landau, Slepian and Pollak in connection with the spectral concentration problem. After years spent out of the limelight while wavelets drew the focus of mathematicians, physicists and electrical engineers, the popularity of the prolates has recently surged through their appearance in certain communication technologies. In this talk we outline some developments in the sampling theory of bandlimited signals that employ the prolates, and the construction of bandpass prolate functions.
    This is joint work with Joe Lakey (New Mexico State University)
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Dr James Wan, Singapore University of Technology and Design
  • Title: Elliptic integrals, L-values and lattice sums
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 11th Apr 2013
  • Abstract:
    We discuss some recently discovered relations between L-values of modular forms and integrals involving the complete elliptic integral K. Gentle and illustrative examples will be given. Such relations also lead to closed forms of previously intractable integrals and (chemical) lattice sums.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Malte Peter, Institute of Mathematics, University of Augsburg
  • Title: A multiscale approach to reaction-diffusion processes in domains with microstructure
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 21st Mar 2013
  • Abstract:

    Reaction-diffusion processes occur in many materials with microstructure such as biological cells, steel or concrete. The main difficulty in modelling and simulating accurately such processes is to account for the fine microstructure of the material. One method of upscaling multi-scale problems, which has proven reliable for obtaining feasible macroscopic models, is the method of periodic homogenisation.

    The talk will give an introduction to multi-scale modelling of chemical mechanisms in domains with microstructure as well as to the method of periodic homogenisation. Moreover, a few aspects of solving the resulting systems of equations numerically will also be discussed.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Florian Luca, Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México
  • Title: Linear independence of certain Lambert series
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Wed, 13th Mar 2013
  • Abstract:

    We prove that if $q\ne0,\pm1$ and $\ell\ge1$ are fixed integers, then the numbers $$ 1, \quad \sum_{n=1}^\infty\frac{1}{q^n-1}, \quad \sum_{n=1}^\infty\frac{1}{q^{n^2}-1}, \quad \dots, \quad \sum_{n=1}^\infty\frac{1}{q^{n^\ell}-1} $$ are linearly independent over $\mathbb{Q}$. This generalizes a result of Erdős who treated the case $\ell=1$. The method is based on the original approaches of Chowla and Erdős, together with some results about primes in arithmetic progressions with large moduli of Ahlford, Granville and Pomerance.

    This is joint work with Yohei Tachiya.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Kevin Hare, University of Waterloo
  • Title: An explicit counter-example to the Lagarias-Wang finiteness conjecture
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 28th Feb 2013
  • Abstract:
    The joint spectral radius of a finite set of real $d \times d$ matrices is defined to be the maximum possible exponential rate of growth of long products of matrices drawn from that set. A set of matrices is said to have the finiteness property if there exists a periodic product which achieves this maximal rate of growth. J. C. Lagarias and Y. Wang conjectured in 1995 that every finite set of real $d \times d$ matrices satisfies the finiteness property. However, T. Bousch and J. Mairesse proved in 2002 that counterexamples to the finiteness conjecture exist, showing in particular that there exists a family of pairs of $2 \times 2$ matrices which contains a counterexample. Similar results were subsequently given by V. D. Blondel, J. Theys and A. A. Vladimirov and by V. S. Kozyakin, but no explicit counterexample to the finiteness conjecture was given. This talk will discuss an explicit counter-example to this conjecture.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: José Burillo, Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya
  • Title: Distortion and metric estimates for finitely generated groups
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Fri, 22nd Feb 2013
  • Abstract:
    After Gromov's work in the 1980s, the modern approach to studying infinite groups is from the geometric point of view, seeing them as metric spaces and using geometric concepts. One of these is the concept of distortion of a subgroup in a group. Here we will give the definition and some examples of distorted and nondistorted subgroups and some recent results on them. The main tools used to establish these results are quasi-metrics or metric estimates, which are quantities which differ from the distance by a multiplicative constant, but which still capture the concept enough to understand distortion.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Mr Dmitriy Drusvyatskiy, School of Operations Research and Information Engineering, Cornell University
  • Title: Active sets, steepest descent, and smooth approximations of functions
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 21st Feb 2013
  • Abstract:
    Three ideas --- active sets, steepest descent, and smooth approximations of functions --- permeate nonsmooth optimization. I will give a fresh perspective on these concepts, and illustrate how many results in these areas can be strengthened in the semi-algebraic setting. This is joint work with A.D. Ioffe (Technion), A.S. Lewis (Cornell), and M. Larsson (EPFL).
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Kevin Hare, University of Waterloo
  • Title: Stolarsky's Conjecture and the sum of digits function
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 7th Feb 2013
  • Abstract:
    Let $s_q(n)$ be the sum of the $q$-ary digits of $n$. For example $s_{10}(1729) = 1 + 7 + 2 + 9 = 19$. It is known what $s_q(n)$ looks like "on average". It can be shown that $s_q(n^h)$ looks $h$ times bigger "on average". This raises the question: is the ratio of these two things $h$ on average? In this talk we will give some history on the sum of digits function, and will give a proof of one of Stolarsky's conjecture concerning the minimal values of the ratio of $s_q(n)$ and $s_q(n^h)$.
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  • CARMA SEMINAR
  • Speaker: Tara Brough, University of St Andrews
  • Title: Automaton Semigroup Constructions
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 24th Jan 2013
  • Abstract:
    Automaton semigroups are a natural generalisation of the automaton groups introduced by Grigorchuk and others in the 1980s as examples of groups having various 'exotic' properties. In this talk I will give a brief introduction to automaton semigroups, and then discuss recent joint work with Alan Cain on the extent to which the class of automaton semigroups is closed under certain semigroup constructions (free products and wreath products).
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Dr Victoria Martín-Márquez, Department of Mathematical Analysis, Universidad de Sevilla
  • Title: On Iterative Methods for Solving Convex Feasibility Problems and applications
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Access Grid Venue: UNewcastle [ENQUIRIES]
  • Time and Date: 4:00 pm, Thu, 6th Dec 2012
  • Abstract:
    Many problems in diverse areas of mathematics and modern physical sciences can be formulated as a Convex Feasibility Problem, consisting of finding a point in the intersection of finitely many closed convex sets. Two other related problems are the Split Feasibility Problem and the Multiple-Sets Split Feasibility Problem, both very useful when solving inverse problems where constraints are imposed in the domain as well as in the range of a linear operator. We present some recent contributions concerning these problems in the setting of Hilbert spaces along with some numerical experiments to illustrate the implementation of some iterative methods in signal processing.
  • [Permanent event link]

  • CARMA SEMINAR
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 2:00 pm, Tue, 4th Dec 2012
  • University of Newcastle participants in the 36th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing will be giving practice runs of their 20 minute conference talks. If you want to give a talk, let Mirka Miller know (mirka.miller@newcastle.edu.au) and she will add you to the schedule. If you wish to come and listen, feel free to drop in.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Prof. Ljiljana Brankovic, School of Electrical Engineering and Computer Science, The University of Newcastle
  • Title: Combining two worlds: Parameterised Approximation for Vertex Cover
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 29th Nov 2012
  • Abstract:

    Parameterised approximation is a relatively new but growing field of interest. It merges two ways of dealing with NP-hard optimisation problems, namely polynomial approximation and exact parameterised (exponential-time) algorithms.

    We explore opportunities for parameterising constant factor approximation algorithms for vertex cover, and we provide a simple algorithm that works on any approximation ratio of the form $\frac{2l+1}{l+1}$, $l=1,2,\dots$, and has complexity that outperforms previously published algorithms by Bourgeois et al. based on sophisticated exact parameterised algorithms. In particular, for $l=1$ (factor-$1.5$ approximation) our algorithm runs in time $\text{O}^*(\text{simpleonefiveapproxbase}^k)$, where parameter $k \leq \frac{2}{3}\tau$, and $\tau$ is the size of a minimum vertex cover.

    Additionally, we present an improved polynomial-time approximation algorithm for graphs of average degree at most four and a limited number of vertices with degree less than two.

  • [Permanent event link]


  • CARMA SEMINAR
  • Speaker: Prof Jeff Linderoth, Department of Industrial and Systems Engineering, University of Wisconsin-Madison
  • Title: Multi-term Relaxations for Multi-linear Programs
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Access Grid Venue: UNewcastle [ENQUIRIES]
  • Time and Date: 4:00 pm, Thu, 22nd Nov 2012
  • Abstract:

    Multi-linear functions appear in many global optimization problems, including reformulated quadratic and polynomial optimization problems. There is a extended formulation for the convex hull of the graph of a multi-linear function that requires the use of an exponential number of variables. Relying on this result, we study an approach that generates relaxations for multiple terms simultaneously, as opposed to methods that relax the nonconvexity of each term individually. In some special cases, we are able to establish analytic bounds on the ratio of the strength of the term-by-term and convex hull relaxations. To our knowledge, these are the first approximation-ratio results for the strength of relaxations of global optimization problems. The results lend insight into the design of practical (non-exponentially sized) relaxations. Computations demonstrate that the bounds obtained in this manner are competitive with the well-known semi-definite programming based bounds for these problems.

    Joint work with Jim Luedtke, University of Wisconsin-Madison, and Mahdi Namazifar, now with Opera Solutions.

  • [Permanent event link]


  • CARMA SEMINAR
  • Speaker: Mr Nick Davis, Department of Mathematics and Statistics, The University of Melbourne
  • Title: Automata groups and their self-similarity graphs
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 15th Nov 2012
  • Abstract:
    Automata groups are a class of groups generated by recursively defined automorphisms of a regular rooted tree. Associated to each automata group is an object known as the self-similarity graph. Nekrashevych showed that in the case where the group satisfies a natural condition known as contracting, the self-similarity graph is Gromov-hyperbolic and has boundary homeomorphic to the limit space of the group action. I will talk about self-similarity graphs of automata groups that do not satisfy the contracting condition.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Mr Meksianis Ndii, School of Mathematical and Physical Sciences, The University of Newcastle
  • Title: Wolbachia intervention in reducing dengue transmission
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 8th Nov 2012
  • Abstract:
    Infecting aedes aegypti with Wolbachia has been proposed as an alternative in reducing dengue transmission. If Wolbachia-infected mosquitoes can invade and dominate the population of aedes aegypti mosquitoes, they can reduce dengue transmission. Cytoplasmic Incompatibility (CI) provides the reproductive advantage for Wolbachia-infected mosquitoes with which they can reproduce more and dominate the population. A mosquito population model is developed in order to determine the survival of Wolbachia-infected mosquiotes when they are released into the wild. The model has two physically stable realistic steady states. The model reveals that once the Wolbachia-infected mosquitoes survive, they ultimately dominate the population.
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  • CARMA SEMINAR
  • Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle
  • Title: Totally disconnected groups from Baumslag-Solitar groups
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 20th Sep 2012
  • Abstract:

    We consider the problem of characterising embeddings of an abstract group into totally disconnected locally compact (tdlc) groups. Specifically, for each pair of nonzero integers $m,n$ we construct a tdlc group containing the Baumslag-Solitar group $BS(m,n)$ as a dense subgroup, and compute the scales of elements and flat rank of the tdlc group.

    This is joint work with George Willis.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Mr Ian Searston, School of Mathematical and Physical Sciences, The University of Newcastle
  • Title: Projection Algorithms in CAT(0) spaces
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 6th Sep 2012
  • Abstract:
    Recently the Alternating Projection Algorithm was extended into CAT(0) spaces. We will look at this and also current work on extending the Douglas Rachford Algorithm into CAT(0) spaces. By using CAT(0) spaces the underlying linear structure of the space is dispensable and this allows certain algorithms to be extended to spaces such as classical hyperbolic spaces, simply connected Riemannian manifolds of non-positive curvature, R-trees and Euclidean buildings.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Prof David Bailey, Berkeley, California
  • Title: Normality and non-normality of mathematical constants
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 30th Aug 2012
  • Abstract:

    Given a positive integer b, we say that a mathematical constant alpha is "b-normal" or "normal base b" if every m-long string of digits appears in the base-b expansion of alpha with precisely the limiting frequency 1/b^m. Although it is well known from measure theory that almost all real numbers are b-normal for all integers b > 1, nonetheless proving normality (or nonnormality) for specific constants, such as pi, e and log(2), has been very difficult.

    In the 21st century, a number of different approaches have been attempted on this problem. For example, a recent study employed a Poisson model of normality to conclude that based on the first four trillion hexadecimal digits of pi, it is exceedingly unlikely that pi is not normal. In a similar vein, graphical techniques, in most cases based on the digit-generated "random" walks, have been successfully employed to detect certain nonnormality in some cases.

    On the analytical front, it was shown in 2001 that the normality of certain reals, including log(2) and pi (or any other constant given by a BBP formula), could be reduced to a question about the behavior of certain specific pseudorandom number generators. Subsequently normality was established for an uncountable class of reals (the "Stoneham numbers"), the simplest of which is: alpha_{2,3} = Sum_{n >= 0} 1/(3^n 2^(3^n)), which is provably normal base 2. Just as intriguing is a recent result that alpha_{2,3}, for instance, is provably NOT normal base 6. These results have now been generalized to some extent, although many open cases remain.

    In this talk I will present an introduction to the theory of normal numbers, including brief mention of new graphical- and statistical-based techniques. I will then sketch a proof of the normality base 2 (and nonnormality base 6) of Stoneham numbers, then suggest some additional lines of research. Various parts of this research were conducted in collaboration with Richard Crandall, Jonathan and Peter Borwein, Francisco Aragon, Cristian Calude, Michael Dinneen, Monica Dumitrescu and Alex Yee.

  • [Permanent event link]

  • SIGMAOPT/CARMA SEMINAR
  • Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle
  • Title: Expectation integrals on fractal sets
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Access Grid Venue: UNewcastle [ENQUIRIES]
  • Time and Date: 3:00 pm, Mon, 13th Aug 2012
  • Abstract:

    (Joint speakers, Jon Borwein and Michael Rose)

    p>Using fractal self-similarity and functional-expectation relations, the classical theory of box integrals is extended to encompass a new class of fractal “string-generated Cantor sets” (SCSs) embedded in unit hypercubes of arbitrary dimension. Motivated by laboratory studies on the distribution of brain synapses, these SCSs were designed for dimensional freedom: a suitable choice of generating string allows for fine-tuning the fractal dimension of the corresponding set. We also establish closed forms for certain statistical moments on SCSs and report various numerical results. The associated paper is at http://www.carma.newcastle.edu.au/jon/papers.html#PAPERS.

  • (Joint talk with Michael Rose.)
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Dr Alexander Plakhov, Center for Research and Development in Mathematics and Applications, University of Aveiro
  • Title: Problems of optimal resistance in Newtonian aerodynamics
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Thu, 5th Jul 2012
  • Abstract:

    A body moves in a rarefied medium of resting particles and at the same time very slowly rotates (somersaults). Each particle of the medium is reflected elastically when hitting the body boundary (multiple reflections are possible). The resulting resistance force acting on the body depends on the time; we are interested in minimizing the time-averaged value of resistance (which is called $R$). The value $R(B)$ is well defined in terms of billiard in the complement of $B$, for any bounded body $B \subset \mathbb{R}^d$, $d\geq 2$ with piecewise smooth boundary.

    Let $C\subset\mathbb{R}^d$ be a bounded convex body and $C_1\subset C$ be another convex body with $\partial C_1 \cap C=\varnothing$. It would be interesting to get an estimate for $$R(C1_,C)= \inf_{C_1\subset B \subset C} R(B) .................. (1)$$ If $\partial C_1$ is close to $\partial C$, problem (1) can be referred to as minimizing the resistance of the convex body $C$ by "roughening" its surface. We cannot solve problem (1); however we can find the limit $$\lim_{\text{dist}(\partial C_1,\partial C)\rightarrow 0} \frac{R(C_1,C)}{R(C)}. .................. (2) $$

    It will be explained that problem (2) can be solved by reduction to a special problem of optimal mass transportation, where the initial and final measurable spaces are complementary hemispheres, $X=\{x=(x_1,...,x_d)\in S^{d-1}: x_1\geq 0\}$ and $Y=\{x\in S^{d-1}:x_1\leq 0\}$. The transportation cost is the squared distance, $c(x,y)=\frac{1}{2}|x-y|^2$, and the measures in $X$ and $Y$ are obtained from the $(d-1)$-dimensional Lebesgue measure on the equatorial circle $\{x=(x_1,...,x_d):|x|\leq 1,x_1=0\}$ by parallel translation along the vector $e_1=(1,0,...,0)$. Let $C(\nu)$ be the total cost corresponding to the transport plan $\nu$ and let $\nu_0$ be the transport plan generated by parallel translation along $e_1$; then the value $\frac{\inf C(\nu)}{C(\nu_0)}$ coincides with the limit in (2).

    Surprisingly, this limit does not depend on the body $C$ and depends only on the dimension $d$.

    In particular, if $d=3$ ($d=2$), it equals (approximately) 0.96945 (0.98782). In other words, the resistance of a 3-dimensional (2-dimensional) convex body can be decreased by 3.05% (correspondingly, 1.22%) at most by roughening its surface.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Dr Francisco Aragón Artacho, CARMA, The University of Newcastle
  • Title: Douglas-Rachford: an algorithm that mysteriously solves sudokus and other non-convex problems
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 21st Jun 2012
  • Abstract:

    The Douglas-Rachford algorithm is an iterative method for finding a point in the intersection of two (or more) closed sets. It is well-known that the iteration (weakly) converges when it is applied to convex subsets of a Hilbert space. Despite the absence of a theoretical justification, the algorithm has also been successfully applied to various non-convex practical problems, including finding solutions for the eight queens problem, or sudoku puzzles. In particular, we will show how these two problems can be easily modelled.

    With the aim providing some theoretical explanation of the convergence in the non-convex case, we have established a region of convergence for the prototypical non-convex Douglas-Rachford iteration which finds a point on the intersection of a line and a circle. Previous work was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given.

    PS: Bring your hardest sudoku puzzle :)

  • Download: Talk slides (4.7 MB)
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Tao Qian, University of Macau
  • Title: Adaptive Fourier Decomposition and Its Applications to Signal and Functional Analysis
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 1:00 pm, Tue, 19th Jun 2012
  • Abstract:
    Based on generalized backward shift operators we introduce adaptive Fourier decomposition. Then we discuss its relations and applications to (i) system identification; (2) computation of Hilbert transform; (3) algorithm for the best order-n rational approximation to functions in the Hardy space H2; (4) forward and backward shift invariant spaces; (5) band preserving in filter designing; (6) phase retrieving; and (7) the Bedrosian identity. The talk also concerns possible generalizations of the theory and applications to higher dimensional spaces.
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  • CARMA SEMINAR
  • Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle
  • Title: What is a self-similar group?
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 14th Jun 2012
  • Abstract:
    I will give a brief introduction to the theory of self-similar groups, focusing on a couple of pertinent examples: Grigorchuk's group of intermediate growth, and the basilica group.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Prof A. Bass Bagayogo, Université de Saint-Boniface
  • Title: TBA
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Tue, 12th Jun 2012
  • Abstract:
    TBA
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Dr Roslyn Hickson, School of Mathematical and Physical Sciences, The University of Newcastle
  • Title: TB or not TB? in the Torres Strait region
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 7th Jun 2012
  • Abstract:
    There is a high prevalence of tuberculosis (TB) in Papua New Guinea (PNG), which is exacerbated by the presence of drug-resistant TB strains and HIV infection. This is an important public health issue not only locally within PNG, but also in Australia due to the high cross-border traffic in the Torres Strait Island–Western Province (PNG) treaty region. A metapopulation model is used to evaluate the effect of varying control strategies in the region, and some initial cost-benefit analysis figures are presented.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Prof Wal Wallis, Department of Mathematics, Southern Illinois University
  • Title: Minimal Pancyclic Graphs
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 1:00 pm, Tue, 5th Jun 2012
  • Abstract:
    A graph on v vertices is called pancyclic if it contains cycles of every length from 3 to v. Obviously such graphs exist — the complete graph on v vertices is an example. We shall look at the question, what is the minimum number of edges in a pancyclic graph? Interestingly, this question was "solved", incorrectly, in 1978. A complete solution is not yet known.
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  • CARMA SEMINAR
  • Speaker: Prof Martin Bunder, University of Wollongong
  • Title: How I got into Logic via John Giles's course on Measure Theory
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 24th May 2012
  • Abstract:
    This involves (in pre-nonstandard analysis times) the development of a simple system of infinites and infinitesmals that help to clarify Cantor's Ternary Set, nonmeasurable sets and Lebesgue integration. The talk will include other memories as a maths student at Newcastle University College, Tighes Hill, from 1959 to 1961.
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  • CARMA SEMINAR
  • Speaker: Joe Lakey, New Mexico State University
  • Title: Time and Band Limiting
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 17th May 2012
  • Abstract:

    This talk will survey some of the classical and recent results concerning operators composed of a projection onto a compact set in time, followed by a projection onto a compact set in frequency. Such "time- and band-limiting" operators were studied by Landau, Slepian, and Pollak in a series of papers published in the Bell Systems Tech. Journal in the early 1960s identifying the eigenfunctions, providing eigenvalue estimates, and describing spaces of "essentially time- and band-limited signals."

    Further progress on time- and band-limiting has been intermittent, but genuine recent progress has been made in terms of numerical analysis, sampling theory, and extensions to multiband signals, all driven to some extent by potential applications in communications. After providing an outline of the historical developments in the mathematical theory of time- and bandlimiting, some details of the sampling theory and multiband setting will be given. Part of the latter represents joint work with Jeff Hogan and Scott Izu.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Karen Smilowitz, Industrial Engineering and Management Sciences, Northwestern University
  • Title: Transportation and logistics models in non-profit settings
  • Location: Room V09, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 10:00 am, Fri, 11th May 2012
  • Abstract:

    This talk will discuss opportunities and challenges related to the development and application of operations research techniques to transportation and logistics problems in non-profit settings. Much research has been conducted on transportation and logistics problems in commercial settings where the goal is either to maximize profit or to minimize cost. Significantly less work has been conducted for non-profit applications. In such settings, the objectives are often more difficult to quantify since issues such as equity and sustainability must be considered, yet efficient operations are still crucial. This talk will present several research projects that introduce new approaches tailored to the objectives and constraints unique to non-profit agencies, which are often concerned with obtaining equitable solutions given limited, and often uncertain, budgets, rather than with maximizing profits.

    This talk will assess the potential of operations research to address the problems faced by non-profit agencies and attempt to understand why these problems have been understudied within the operations research community. To do so, we will ask the following questions: Are non-profit operations problems rich enough for academic study? and Are solutions to non-profit operations problems applicable to real communities?

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  • CARMA SEMINAR
  • Speaker: Sergey Ajiev, University of NSW
  • Title: Analysis on infinite-dimensional spaces: from qualitative stability to quantitative
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 3rd May 2012
  • Abstract:

    Approximation theory is a classical part of the analysis of functions defined on an Euclidean space or its subset and the foundation of its applications, while the problems related to high or infinite dimensions create known challenges even in the setting of Hilbert spaces. The stability (uniform continuity) of a mapping is one of the traditional properties investigated in various branches of pure and applied mathematics and further applications in engineering. Examples include analysis of linear and non-linear PDEs, (short-term) prediction problems and decision-making and data evolution.

    We describe the uniform approximation properties of the uniformly continuous mappings between the pairs of Banach and, occasionally, metric spaces from various wide parameterised and non-parameterised classes of spaces with or without the local unconditional structure in a quantitative manner. The striking difference with the finite-dimensional setting is represented by the presence of Tsar'kov's phenomenon. Many tools in use are developed under the scope of our quasi-Euclidean approach. Its idea seems to be relatively natural in light of the compressed sensing and distortion phenomena.

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  • CARMA SEMINAR
  • Speaker: Dr Paul Leopardi, Australian National University
  • Title: New constructions for Hadamard matrices
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:30 pm, Thu, 26th Apr 2012
  • Abstract:
    The talk will outline some topics associated with constructions for Hadamard matrices, in particular, a relatively simple construction, given by a sum of Kronecker products of ingredient matrices obeying certain conditions. Consideration of the structure of the ingredient matrices leads, on the one hand, to consideration of division algebras and Clifford algebras, and on the other hand, to searching for multisets of {-1,1} ingredient matrices. Structures within the sets of ingredient matrices can make searching more efficent.
  • Please note the start time.
  • [Permanent event link]

  • CARMA SEMINAR
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Dates: Mon, 23rd Apr 2012 - Mon, 23rd Apr 2012
  • 12:00-1:00Michael Coons (University of Waterloo)
    1:00-2:00Claus Koestler (Aberystwyth University)
    2:00-3:00Eric Mortenson (The University of Queensland)
    3:00-4:00Ekaterina Shemyakova (University of Western Ontario)
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  • CARMA SEMINAR
  • Speaker: Prof Brian Alspach, CARMA, The University of Newcastle
  • Title: The Coxeter Group Project: A Progress Report
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 19th Apr 2012
  • Abstract:
    I have embarked on a project of looking for Hamilton paths in Cayley graphs on finite Coxeter groups. This talk is a report on the progress thus far.
  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Darryn Bryant, The University of Queensland
  • Title: Graph decomposition and the Oberwolfach problem
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 12th Apr 2012
  • Abstract:
    This will be an introductory talk which begins by describing the four colour theorem and finite projective planes in the setting of graph decompositions. A problem posed by Ringel at a graph theory meeting in Oberwolfach in 1967 will then be discussed. This problem is now widely known as the Oberwolfach Problem, and is a generalisation of a question asked by Kirkman in 1850. It concerns decompositions of complete graphs into isomorphic copies of spanning regular graphs of degree two.
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  • CARMA SEMINAR
  • Speaker: Graham White, The University of Sydney
  • Title: Automorphisms of geometric structures associated to Coxeter groups
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 5th Apr 2012
  • Abstract:
    In this talk, we consider the automorphism groups of the Cayley graph with respect to the Coxeter generators and the Davis complex of an arbitrary Coxeter group. We determine for which Coxeter groups these automorphism groups are discrete. In the case where they are discrete, we express them as semidirect products of two obvious families of automorphisms. This extends a result of Haglund and Paulin.
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  • CARMA SEMINAR
  • Speaker: Ernst Stephan, Insitut fur Angewandte Mathematik (IfAM), Leibniz Universitat Hannover
  • Title: hp-adaptive DG-FEM for Parabolic Obstacle Problems
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Tue, 13th Mar 2012
  • Abstract:
    Parabolic obstacle problems find applications in the financial markets for pricing American put options. We present a mixed and an equivalent variational inequality hp-interior penalty DG (IPDG) method combined with an hp-time DG (TDG) method to solve parabolic obstacle problems approximatively. The contact conditions are resolved by a biorthogonal Lagrange multiplier and are component-wise decoupled. These decoupled contact conditions are equivlent to finding the root of a non-linear complementary function. This non-linear problem can in turn be solved efficiently by a semi-smooth Newton method. For the hp-adaptivity a p-hierarchical error estimator in conjunction with a local analyticity estimate is employed. For the considered stationary problem, this leads to exponential convergence, and for the instationary problem to greatly improved convergence rates. Numerical experiments are given demonstrating the strengths and limitations of the approaches.
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  • CARMA SEMINAR
  • Speaker: Mr Neil Gillespie, School of Mathematics and Statistics, University of Western Australia
  • Title: On connections between neighbour transitive codes and power line communication
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 1st Mar 2012
  • Abstract:
    Power line communication has been proposed as a possible solution to the "last mile" problem in telecommunications i.e. providing economical high speed telecommunications to millions of end users. As well as the usual background interference (noise), two other types of noise must also be considered for any successful practical implementation of power line communication. Coding schemes have traditionally been designed to deal only with background noise, and in such schemes it is often assumed that background noise affects symbols in codewords independently at random. Recently, however, new schemes have been proposed to deal with the extra considerations in power line communication. We introduce neighbour transitive codes as a group theoretic analogue to the assumption that background noise affects symbols independently at random. We also classify a family of neighbour transitive codes, and show that such codes have the necessary properties to be useful in power line communication.
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  • CARMA SEMINAR
  • Speaker: Wilson Ong, Department of Mathematics, Australian National University
  • Title: A simplified proof of Hesselholts conjecture on Galois cohomology of Witt vectors of algebraic integers
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 23rd Feb 2012
  • Abstract:
    Let $K$ be a complete discrete valuation field of characteristic zero with residue field $k_K$ of characteristic $p > 0$. Let $L/K$ be a finite Galois extension with Galois group $G = \text{Gal}(L/K)$ and suppose that the induced extension of residue fields $k_L/k_K$ is separable. Let $W_n(.)$ denote the ring of $p$-typical Witt vectors of length $n$. Hesselholt [Galois cohomology of Witt vectors of algebraic integers, Math. Proc. Cambridge Philos. Soc. 137(3) (2004), 551557] conjectured that the pro-abelian group ${H^1(G,W_n(O_L))}_{n>0}$ is isomorphic to zero. Hogadi and Pisolkar [On the cohomology of Witt vectors of $p$-adic integers and a conjecture of Hesselholt, J. Number Theory 131(10) (2011), 17971807] have recently provided a proof of this conjecture. In this talk, we present a simplified version of the original proof which avoids many of the calculations present in that version.
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  • CARMA OPTIMIZATION SEMINAR
  • Speaker: Conjoint Prof Steve Wright, Computer Sciences Department and Wisconsin Institute for Discovery, University of Wisconsin-Madison
  • Title: Packing Ellipsoids and Circles (with Application to Chromosome Arrangement)
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 2:00 pm, Mon, 23rd Jan 2012
  • Abstract:
    We consider the problem of packing ellipsoids of different size and shape in an ellipsoidal container so as to minimize a measure of total overlap. The motivating application is chromosome organization in the human cell nucleus. A bilevel optimization formulation is described, together with an algorithm for the general case and a simpler algorithm for the special case in which all ellipsoids are in fact spheres. We prove convergence to stationary points of this nonconvex problem, and describe computational experience. The talk describes joint work with Caroline Uhler (IST, Vienna).
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  • CARMA SEMINAR
  • Speaker: Nina Narodytska, unknown or leave blank,
  • Title: Complexity of and Algorithms for Borda Manipulation
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Tue, 10th Jan 2012
  • Abstract:

    We prove the it is NP-hard for a coalition of two manipulators to compute how to manipulate the Borda voting rule. This resolves one of the last open problems in the computational complexity of manipulating common voting rules. Because of this NP-hardness, we treat computing a manipulation as an approximation problem where we try to minimize the number of manipulators. Based on ideas from bin packing and multiprocessor scheduling, we propose two new approximation methods to compute manipulations of the Borda rule. Experiments show that these methods significantly outperform the previous best known approximation method. We are able to find optimal manipulations in almost all the randomly generated elections tested. Our results suggest that, whilst computing a manipulation of the Borda rule by a coalition is NP-hard, computational complexity may provide only a weak barrier against manipulation in practice.

    We also consider Nanson’s and Baldwin’s voting rules that select a winner by successively eliminating candidates with low Borda scores. We theoretically and experimentally demonstrate that these rules are significantly more difficult to manipulate compared to Borda rule. In particular, with unweighted votes, it is NP-hard to manipulate either rule with one manipulator, whilst with weighted votes, it is NP-hard to manipulate either rule with a small number of candidates and a coalition of manipulators.

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  • CARMA SEMINAR
  • Speaker: Dr Neil Saunders, The University of Sydney
  • Title: Minimal Faithful Permutation Representations of Finite Groups
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 15th Dec 2011
  • Abstract:

    The minimal degree of a finite group $G$ is the smallest non-negative integer $n$ such that $G$ embeds in $\Sym(n)$. This defines an invariant of the group $\mu(G)$. In this talk, I will present some interesting examples of calculating $\mu(G)$ and examine how this invariant behaves under taking direct products and homomorphic images.

    In particular, I will focus on the problem of determining the smallest degree for which we obtain a strict inequality $\mu(G \times H) < \mu(G) + \mu(H)$, for two groups $G$ and $H$. The answer to this questions also leads us to consider the problem of exceptional permutation groups. These are groups $G$ that possess a normal subgroup $N$ such that $\mu(G/N) > \mu(G)$. They are somewhat mysterious in the sense that a particular homomorphic image becomes 'harder' to faithfully represent than the group itself. I will present some recent examples of exceptional groups and detail recent developments in the 'abelian quotients conjecture' which states that $\mu(G/N) < \mu(G)$, whenever $G/N$ is abelian.

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  • CARMA SEMINAR
  • Speaker: Prof John Giles, School of Mathematical and Physical Sciences, The University of Newcastle
  • Title: Persistence properties for Banach spaces
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 8th Sep 2011
  • Abstract:

    We are interested in local geometrical properties of a Banach space which are preserved under natural embeddings in all even dual spaces. An example of this behaviour which we generalise is:

    if the norm of the space $X$ is Fréchet differentiable at $x \in S(X)$ then the norm of the second dual $X^{**}$ is Fréchet differentiable at $\hat{x}\in S(X)$ and of $X^{****}$ at $\hat{\hat{x}} \in S(X^{****})$ and so on....

    The results come from a study of Hausdorff upper semicontinuity properties of the duality mapping characterising general differentiability conditions satisfied by the norm.

  • [Permanent event link]

  • SIGMAOPT/CARMA SEMINAR
  • Speaker: Liangjin Yao, CARMA, The University of Newcastle
  • Title: The sum of a maximally monotone linear relation and the subdifferential of a proper lower semicontinuous convex function is maximally monotone
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Access Grid Venue: UNewcastle [ENQUIRIES]
  • Time and Date: 4:00 pm, Thu, 11th Aug 2011
  • Abstract:
    The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this talk, we prove the maximal monotonicity of the sum of a maximally monotone linear relation and the subdifferential of a proper lower semicontinuous convex function satisfying Rockafellar's constraint qualification. Moreover, we show that this sum operator is of type (FPV).
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  • CARMA SEMINAR
  • Speaker: Dr Erick Li, The University of Sydney
  • Title: On Designing Optimal Permission Sets for Project Selection
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 1:30 pm, Wed, 10th Aug 2011
  • Abstract:
    This paper considers designing permission sets to influence the project selection decision made by a better-informed agent. The project characteristics are two-dimensional. The principal can verify the characteristics of the project selected by the agent. However, the principal cannot observe the number and characteristics of those projects that the agent could, but does not, propose. The payoffs to the agent and the principal are different. Using calculus of variations, we solve the optimal permission set, which can be characterized by a threshold function. We obtain comparative statics on the preference alignment and expected number of projects available. When outcome-based incentives are feasible, we discuss the use of financial inducement to maximize the social welfare. We also extend our analysis to two cases: 1) when one of the project characteristics is unobservable; and 2) when there are multiple agents with private preferences and the principal must establish a universal permission set.
    Key words: calculus of variations, optimal permission set, project management.
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  • CARMA SEMINAR
  • Speaker: Wojciech Kozlowski, University of NSW
  • Title: Common fixed points for semigroups of pointwise Lipschitzian mappings in Banach spaces
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 2:00 pm, Fri, 22nd Jul 2011
  • Abstract:
    We will investigate the existence of common fixed points for point-wise Lipschitzian semigroups of nonlinear mappings $Tt : C - C$ where $C$ is a bounded, closed, convex subset of a uniformly convex Banach space $X$, i.e. a family such that $T0(x) = x$, $Ts+t = Ts(Tt(x))$, where each $Tt$ is pointwise Lipschitzian, i.e. there exists a family of functions $at : C - [0;x)$ such that $||Tt(x)-Tt(y)|| < at(x)||x-y||$ for $x$, $y \in C$. We will also demonstrate how the asymptotic aspect of the pointwise Lipschitzian semigroups can be expressed in terms of the respective Frechet derivatives. We will discuss some questions related to the weak and strong convergence of certain iterative algorithms for the construction of the stationary and periodic points for such semigroups.
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  • CARMA SEMINAR
  • Speaker: Dr Riki Brown, University College London and University of Newcastle Upon Tyne
  • Title: Metric Projections in Spaces of Continuous Functions
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:00 pm, Wed, 15th Jun 2011
  • Abstract:
    Let $T$ be a topological space (a compact subspace of ${\mathbb R^m}$, say) and let $C(T)$ be the space of real continuous functions on $T$, equipped with the uniform norm: $||f|| = \text{max}_{t\in T}|f(t)|$ for all $f \in C(T)$. Let $G$ be a finite-dimensional linear subspace of $C(T)$. If $f \in C(T)$ then $$d(f,G) = \text{inf}\{||f−g|| : g \in G\}$$ is the distance of $f$ from $G$, and $$P_G(f) = \{g \in G : ||f−g|| = d(f,G)\}$$ is the set of best approximations to $f$ from $G$. Then $$P_G : C(T) \rightarrow P(G)$$ is the set-valued metric projection of $C(T)$ onto $G$. In the 1850s P. L. Chebyshev considered $T = [a, b]$ and $G$ the space of polynomials of degree $\leq n − 1$. Our concern is with possible properties of $P_G$. The historical development, beginning with Chebyshev, Haar (1918) and Mairhuber (1956), and the present state of knowledge will be outlined. New results will demonstrate that the story is still incomplete.
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  • CARMA SEMINAR
  • Speaker: Coenraad Labuschagne, University of South Australia
  • Title: The Chaney-Shaefer $\ell$-Tensor Product $E\tilde{\otimes}_{\ell}Y$
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 21st Apr 2011
  • Abstract:
    The Chaney-Schaefer $\ell$-tensor product $E\tilde{\otimes}_{\ell}Y$ of a Banach lattice $E$ and a Banach space $Y$ may be viewed as an extension of the Bochner space $L^p(\mu,Y) (1\leq p < \infty)$. We consider an extension of a classical martingale characterization of the Radon Nikodým property in $L^p(\mu,Y)$, for $1 < p < 1$, to $E\tilde{\otimes}_{\ell}Y$. We consider consequences of this extension, and time permitting, use it to represent set-valued measures of risk de ned on Banach lattice-valued Orlicz hearts.
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  • CARMA SEMINAR
  • Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle
  • Title: Finding short words in the first Grigorchuk group
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 24th Mar 2011
  • Abstract:

    In the 80's R.Grigorchuk found a finitely generated group such that the number of elements that can be written as a product of at most \(n\) generators grows faster than any polynomial in \(n\), but slower than any exponential in \(n\), so-called "intermediate" growth.

    It can be described as an group of automorphisms of an infinite rooted binary tree, or in terms of abstract computing devices called "non-initial finite transducers".

    In this talk I will describe what some of these short words/products of generators look like, and speculate on the asymptotic growth rate of all short words of length \(n\).

    This is joint unpublished work with Mauricio Gutierrez (Tufts) and Zoran Sunic (Texas A&M).

  • [Permanent event link]


  • CARMA SEMINAR
  • Speaker: Various Members, CARMA, The University of Newcastle
  • Title: CARMA Show and Tell Part II
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 1:30 pm, Mon, 7th Feb 2011
  • Abstract:

    Various Vacation Scholars, HRD students and CARMA RAs will report on their work. This involves visualization and computation, practice and theory. Everyone is welcome to see what they have done and what they propose to do.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Various Members, CARMA, The University of Newcastle
  • Title: CARMA Show and Tell
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 1:30 pm, Mon, 24th Jan 2011
  • Abstract:

    Various Vacation Scholars, HRD students and CARMA RAs will report on their work. This involves visualization and computation, practice and theory. Everyone is welcome to see what they have done and what they propose to do.

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Prof Shing-Tung Yau, Department of Mathematics, Harvard University
  • Title: The Shape of Inner Space: String theory and the geometry of the universe's hidden dimensions
  • Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Access Grid Venue: Monash University [ENQUIRIES]
  • Time and Date: 11:00 am, Thu, 25th Nov 2010
  • Abstract:

    See flyer [PDF]

  • [Permanent event link]

  • CARMA SEMINAR
  • Speaker: Prof Michael Barnsley, Mathematical Sciences Institute, Australian National University
  • Title: Real Projective Iterated Function Systems
  • Location: Room VG10, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 10:30 am, Fri, 11th Jun 2010
  • Abstract:
    I will describe four recent theorems, developed jointly with Andrew Vince and David C. Wilson (both of the University of Florida) that reveal a surprisingly rich theory associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor that avoids a hyperplane. The second theorem establishes that a projective IFS has at most one attractor. In the third theorem the classical duality between points and hyperplanes in projective space leads to connections between attractors that avoid hyperplanes and repellers that avoid points and an associated index, which is a nontrivial projective invariant, is defined. I will link these results to the Conley decomposition theorem.
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