Priority Research Centre for Computer-AssistedResearch Mathematics and its Applications
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## Upcoming CARMA Events

 THE UNDERGRADUATE TALKS IN MATHEMATICS Speaker: Dr Murray Elder, CARMA, The University of Newcastle Title: Solving Equations in Free Groups Location: V104, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 12:00 pm, Tue, 28th Apr 2015 Abstract: I will explain what an equation in a free group is, why they are interesting, and how to solve them. The talk will be accessible to anyone interested in maths or computer science or logic. [Permanent link] CARMA DISCRETE MATHEMATICS SEMINAR Speaker: Paul Leopardi, Title: Twin bent functions, Cayley graphs, and Radon-Hurwitz theory Location: VG25, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 1:00 pm, Wed, 29th Apr 2015 Abstract: I have recently [2] shown that each group $Z_2^{2m}$ gives rise to a pair of bent functions with disjoint support, whose Cayley graphs are a disjoint pair of strongly regular graphs $\Delta_m[-1]$, $\Delta_m[1]$ on $4^m$ vertices. The two strongly regular graphs are twins in the sense that they have the same parameters $(\nu, k, \lambda, \mu)$. For $m < 4$, the two strongly regular graphs are isomorphic. For $m \geq 4$, they are not isomorphic, because the size of the largest clique differs. In particular, the largest clique size of $\Delta_m[-1]$ is $\rho(2^m)$ and the largest clique in $\Delta_m[1]$ has size at least $2^m$, where $\rho(n)$ is the Hurwitz-Radon function. This non-isomorphism result disproves a number of conjectures that I made in a paper on constructions of Hadamard matrices [1]. [1] Paul Leopardi, "Constructions for Hadamard matrices, Clifford algebras, and their relation to amicability - anti-amicability graphs", Australasian Journal of Combinatorics, Volume 58(2) (2014), pp. 214–248. [2] Paul Leopardi, "Twin bent functions and Clifford algebras", accepted 13 January 2015 by the Springer Proceedings in Mathematics and Statistics (PROMS): Algebraic Design Theory and Hadamard Matrices (ADTHM 2014). [Permanent link] HONOURS SEMINARS Location: V205, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 4:00 pm, Thu, 30th Apr 2015 Our honours students will present the problems that they are working on, progress and plan for the rest of the year, in 15-minute talks. Speaker: Geoffrey Lee Title: EDT0L languages, word problems and multiplication tables for finitely generated groups Abstract:      Supervisor: Murray Elder Speaker: Riordan Dose Title: Waves and Stretchy Things: Modelling Mechanical Metamaterials Abstract:      Supervisor: Mike Meylan Speaker: Milutin Brankovic Title: Mahler Measures and Convex Lattice Polygons Abstract:      Supervisor: Wadim Zudulin [Permanent link] CARMA WORKSHOP Newcastle Maths Educators Conference Location: , The Great Hall, The University of Newcastle (Callaghan), The University of Newcastle Dates: 9:00 am - 5:00 pm, Fri, 1st May 2015 A conference to initiate a mathematics community that supports educators across the Hunter region at all levels. More details are available on the conference webpage. [Permanent link] CARMA RHD MEETING Speaker: Mr Daniel Sutherland, CARMA, The University of Newcastle Title: Arithmetic Applications of Hankel Determinants Location: V205, Mathematics Building (Callaghan), The University of Newcastle Dates: 1:00 pm - 3:00 pm, Tue, 5th May 2015 Abstract: In this talk I will present the main results of my PhD thesis (by the same name), which focuses on the application of matrix determinants as a means of producing number-theoretic results. Motivated by an investigation of properties of the Riemann zeta function, we examine the growth rate of certain determinants of zeta values. We begin with a generalisation of determinants based on the Hurwitz zeta function, where we describe the arithmetic properties of its denominator and establish an asymptotic bound. We later employ a determinant identity to bound the growth of positive Hankel determinants. Noting the positivity of determinants of Dirichlet series allows us to prove specific bounds on determinants of zeta values in particular, and of Dirichlet series in general. Our results are shown to be the best that can be obtained from our method of bounding, and we conjecture a slight improvement could be obtained from an adjustment to our specific approach. Within the course of this investigation we also consider possible geometric properties which are necessary for the positivity of Hankel determinants, and we examine the role of Hankel determinants in irrationality proofs via their connection with Padé approximation. [Permanent link] CARMA AND AMSI LECTURE SERIES Mathematical Logic and Philosophy Location: V206, Mathematics Building (Callaghan), The University of Newcastle Dates: 2:00 pm - 4:00 pm, 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. [Permanent link] CARMA RHD MEETING Speaker: Laureate Prof Jon Borwein, CARMA, The University of Newcastle Title: The 2010 Flash crash Location: V205, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 1:00 pm, Tue, 12th May 2015 [Permanent link] CARMA COLLOQUIUM Speaker: Michael Whittaker , University of Wollongong Title: Fractal substitution tilings and applications to noncommutative geometry Location: V205, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 4:00 pm, Thu, 14th May 2015 Abstract: Starting with a substitution tiling, such as the Penrose tiling, we demonstrate a method for constructing infinitely many new substitution tilings. Each of these new tilings is derived from a graph iterated function system and the tiles typically have fractal boundary. As an application of fractal tilings, we construct an odd spectral triple on a C*-algebra associated with an aperiodic substitution tiling. Even though spectral triples on substitution tilings have been extremely well studied in the last 25 years, our construction produces the first truly noncommutative spectral triple associated with a tiling. My work on fractal substitution tilings is joint with Natalie Frank and Sam Webster, and my work on spectral triples is joint with Michael Mampusti. [Permanent link] CARMA AND AMSI LECTURE SERIES Mathematical Logic and Philosophy Location: V206, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 2:00 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. [Permanent link] CARMA RHD MEETING Location: V205, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 1:00 pm, Tue, 19th May 2015 [Permanent link] CARMA AND AMSI LECTURE SERIES Mathematical Logic and Philosophy Location: V206, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 2:00 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. [Permanent link] CARMA RHD MEETING Location: V205, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 1:00 pm, Tue, 26th May 2015 [Permanent link] CARMA RHD MEETING Location: V205, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 1:00 pm, Tue, 2nd Jun 2015 [Permanent link] CARMA RHD MEETING Location: V205, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 1:00 pm, Tue, 9th Jun 2015 [Permanent link] CARMA RHD MEETING Location: V205, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 1:00 pm, Tue, 16th Jun 2015 [Permanent link] CARMA WORKSHOP Mathematics and Computation Location: V205, Mathematics Building (Callaghan), The University of Newcastle Dates: Fri, 19th Jun 2015 - Sun, 21st Jun 2015 More information is available on the workshop website. [Permanent link] CARMA RHD MEETING Location: V205, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 1:00 pm, Tue, 23rd Jun 2015 [Permanent link] CARMA RHD MEETING Location: V205, Mathematics Building (Callaghan), The University of Newcastle Time and Date: 1:00 pm, Tue, 30th Jun 2015 [Permanent link] CARMA WORKSHOP Celebration for Brailey Sims Location: CARMA, Mathematics Building (Callaghan), The University of Newcastle Dates: 9:00 am - 5:00 pm, Fri, 21st Aug 2015 For more details please visit the workshop website. [Permanent link] CARMA AND AMSI CONFERENCE Number Theory Down Under Location: VG01, Mathematics Building (Callaghan), The University of Newcastle Dates: Fri, 18th Sep 2015 - Sat, 19th Sep 2015 For more information, please visit the conference website. [Permanent link] CARMA CONFERENCE ANZAMP 2015 Location: TBAThe University of Newcastle Dates: Wed, 9th Dec 2015 - Fri, 11th Dec 2015 More details will be added closer to the event. [Permanent link] CARMA WORKSHOP ANZAMP Satellite Meeting Location: Dates: 9:00 am - 5:00 pm, Sat, 12th Dec 2015 Details will be available closer to the event. [Permanent link]

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