# CARMA OANT Seminar

## Wednesday, 22nd Oct 2014

V205, Mathematics Building

# A/Prof Simon Kristensen

(Aarhus University)

# Diophantine approximation in positive characteristic

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.

# CARMA RHD Meeting

## Thursday, 23rd Oct 2014

V205, Mathematics Building

# CARMA Seminar

## Thursday, 23rd Oct 2014

V205, Mathematics Building

# Nathan Clisby

(The University of Melbourne)

# Monte Carlo simulation of self-avoiding walks

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.

# Number Theory Down Under

## Friday, 24th Oct 2014

Harbourview Function Centre [Newcastle, NSW]

# CARMA Finance Meeting

## Monday, 27th Oct 2014

V205, Mathematics Building

(CARMA, The University of Newcastle)

# CARMA OANT Seminar

## Monday, 27th Oct 2014

V205, Mathematics Building

# Yohei Tachiya

(Graduate School of Science and Technology, Hirosaki University)

# Algebraic independence results for the generating functions of pattern sequences

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.

# Tools for Mathematical Computation

## Tuesday, 28th Oct 2014

V206, Mathematics Building

As part of Jon Borwein's Experimental Mathematics Course, he is exploring the uses of the currently available tools for mathematical computation. Each lecture should be independently accessible, so feel free to drop in.

# CARMA OANT Seminar

## Wednesday, 29th Oct 2014

V205, Mathematics Building

(Department of Mathematical Sciences, Durham University)

# On continued fraction expansion of potential counterexamples to mixed Littlewood conjecture

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.

# CARMA RHD Meeting

## Thursday, 30th Oct 2014

V205, Mathematics Building

# Tools for Mathematical Computation

## Tuesday, 4th Nov 2014

V206, Mathematics Building

As part of Jon Borwein's Experimental Mathematics Course, he is exploring the uses of the currently available tools for mathematical computation. Each lecture should be independently accessible, so feel free to drop in.

# CARMA RHD Meeting

## Thursday, 6th Nov 2014

V205, Mathematics Building

# CARMA RHD Meeting

## Thursday, 13th Nov 2014

V205, Mathematics Building

# CARMA RHD Meeting

## Thursday, 20th Nov 2014

V205, Mathematics Building

# EViMS 2: Effective use of Visualisation in the Mathematical Sciences

## Friday, 21st Nov 2014

[Australian National University]

The Mathematical Sciences Institute will host a three day workshop on more effective use of visualization in mathematics, physics, and statistics, from the perspectives of education, research and outreach. This is the second EViMS meeting, following the highly successful one held in Newcastle in November 2012. Our aim for the workshop is to help mathematical scientists understand the opportunities, risks and benefits of visualization, in research and education, in a world where visual content and new methods are becoming ubiquitous.

# New Directions in Fractal Geometry

## Sunday, 23rd Nov 2014

[Australian National University]

This conference will cover some emerging hot topics in Fractal Geometry and will stimulate collaboration between theory and applications. Details are available on the conference website.

# CARMA RHD Meeting

## Thursday, 27th Nov 2014

V205, Mathematics Building

# CARMA RHD Meeting

## Thursday, 4th Dec 2014

V205, Mathematics Building

# 2014 ANZAMP annual meeting

## Monday, 8th Dec 2014

[The University of Melbourne]

The annual meeting of the Australian and New Zealand Association of Mathematical Physics will be incorporated into the 8th Australia New Zealand Mathematics Convention at the University of Melbourne. For details, please visit the convention website.

# CARMA RHD Meeting

## Thursday, 11th Dec 2014

V205, Mathematics Building

# CARMA RHD Meeting

## Thursday, 18th Dec 2014

V205, Mathematics Building

# AMSI Summer School in the Mathematical Sciences

## Saturday, 3rd Jan 2015

Details will be available later.

# 2015 AMSI Summer School

## Monday, 5th Jan 2015

The AMSI Summer School is an exciting opportunity for mathematical sciences students from around Australia to come together over the summer break to develop their skills and networks. Further details are available on AMSI's website.

# HMEC: Hunter Maths Educators Conference

## Friday, 6th Feb 2015

Mathematics Building

Details will be available on the conference webpage.

# SPCOM 2015: South Pacific Continuous Optimization Meeting

## Sunday, 8th Feb 2015

[University of South Australia]

SPCOM 2015 will offer a rich scientific program consisting of Conference Talks, a Fitzpatrick Workshop, two half-day Tutorials, and a Poster Session. Further details and a list of speakers are available on the conference website.

# Spring School on Variational Analysis VI

## Sunday, 19th Apr 2015

Ffollowing a longstanding tradition, the Faculty of Mathematics and Physics of Charles University in Prague and the Academy of Sciences of the Czech Republic will organize the Spring School on Variational Analysis VI. The School will be held in Paseky nad Jizerou, in a chalet in the Krkonose Mountains, April 19 - 25, 2015. The program will consist of series of lectures on Variational Analysis and its Applications.

The lectures will be given by

• Jonathan M. Borwein (The University of Newcastle, Australia)
Theory and Applications of Convex and Non-convex Feasibility Problems
• Marian Fabian (Academy of Sciences of the Czech Republic)
Separable Reductions and Rich Families in Theory of Frechet Subdifferentials
• Alexander Ioffe (Technion, Haifa, Israel)
Variational Analysis and Optimization Theory
• David Russel Luke (Georg-August-Universitaet Goettingen, Germany)
Variational Methods in Numerical Analysis

Further informations can be found on the website http://www.karlin.mff.cuni.cz/katedry/kma/ss/apr15.

# ANZAMP 2015

## Wednesday, 9th Dec 2015

More details will be added closer to the event.

# ANZAMP Satellite Meeting

## Saturday, 12th Dec 2015

More details will be added closer to the event.