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

[Note: events are listed by descending date.]
 CARMA OANT SEMINAR Speaker: Assoc Prof Regina Burachik, University of South Australia Title: An additive subfamily of enlargements of a maximally monotone Operator Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: SeeVogh (non-AG) [ENQUIRIES] Time and Date: 1:30 pm, Mon, 27th Apr 2015 Abstract: We introduce a subfamily of additive enlargements of a maximally monotone operator $T$. Our definition is inspired by the seminal work of Fitzpatrick presented in 1988. These enlargements are a subfamily of the family of enlargements introduced by Svaiter in 2000. For the case $T = \partial f$, we prove that some members of the subfamily are smaller than the $\varepsilon$-subdifferential enlargement. For this choice of $T$, we can construct a specific enlargement which coincides with the$\varepsilon$-subdifferential. Since these enlargements are all additive, they can be seen as structurally closer to the $\varepsilon$-subdifferential enlargement. Joint work with Juan Enrique Martínez-Legaz (Universitat Autonoma de Barcelona), Mahboubeh Rezaei (University of Isfahan, Iran), and Michel Théra (University of Limoges). [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Dzmitry Badziahin, Department of Mathematical Sciences, Durham University Title: On continued fraction expansion of potential counterexamples to mixed Littlewood conjecture Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: SeeVogh (non-AG) [ENQUIRIES] Time and Date: 10:00 am, Wed, 5th Nov 2014 Abstract: Mixed Littlewood conjecture proposed by de Mathan and Teulie in 2004 states that for every real number $x$ one has $\liminf q * |q|_D * ||qx|| = 0,$ where $|q|_D$ is a so called pseudo norm which generalises the standard p-adic norm. In the talk we'll consider the set mad of potential counterexamples to this conjecture. Thanks to the results of Einsiedler and Kleinbock we already know that the Haudorff dimension of mad is zero, so this set is very tiny. During the talk we'll see that the continued fraction expansion of every element in mad should satisfy some quite restrictive conditions. As one of them we'll see that for these expansions, considered as infinite words, the complexity function can neither grow too fast nor too slow. SeeVogh meeting number 9743677479. [Permanent event link] CARMA OANT SEMINAR Speaker: Yohei Tachiya, Graduate School of Science and Technology, Hirosaki University Title: Algebraic independence results for the generating functions of pattern sequences Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 4:00 pm, Mon, 27th Oct 2014 Abstract: We first introduce the notations of pattern sequence, which is defined by the number of (possibly) overlapping occurrences of a given word in the $\langle q,r\rangle$-numeration system. After surveying several properties of pattern sequence, we will give necessary and sufficient criteria for the algebraic independence of their generating functions. As applications, we deduce the linear relations between pattern sequences. The proofs of the theorem and the corollaries are based on Mahler's method. SeeVogh meeting 3144213387. [Permanent event link] CARMA OANT SEMINAR Speaker: A/Prof Simon Kristensen, Aarhus University Title: Diophantine approximation in positive characteristic Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: SeeVogh (non-AG) [ENQUIRIES] Time and Date: 10:00 am, Wed, 22nd Oct 2014 Abstract: The completion with respect to the degree valuation of the field of rational functions over a finite field is often a fruitful analogue to consider when one would like to test ideas, methods and conjectures in Diophantine approximation for the real numbers. In many respects, this setting behaves very similarly to the real numbers, and in particular the metric theory of Diophantine approximation in this setup is well-developed and and in some respects more is known to be true in this setup than in the real numbers. However, natural analogues of other classical theorems in Diophantine approximation fail spectacularly in positive characteristic. In this talk, I will introduce the topic and give old and new results underpinning the similarities and differences of the theories of Diophantine approximation in positive characteristic and in characteristic zero. SeeVogh meeting number 7876118766. [Permanent event link] CARMA OANT SEMINAR Speaker: Assoc Prof Regina Burachik, University of South Australia Title: An additive subfamily of enlargements of a maximally monotone operator Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 10:00 am, Wed, 15th Oct 2014 Abstract: We introduce a subfamily of enlargements of a maximally monotone operator $T$. Our definition is inspired by a 1988 publication of Fitzpatrick. These enlargements are elements of the family of enlargements $\mathbb{E}(T)$ introduced by Svaiter in 2000. These new enlargements share with the $\epsilon$-subdifferential a special additivity property, and hence they can be seen as structurally closer to the $\epsilon$-subdifferential. For the case $T=\nabla f$, we prove that some members of the subfamily are smaller than the $\epsilon$-subdifferential enlargement. In this case, we construct a specific enlargement which coincides with the $\epsilon$-subdifferential. Joint work with Juan Enrique Martínez Legaz, Mahboubeh Rezaei, and Michel Théra. [Permanent event link] CARMA OANT SEMINAR Joint CARMA OANT and EECS Seminar Speaker: A/Prof Christopher Kellett, School of Electrical Engineering and Computer Science, The University of Newcastle Title: Converse Theorems in Lyapunov's Second Method and Constructive Methods: Part II Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 10:00 am, Wed, 1st Oct 2014 Abstract: More than 120 years after their introduction, Lyapunov's so-called First and Second Methods remain the most widely used tools for stability analysis of nonlinear systems. Loosely speaking, the Second Method states that if one can find an appropriate Lyapunov function then the system has some stability property. A particular strength of this approach is that one need not know solutions of the system in order to make definitive statements about stability properties. The main drawback of the Second Method is the need to find a Lyapunov function, which is frequently a difficult task. Converse Lyapunov Theorems answer the question: given a particular stability property, can one always (in principle) find an appropriate Lyapunov function? In the first installment of this two-part talk, we will survey the history of the field and describe several such Converse Lyapunov Theorems for both continuous and discrete-time systems. In the second instalment we will discuss constructive techniques for numerically computing Lyapunov functions. [Permanent event link] CARMA OANT SEMINAR Joint CARMA OANT and EECS Seminar Speaker: A/Prof Christopher Kellett, School of Electrical Engineering and Computer Science, The University of Newcastle Title: Converse Theorems in Lyapunov's Second Method and Constructive Methods: Part I Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 10:00 am, Wed, 24th Sep 2014 Abstract: More than 120 years after their introduction, Lyapunov's so-called First and Second Methods remain the most widely used tools for stability analysis of nonlinear systems. Loosely speaking, the Second Method states that if one can find an appropriate Lyapunov function then the system has some stability property. A particular strength of this approach is that one need not know solutions of the system in order to make definitive statements about stability properties. The main drawback of the Second Method is the need to find a Lyapunov function, which is frequently a difficult task. Converse Lyapunov Theorems answer the question: given a particular stability property, can one always (in principle) find an appropriate Lyapunov function? In the first installment of this two-part talk, we will survey the history of the field and describe several such Converse Lyapunov Theorems for both continuous and discrete-time systems. In the second instalment we will discuss constructive techniques for numerically computing Lyapunov functions. [Permanent event link] CARMA OANT SEMINAR Speaker: Christophe Vignat, Tulane University Title: An introduction to umbral calculus with applications Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 10:00 am, Wed, 3rd Sep 2014 Abstract: Classical umbral calculus was introduced by Blissard in the 1860's and later studied by E. T. Bell and Rota. It is a symbolic computation method that is particularly efficient for proving identities involving elementary special functions such as Bernoulli or Hermite polynomials. I will show the link between this technique and moment representation, and provide examples of its application. [Permanent event link] CARMA OANT SEMINAR Joint CARMA OANT and EECS Seminar Speaker: Prof Dr Lars Grüne, Chair of Applied Mathematics, University of Bayreuth Title: Economic Model Predictive Control without terminal conditions - theory, applications, and the gap in between Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 4:00 pm, Mon, 1st Sep 2014 Abstract: In this talk we consider economic Model Predictive Control (MPC) schemes. "Economic" means that the MPC stage cost models economic considerations (like maximal yield, minimal energy consumption...) rather than merely penalizing the distance to a pre-computed steady state or reference trajectory. In order to keep implementation and design simple, we consider schemes without terminal constraints and costs. In the first (longer) part of the talk, we summarize recent results on the performance and stability properties of such schemes for nonlinear discrete time systems. Particularly, we present conditions under which one can guarantee practical asymptotic stability of the optimal steady state as well as approximately optimal averaged and transient performance. Here, dissipativity of the underlying optimal control problems and the turnpike property are shown to play an important role (this part is based on joint work with Tobias Damm, Marleen Stieler and Karl Worthmann). In the second (shorter) part of the talk we present an application of an economic MPC scheme to a Smart Grid control problem (based on joint work with Philipp Braun, Christopher Kellett, Steven Weller and Karl Worthmann). While economic MPC shows good results for this control problem in numerical simulations, several aspects of this application are not covered by the available theory. This is explained in the last part of the talk, along with some suggestions on how to overcome this gap. [Permanent event link] CARMA OANT SEMINAR Speaker: Qiji Jim Zhu, Department of Mathematics, Western Michigan University Title: Variational Approach to Lagrange Multipliers: Part 2 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Thu, 17th Jul 2014 Abstract: Lagrange multiplier method is fundamental in dealing with constrained optimization problems and is also related to many other important results. In these two talks we first survey several different ideas in proving the Lagrange multiplier rule and then concentrate on the variational approach. We will first discuss the idea, a variational proof the Lagrange multiplier rule in the convex case and then consider the general case and relationship with other results. These talks are continuation of the e-mail discussions with Professor Jon Borwein and are very informal. [Permanent event link] CARMA OANT SEMINAR Speaker: Qiji Jim Zhu, Department of Mathematics, Western Michigan University Title: Variational Approach to Lagrange Multipliers: Part 1 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Mon, 14th Jul 2014 Abstract: Lagrange multiplier method is fundamental in dealing with constrained optimization problems and is also related to many other important results. In these two talks we first survey several different ideas in proving the Lagrange multiplier rule and then concentrate on the variational approach. We will first discuss the idea, a variational proof the Lagrange multiplier rule in the convex case and then consider the general case and relationship with other results. These talks are continuation of the e-mail discussions with Professor Jon Borwein and are very informal. [Permanent event link] CARMA OANT SEMINAR Speaker: Prof David Bailey, Berkeley, California Title: Big data computing: Science and pseudoscience Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Fri, 11th Jul 2014 Download: Flyer (416 K) Abstract: The relentless advance of computer technology, a gift of Moore's Law, and the data deluge available via the Internet and other sources, has been a gift to both scientific research and business/industry. Researchers in many fields are hard at work exploiting this data. The discipline of "machine learning," for instance, attempts to automatically classify, interpret and find patterns in big data. It has applications as diverse as supernova astronomy, protein molecule analysis, cybersecurity, medicine and finance. However, with this opportunity comes the danger of "statistical overfitting," namely attempting to find patterns in data beyond prudent limits, thus producing results that are statistically meaningless. The problem of statistical overfitting has recently been highlighted in mathematical finance. A just-published paper by the present author, Jonathan Borwein, Marcos Lopez de Prado and Jim Zhu, entitled "Pseudo-Mathematics and Financial Charlatanism," draws into question the present practice of using historical stock market data to "backtest" a new proposed investment strategy or exchange-traded fund. We demonstrate that in fact it is very easy to overfit stock market data, given powerful computer technology available, and, further, without disclosure of how many variations were tried in the design of a proposed investment strategy, it is impossible for potential investors to know if the strategy has been overfit. Hence, many published backtests are probably invalid, and this may explain why so many proposed investment strategies, which look great on paper, later fall flat when actually deployed. In general, we argue that not only do those who directly deal with "big data" need to be better aware of the methodological and statistical pitfalls of analyzing this data, but those who observe these problems of this sort arising in their profession need to be more vocal about them. Otherwise, to quote our "Pseudo-Mathematics" paper, "Our silence is consent, making us accomplices in these abuses." [Permanent event link] CARMA OANT SEMINAR Speaker: Prof Mark Giesbrecht, University of Waterloo Title: Algorithms and statistics for additive polynomials Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 24th Jun 2014 Abstract: The additive or linearized polynomials were introduced by Ore in 1933 as an analogy over finite fields to his theory of difference and difference equations over function fields. The additive polynomials over a finite field $F=GF(q)$, where $q=p^e$ for some prime $p$, are those of the form $f = f_0 x + f_1 x^p + f_2 x^{p^2} + ... + f_m x^{p^m}$ in $F[x]$ They form a non-commutative left-euclidean principal ideal domain under the usual addition and functional composition, and possess a rich structure in both their decomposition structures and root geometries. Additive polynomials have been employed in number theory and algebraic geometry, and applied to constructing error-correcting codes and cryptographic protocols. In this talk we will present fast algorithms for decomposing and factoring additive polynomials, and also for counting the number of decompositions with particular degree sequences. Algebraically, we show how to reduce the problem of decomposing additive polynomials to decomposing a related associative algebra, the eigenring. We give computationally efficient versions of the Jordan-Holder and Krull-Schmidt theorems in this context to describe all possible factorization. Geometrically, we show how to compute a representation of the Frobenius operator on the space of roots, and show how its Jordan form can be used to count the number of decompositions. We also describe an inverse theory, from which we can construct and count the number of additive polynomials with specified factorization patterns. Some of this is joint work with Joachim von zur Gathen (Bonn) and Konstantin-Ziegler (Bonn). [Permanent event link] CARMA OANT SEMINAR Speaker: Prof Joydeep Dutta, Department of Mathematics and Statistics, Indian Institute of Technology Kanpur Title: Gap Functions, Error Bounds and Regularization of Variational Inequalities: Part 2 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 17th Jun 2014 Abstract: Our aim in this talk is to show that D-gap function can play a pivotal role in developing inexact descent methods to solve monotone variational inequality problem where the feasible set of the variational inequality is a closed convex set rather than just the non-negative orthant. We also focus on the issue of regularization of variational inequality. Freidlander and Tseng has shown in 2007 that by the regularizing the convex objective function by using another convex function which in practice is chosen correctly can make the solution of the problem simpler. Tseng and Freiedlander has provided a criteria for exact regularization of convex optimization problems. In this section we ask the question as to what extent one can extend the idea of exact regularization in the context of variational inequalities. We study this in this talk and we show the central role played by the dual gap function in this analysis. [Permanent event link] CARMA OANT SEMINAR Speaker: Prof Joydeep Dutta, Department of Mathematics and Statistics, Indian Institute of Technology Kanpur Title: Gap Function, Error Bounds and Regularization of Variational Inequalities: Part 1 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 10th Jun 2014 Abstract: Using gap functions to devise error bounds for some special classes of monotone variational inequality is a fruitful venture since it allows us to obtain error bounds for certain classes of convex optimization problem. It is to be noted that if we take a Hoffman type approach to obtain error bounds to the solution set of a convex programming problem it does not turn out to be fruitful and thus using the vehicle of variational inequality seems fundamental in this case. We begin the discussion by introducing several popular gap functions for variational inequalities like the Auslender gap function and the Fukushima's regularized gap function and how error bounds can be created out of them. We then also spent a brief time with gap functions for variational inequalities with set-valued maps which correspond to the non-smooth convex optimization problems. We then quickly shift our focus on the creating error bounds using the dual gap function which is possibly the only convex gap function known in the literature to the best of our knowledge. In fact this gap function was never used for creating error bounds. Error bounds can be used as stopping criteria and this the dual gap function can be used to solve the variational inequality and also be used to develop a stopping criteria. We present several recent research on error bounds using the dual gap function and also provide an application to quasiconvex optimization. [Permanent event link] CARMA OANT SEMINAR Speaker: Hans Mittelmann, School of Mathematical and Statistical Sciences, Arizona State University Title: Computing Strong Bounds in Combinatorial Optimization Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Mon, 24th Feb 2014 Abstract: As is well-known semidefinite relaxations of discrete optimization problems can yield excellent bounds on their solutions. We present three examples from our collaborative research. The first addresses the quadratic assignment problem and a formulation is developed which yields the strongest lower bounds known for larger dimensions. Utilizing the latest iterative SDP solver and ideas from verified computing a realistic problem from communications is solved for dimensions up to 512. A strategy based on the Lovasz theta function is generalized to compute upper bounds on the spherical kissing number utilizing SDP relaxations. Multiple precision SDP solvers are needed and improvements on known results for all kissing numbers in dimensions up to 23 are obtained. Finally, generalizing ideas of Lex Schrijver improved upper bounds for general binary codes are obtained in many cases. [Permanent event link] CARMA OANT SEMINAR Speaker: Oleg Burdakov, Linkoping University Title: An approach to solving decomposable optimization problems with coupling constraints Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 3:00 pm, Tue, 10th Dec 2013 Abstract: We consider a problem of minimising $f_1(x)+f_2(y)$ over $x \in X \subseteq R^n$ and $y \in Y \subseteq R^m$ subject to a number of extra coupling constraints of the form $g_1(x) g_2(y) \geq 0$. Due to these constraints, the problem may have a large number of local minima. For any feasible combination of signs of $g_1(x)$ and $g_2(y)$, the coupled problem is decomposable, and the resulting two problems are assumed to be easily solved. An approach to solving the coupled problem is presented. We apply it to solving coupled monotonic regression problems arising in experimental psychology. [Permanent event link] CARMA OANT SEMINAR Speaker: Prof Robert Corless, University of Western Ontario Title: High-order, high-accuracy solution of a nonlinear PDE arising in a two-dimensional heat transfer model Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 3:00 pm, Mon, 9th Dec 2013 Abstract: A classical nonlinear PDE used for modelling heat transfer between concentric cylinders by fluid convection and also for modelling porous flow can be solved by hand using a low-order perturbation method. Extending this solution to higher order using computer algebra is surprisingly hard owing to exponential growth in the size of the series terms, naively computed. In the mid-1990's, so-called "Large Expression Management" tools were invented to allow construction and use of so-called "computation sequences" or "straight-line programs" to extend the solution to 11th order. The cost of the method was O(N^8) in memory, high but not exponential. Twenty years of doubling of computer power allows this method to get 15 terms. A new method, which reduces the memory cost to O(N^4), allows us to compute to N=30. At this order, singularities can reliably be detected using the quotient-difference algorithm. This allows confident investigation of the solutions, for different values of the Prandtl number. This work is joint with Yiming Zhang (PhD Oct 2013). [Permanent event link] CARMA OANT SEMINAR Speaker: Assoc Prof Regina Burachik, University of South Australia Title: Interior Epigraph Directions Method for Nonsmooth and Nonconvex Optimization via Generalized Augmented Lagrangian Duality Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 2:00 pm, Tue, 26th Nov 2013 Abstract: We propose and study a new method, called the Interior Epigraph Directions (IED) method, for solving constrained nonsmooth and nonconvex optimization. The IED method considers the dual problem induced by a generalized augmented Lagrangian duality scheme, and obtains the primal solution by generating a sequence of iterates in the interior of the dual epigraph. First, a deflected subgradient (DSG) direction is used to generate a linear approximation to the dual problem. Second, this linear approximation is solved using a Newton-like step. This Newton-like step is inspired by the Nonsmooth Feasible Directions Algorithm (NFDA), recently proposed by Freire and co-workers for solving unconstrained, nonsmooth convex problems. We have modified the NFDA so that it takes advantage of the special structure of the epigraph of the dual function. We prove that all the accumulation points of the primal sequence generated by the IED method are solutions of the original problem. We carry out numerical experiments by using test problems from the literature. In particular, we study several instances of the Kissing Number Problem, previously solved by various approaches such as an augmented penalty method, the DSG method, as well as the popular differentiable solvers ALBOX (a predecessor of ALGENCAN), Ipopt and LANCELOT. Our experiments show that the quality of the solutions obtained by the IED method is comparable with (and sometimes favourable over) those obtained by the other solvers mentioned. Joint work with Wilhelm P. Freire and C. Yalcin Kaya. Note earlier starting time. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr C. Yalcin Kaya, University of South Australia Title: A Numerical Method for Multi-objective Optimal Control Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 2:00 pm, Tue, 19th Nov 2013 Abstract: A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obtain points which are spread over the Pareto front. The technique is illustrated on problems involving tumor anti-angiogenesis and a fed-batch bioreactor, which exhibit bang–bang, singular and boundary types of optimal control. We illustrate that the Bolza form, the traditional scalarization in optimal control, fails to represent all the compromise, i.e., Pareto optimal, solutions. Joint work with Helmut Maurer. C. Y. Kaya and H. Maurer, A numerical method for nonconvex multi-objective optimal control problems, Computational Optimization and Applications, (appeared online: September 2013, DOI 10.1007/s10589-013-9603-2) Note change of time. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Victoria Martín-Márquez, Department of Mathematical Analysis, Universidad de Sevilla Title: Solving Convex Split Feasibility Problems and Applications Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 3:00 pm, Tue, 12th Nov 2013 Abstract: The split feasibility problem (SFP) consists in finding a point in a closed convex subset of a Hilbert space such that its image under a bounded linear operator belongs to a closed convex subset of another Hilbert space. Since its inception in 1994 by Censor and Elfving, it has received much attention thanks mainly to its applications to signal processing and image reconstruction. Iterative methods can be employed to solve the SFP. One of the most popular iterative method is Byrne's CQ algorithm. However, this algorithm requires prior knowledge (or at least an estimate) of the norm of the bounded linear operator. We introduce a stepsize selection method so that the implementation of the CQ algorithm does not need any prior information regarding the operator norm. Furthermore, a relaxed CQ algorithm, where the two closed convex sets are both level sets of convex functions, and a Halpern-type algorithm are studied under the same stepsize rule, yielding both weak and strong convergence. A more general problem, the Multiple-sets split feasibility problem, will be also presented. Numerical experiments are included to illustrate the applications to signal processing and, in particular, to compressed sensing and wavelet-based signal restoration. Based on joint works with G. López and H-K Xu. [Permanent event link] CARMA OANT SEMINAR Speaker: Prof Andrew Eberhard, School of Mathematical and Geospatial Sciences, RMIT University Title: On the Maximal Extensions of Monotone Operators, Criteria for Maximality, and the Sum Theorem Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 22nd Oct 2013 Abstract: Within a nonzero, real Banach space we study the problem of characterising a maximal extension of a monotone operator in terms of minimality properties of representative functions that are bounded by the Penot and Fitzpatrick functions. We single out a property of the space of representative functions that enable a very compact treatment of maximality and pre-maximality issues. As this treatment does not assume reflexivity and we characterises this property the existence of a counter example has a number of consequences for the search for a suitable certificate for maximality in non-reflexive spaces. In particular one is lead to conjecture that some extra side condition to the usual CQ is inevitable. We go on to look at the simplest such condition which is boundedness of the domain of the monotone operator and obtain some positive results. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle Title: A Social Welfare Optimal Sequential Allocation Procedure Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 8th Oct 2013 Abstract: There exist a variety of mechanisms to share indivisible goods between agents. One of the simplest is to let the agents take turns to pick an item. This mechanism is parameterized by a policy, the order in which agents take turns. A simple model of this mechanism was proposed by Bouveret and Lang in 2011. We show that in their setting the natural policy of letting the agents alternate in picking items is optimal. We also present a number of potential generalizations and extensions. This is joint work with Nina Narodytska and Toby Walsh. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Jean Lasserre, LAAS-CNRS, Université de Toulouse Title: Tractable characterizations of nonnegativity on closed sets via Linear Matrix Inequalities Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 24th Sep 2013 Abstract: In many problems in control, optimal and robust control, one has to solve global optimization problems of the form: $\mathbf{P}:f^\ast=\min_{\mathbf x}\{f(\mathbf x):\mathbf x\in\mathbf K\}$, or, equivalently, $f^\ast=\max\{\lambda:f-\lambda\geq0\text{ on }\mathbf K\}$, where $f$ is a polynomial (or even a semi-algebraic function) and $\mathbf K$ is a basic semi-algebraic set. One may even need solve the "robust" version $\min\{f(\mathbf x):\mathbf x\in\mathbf K;h(\mathbf x,\mathbf u)\geq0,\forall \mathbf u\in\mathbf U\}$ where $\mathbf U$ is a set of parameters. For instance, some static output feedback problems can be cast as polynomial optimization problems whose feasible set $\mathbf K$ is defined by a polynomial matrix inequality (PMI). And robust stability regions of linear systems can be modeled as parametrized polynomial matrix inequalities (PMIs) where parameters $\mathbf u$ account for uncertainties and (decision) variables x are the controller coefficients. Therefore, to solve such problems one needs tractable characterizations of polynomials (and even semi-algebraic functions) which are nonnegative on a set, a topic of independent interest and of primary importance because it also has implications in many other areas. We will review two kinds of tractable characterizations of polynomials which are non-negative on a basic closed semi-algebraic set $\mathbf K\subset\mathbb R^n$. The first type of characterization is when knowledge on $\mathbf K$ is through its defining polynomials, i.e., $\mathbf K=\{\mathbf x:g_j(\mathbf x)\geq 0, j =1,\dots, m\}$, in which case some powerful certificates of positivity can be stated in terms of some sums of squares (SOS)-weighted representation. For instance, this allows to define a hierarchy fo semidefinite relaxations which yields a monotone sequence of lower bounds converging to $f^\ast$ (and in fact, finite convergence is generic). There is also another way of looking at nonnegativity where now knowledge on $\mathbf K$ is through moments of a measure whose support is $\mathbf K$. In this case, checking whether a polynomial is nonnegative on $\mathbf K$ reduces to solving a sequence of generalized eigenvalue problems associated with a count- able (nested) family of real symmetric matrices of increasing size. When applied to $\mathbf P$, this results in a monotone sequence of upper bounds converging to the global minimum, which complements the previous sequence of upper bounds. These two (dual) characterizations provide convex inner (resp. outer) approximations (by spectrahedra) of the convex cone of polynomials nonnegative on $\mathbf K$. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Hamish Waterer, School of Mathematical and Physical Sciences, The University of Newcastle Title: A Bucket-Indexed Formulation for Nonpreemptive Single Machine Scheduling Problems Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 17th Sep 2013 Abstract: An exact bucket indexed (BI) mixed integer linear programming formulation for nonpreemptive single machine scheduling problems is presented that is a result of an ongoing investigation into strategies to model time in planning applications with greater efficacy. The BI model is a generalisation of the classical time indexed (TI) model to one in which at most two jobs can be processing in each time period. The planning horizon is divided into periods of equal length, but unlike the TI model, the length of a period is a parameter of the model and can be chosen to be as long as the processing time of the shortest job. The two models are equivalent if the problem data are integer and a period is of unit length, but when longer periods are used in the BI model, it can have significantly fewer variables and nonzeros than the TI model at the expense of a greater number of constraints. A computational study using weighted tardiness instances reveals the BI model significantly outperforms the TI model on instances where the mean processing time of the jobs is large and the range of processing times is small, that is, the processing times are clustered rather than dispersed. Joint work with Natashia Boland and Riley Clement. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Mumtaz Hussain, CARMA, The University of Newcastle Title: Measure theoretic results for small linear forms Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 10th Sep 2013 Abstract: I will talk about the metrical theory of Diophantine approximation associated with linear forms that are simultaneously small in terms of absolute value rather than the classical nearest integer norm. In other words, we consider linear forms which are simultaneously close to the origin. A complete Khintchine-Groshev type theorem for monotonic approximating functions is established within the absolute value setup. Furthermore, the Hausdorff measure generalization of the Khintchine-Groshev type theorem is obtained. As a consequence we obtain the complete Hausdorff dimension theory. Staying within the absolute value setup, we prove that the corresponding set of badly approximable vectors is of full dimension. [Permanent event link] CARMA OANT SEMINAR Speaker: Prof Wadim Zudilin, CARMA, The University of Newcastle Title: Mock theta functions Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 3rd Sep 2013 Abstract: In his deathbed letter to G.H. Hardy, Ramanujan gave a vague definition of a mock modular function: at each root of unity its asymptotics matches the one of a modular form, though a choice of the modular function depends on the root of unity. Recently Folsom, Ono and Rhoades have proved an elegant result about the match for a general family related to Dyson’s rank (mock theta) function and the Andrews—Garvan crank (modular) function. In my talk I will outline some heuristics and elementary ingredients of the proof. [Permanent event link] CARMA OANT SEMINAR Speaker: Prof Frank Garvan, University of Florida Title: Dyson's Rank Function and Andrews's SPT Function. Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 20th Aug 2013 Abstract: Let spt(n) denote the number of smallest parts in the partitions of n. In 2008, Andrews found surprising congruences for the spt-function mod 5, 7 and 13. We discuss new congruences for spt(n) mod powers of 2. We give new generating function identities for the spt-function and Dyson's rank function. Recently with Andrews and Liang we found a spt-crank function that explains Andrews spt-congruences mod 5 and 7. We extend these results by finding spt-cranks for various overpartition-spt-functions of Ahlgren, Bringmann, Lovejoy and Osburn. This most recent work is joint with Chris Jennings-Shaffer. [Permanent event link] CARMA OANT SEMINAR Speaker: Assoc. Prof. Brailey Sims, CARMA, The University of Newcastle Title: Projections in geodesic metric spaces - Part II Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 13th Aug 2013 Abstract: The feasibility problem associated with nonempty closed convex sets $A$ and $B$ is to find some $x\in A \cap B$. Projection algorithms in general aim to compute such a point. These algorithms play key roles in optimization and have many applications outside mathematics - for example in medical imaging. Until recently convergence results were only available in the setting of linear spaces (more particularly, Hilbert spaces) and where the two sets are closed and convex. The extension into geodesic metric spaces allows their use in spaces where there is no natural linear structure, which is the case for instance in tree spaces, state spaces, phylogenomics and configuration spaces for robotic movements. After reviewing the pertinent aspects of CAT(0) spaces introduced in Part I, including results for von Neumann's alternating projection method, we will focus on the Douglas-Rachford algorithm, in CAT(0) spaces. Two situations arise; spaces with constant curvature and those with non-constant curvature. A prototypical space of the later kind will be introduced and the behavior of the Douglas-Rachford algorithm within it examined. [Permanent event link] CARMA OANT SEMINAR Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle Title: Variational analysis in the presence of symmetry (Part II) Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 6th Aug 2013 Abstract: I will discuss Symmetric criticality and the Mountain pass lemma. I will provide the needed background for anyone who did not come to Part 1. This talk is available at http://carma.newcastle.edu.au/jon/symva-talk.pdf and the related paper is at http://carma.newcastle.edu.au/jon/symmetry.pdf. It has recently appeared in Advances in Nonlinear Analysis. [Permanent event link] CARMA OANT SEMINAR Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle Title: Variational analysis in the presence of symmetry (Part I) Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 30th Jul 2013 Abstract: I will report on work I performed with Jim Zhu over the past three years on how to exploit different forms of symmetry in variational analysis. Various open problems will be flagged. This talk is available at http://carma.newcastle.edu.au/jon/symva-talk.pdf and the related paper is at http://carma.newcastle.edu.au/jon/symmetry.pdf. It has recently appeared in Advances in Nonlinear Analysis. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Vera Roshchina, Collaborative Research Network, The University of Ballarat Title: Preconditioners for systems of linear inequalities Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:30 pm, Mon, 15th Jul 2013 Abstract: We show that a combination of two simple preprocessing steps would generally improve the conditioning of a homogeneous system of linear inequalities. Our approach is based on a comparison among three different notions of condition numbers for linear inequalities. The talk is based on a joint work with Javier Peña and Negar Soheili (Carnegie-Mellon University). [Permanent event link] CARMA OANT SEMINAR Speaker: Assoc. Prof. Brailey Sims, CARMA, The University of Newcastle Title: Projections in geodesic metric spaces - Part I Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:30 pm, Mon, 1st Jul 2013 Abstract: Geodesic metric spaces provide a setting in which we can develop much of nonlinear, and in particular convex, analysis in the absence of any natural linear structure. For instance, in a state space it often makes sense to speak of the distance between two states, or even a chain of connecting intermediate states, whereas the addition of two states makes no sense at all. We will survey the basic theory of geodesic metric spaces, and in particular Gromov's so called CAT($\kappa$) spaces. And if there is time (otherwise in a later talk), we will examine some recent results concerning alternating projection type methods, principally the Douglas--Rachford algorithm, for solving the two set feasibility problem in such spaces. [Permanent event link] CARMA OANT SEMINAR Speaker: Prof Miguel Ángel Goberna Torrent, Departamento de Estadística e Investigación Operativa, University of Alicante Title: Voronoi cells of arbitrary sets Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 3:30 pm, Mon, 24th Jun 2013 Abstract: Given a set T of the Euclidean space, whose elements are called sites, and a particular site s, the Voronoi cell of s is the set formed by all points closer to s than to any other site. The Voronoi diagram of T is the family of Voronoi cells of all the elements of T. In this talk we show some applications of the Voronoi diagrams of finite and infinite sets and analyze direct and inverse problems concerning the cells. We also discuss the stability of the cells under different types of perturbations and the effect of assigning weights to the sites. [Permanent event link] CARMA OANT SEMINAR Speaker: Prof Jörg Fliege, CORMSIS, University of Southampton Title: Optimisation in Space: Problems in Spacecraft Trajectory Optimization Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 11:00 am, Tue, 18th Jun 2013 Abstract: In trajectory optimization, the optimal path of a flight system or a group of flight systems is searched for, often in an interplanetary setting: we are in search of trajectories for one or more spacecrafts. On the one hand, this is a well-developed field of research, in which commercial software packages are already available for various scenarios. On the other hand, the computation of such trajectories can be rather demanding, especially when low-thrust missions with long travel times (e.g., years) are considered. Such missions invariably involve gravitational slingshot maneuvers at various celestial bodies in order to save propellant or time. Such maneuvers involve vastly different time scales: years of coasting can be followed by course corrections on a daily basis. In this talk, we give an overview over trajectory optimization for space vehicles and highlight some recent algorithmic developments. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Liangjin Yao, CARMA, The University of Newcastle Title: Analysis of the convergence rate for the cyclic projection algorithm applied to semi-algebraic convex sets Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:30 pm, Mon, 3rd Jun 2013 Abstract: In this talk, we study the rate of convergence of the cyclic projection algorithm applied to finitely many semi-algebraic convex sets. We establish an explicit convergence rate estimate which relies on the maximum degree of the polynomials that generate the semi-algebraic convex sets and the dimension of the underlying space. We achieve our results by exploiting the algebraic structure of the semi-algebraic convex sets. This is the joint work with Jon Borwein and Guoyin Li. [Permanent event link] CARMA OANT SEMINAR Speaker: Matt Skerritt, School of Mathematical and Physical Sciences, The University of Newcastle Title: Computation of an Improved Lower Bound to Giuga’s Primality Conjecture Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:30 pm, Mon, 27th May 2013 Abstract: Our most recent computations tell us that any counterexample to Giuga’s 1950 primality conjecture must have at least 19,907 digits. Equivalently, any number which is both a Giuga and a Carmichael number must have at least 19,907 digits. This bound has not been achieved through exhaustive testing of all numbers with up to 19,907 digits, but rather through exploitation of the properties of Giuga and Carmichael numbers. We introduce the conjecture and an algorithm for finding lower bounds to a counterexample, then present our recent results and discuss challenges to further computation. [Permanent event link] CARMA OANT SEMINAR Speaker: Mr Matthew Tam, School of Mathematical and Physical Sciences, The University of Newcastle Title: Cyclic Douglas-Rachford Iterations Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:30 pm, Mon, 20th May 2013 Abstract: In this talk we introduce a Douglas-Rachford inspired projection algorithm, the cyclic Douglas-Rachford iteration scheme. We show, unlike the classical Douglas-Rachford scheme, that the method can be applied directly to convex feasibility problems in Hilbert space without recourse to a product space formulation. Initial results, from numerical experiments comparing our methods to the classical Douglas-Rachford scheme, are promising. This is joint work with Prof. Jonathan Borwein. [Permanent event link] CARMA OANT SEMINAR Speaker: Assoc Prof Regina Burachik, University of South Australia Title: Conditions for zero duality gap in convex programming Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 3:30 pm, Mon, 13th May 2013 Abstract: We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is weaker than all existing constraint qualifications, including the closed epigraph condition. Our dual condition was inspired by, and is weaker than, the so-called Bertsekas’ condition for monotropic programming problems. We give several corollaries of our result and special cases as applications. We pay special attention to the polyhedral and sublinear cases, and their implications in convex optimization. This research is a joint work with Jonathan M. Borwein and Liangjin Yao. [Permanent event link] CARMA OANT SEMINAR Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle Title: Best approximation in reflexive Banach space (Part IV) Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:30 pm, Mon, 22nd Apr 2013 Abstract: I will survey what is known and some of the open questions. [Permanent event link] CARMA OANT SEMINAR Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle Title: Best approximation in reflexive Banach space (Part III) Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:30 pm, Mon, 15th Apr 2013 Abstract: I will survey what is known and some of the open questions. [Permanent event link] CARMA OANT SEMINAR Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle Title: Best approximation in reflexive Banach space (Part II) Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:30 pm, Mon, 8th Apr 2013 Abstract: I will survey what is known and some of the open questions. [Permanent event link] CARMA OANT SEMINAR Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle Title: Best approximation in reflexive Banach space (Part I) Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:30 pm, Mon, 25th Mar 2013 Abstract: I will survey what is known and some of the open questions. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Yoshitaka Sasaki, Osaka University of Health and Sport Sciences Title: On poly-Euler numbers and the related L-function Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 4th Mar 2013 Abstract: In 1997, Kaneko introduced the poly-Bernoulli number. Poly-Euler numbers are introduced as a generalization of the Euler numbers in a manner similar to the introduction of the poly-Bernoulli numbers. In my talk, some properties of poly-Euler numbers, for example, explicit formulas, sign change, Clausen-von Staudt type formula, combinatorial interpretations and so on are showed. This research is a joint work with Yasuo Ohno. [Permanent event link] CARMA OANT SEMINAR Speaker: Mr Michael Rose, School of Mathematical and Physical Sciences, The University of Newcastle Title: Expectations on Fractal Sets Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 3rd Dec 2012 Abstract: Motivated by laboratory studies on the distribution of brain synapses, the classical theory of box integrals - being expectations on unit hypercubes - is extended to a new class of fractal "string-generated Cantor sets" that facilitate fine-tuning of their fractal dimension through a suitable choice of generating string. Closed forms for certain statistical moments on these fractal sets will be presented, together with a precision algorithm for higher embedding dimensions. This is based on joint work with Laur. Prof. Jon Borwein, Prof. David Bailey and Dr. Richard Crandall. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Victoria Martín-Márquez, Department of Mathematical Analysis, Universidad de Sevilla Title: Right Bregman nonexpansive operators in Banach spaces Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 26th Nov 2012 Abstract: Nonexpansive operators in Banach spaces are of utmost importance in Nonlinear Analysis and Optimization Theory. We are concerned in this talk with classes of operators which are, in some sense, nonexpansive not with respect to the norm, but with respect to Bregman distances. Since these distances are not symmetric in general, it seems natural to distinguish between left and right Bregman nonexpansive operators. Some left classes have already been studied quite intensively, so this talk is mainly devoted to right Bregman nonexpansive operators and the relationship between both classes. This talk is based on joint works with Prof. Simeon Reich and Shoham Sabach from Technion-Israel Institute of Technology, Haifa. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr David Harvey, University of NSW Title: Counting points on hyperelliptic curves Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 19th Nov 2012 Abstract: I will discuss a new algorithm for counting points on hyperelliptic curves over finite fields. [Permanent event link] CARMA OANT SEMINAR Speaker: Matt Skerritt, School of Mathematical and Physical Sciences, The University of Newcastle Title: Computing a Counterexample to Giuga's Conjecture Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 12th Nov 2012 Abstract: Giuga's conjecture will be introduced, and we will discuss what's changed in the computation of a counterexample in the last 17 years. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr C. Yalcin Kaya, University of South Australia Title: Finding interpolating curves using optimal control Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 3:00 pm, Mon, 5th Nov 2012 Abstract: We study the problem of finding an interpolating curve passing through prescribed points in the Euclidean space. The interpolating curve minimizes the pointwise maximum length, i.e., L∞-norm, of its acceleration. We re-formulate the problem as an optimal control problem and employ simple but effective tools of optimal control theory. We characterize solutions associated with singular (of infinite order) and nonsingular controls. We reduce the infinite dimensional interpolation problem to an ensuing finite dimensional one and derive closed form expressions for interpolating curves. Consequently we devise numerical techniques for finding interpolating curves and illustrate these techniques on examples. [Permanent event link] CARMA OANT SEMINAR Speaker: Prof Wadim Zudilin, CARMA, The University of Newcastle Title: Legendre polynomials squared Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 29th Oct 2012 Abstract: We discuss how the title is related to π. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Francisco Aragón Artacho, CARMA, The University of Newcastle Title: Walking on real numbers Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 22nd Oct 2012 Abstract: Motivated by the desire to visualise large mathematical data sets, especially in number theory, we offer various tools for representing floating point numbers as planar walks and for quantitatively measuring their “randomness”. What to expect: some interesting ideas, many beautiful pictures (including a 108-gigapixel picture of π), and some easy-to-understand maths. What you won’t get: too many equations, difficult proofs, or any “real walking”. This is a joint work with David Bailey, Jon Borwein and Peter Borwein. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Michael Coons, CARMA, The University of Newcastle Title: The rational-transcendental dichotomy of Mahler functions Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 15th Oct 2012 Abstract: In this talk, we will show that a D-finite Mahler function is necessarily rational. This gives a new proof of the rational-transcendental dichotomy of Mahler functions due to Nishioka. Using our method of proof, we also provide a new proof of a Pólya-Carlson type result for Mahler functions due to Randé; that is, a Mahler function which is meromorphic in the unit disk is either rational or has the unit circle as a natural boundary. This is joint work with Jason Bell and Eric Rowland. [Permanent event link] CARMA OANT SEMINAR Speaker: Timothy Trudgian, Australian National University Title: By how much does Mertens' conjecture fail? Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 8th Oct 2012 Abstract: If some arithmetical sums are small then the complex zeroes of the zeta-function are linearly dependent. Since we don't believe the conclusion we ought not to believe the premise. I will show that the zeroes are 'almost linearly independent' which implies, in particular, that the Mertens conjecture fails more drastically than was previously known. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Mike Meylan, CARMA, The University of Newcastle Title: Linear Water Waves in the Time-Domain Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 17th Sep 2012 Abstract: Linear Water Wave theory is one of the most important branches on fluid mechanics. Practically it underpins most of the engineering design of ships, offshore structures, etc. It also has a very rich history in the development of applied mathematics. In this talk I will focus on the connection between solutions in the frequency and time-domains and show how we can use various formulations to make numerical calculations and to construct approximate solutions. I will illustrate these methods with application to some simple wave scattering problems. [Permanent event link] CARMA OANT SEMINAR Speaker: Dr Liangjin Yao, CARMA, The University of Newcastle Title: Legendre-type integrands and convex integral functions Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 10th Sep 2012 Abstract: In this talk, we study the properties of integral functionals induced on $L_\text{E}^1(S,\mu)$ by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and give various limiting counter-example. This is joint work with Jon Borwein. [Permanent event link] CARMA OANT SEMINAR Speaker: Prof David Bailey, Berkeley, California Title: Hand to hand combat with thousand-digit integrals Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 3rd Sep 2012 Abstract: A frequent theme of 21st century experimental math is the computer discovery of identities, typically done by means of computing some mathematical entity (a sum, limit, integral, etc) to very high numeric precision, then using the PSLQ algorithm to identify the entity in terms of well known constants. Perhaps the most successful application of this methodology has been to identify integrals arising in mathematical physics. This talk will present numerous examples of this type, including integrals from quantum field theory, Ising theory, random walks, 3D lattice problems, and even mouse brains. In some cases, it is necessary to compute these integrals to 3000-digit precision, and developing techniques to do such computations is a daunting technical challenge. [Permanent event link]