# CARMA OANT Seminar

## 10:00 am

## Wednesday, 22^{nd} 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 Seminar

## 4:00 pm

## Thursday, 23^{rd} 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.

# CARMA and AMSI Conference

*Number Theory Down Under*

## 9:00 am

## Friday, 24^{th} Oct 2014

**Harbourview Function Centre**[Newcastle, NSW]

For more information, please visit the conference website.

# CARMA Finance Meeting

## 1:00 pm

## Monday, 27^{th} Oct 2014

**V205, Mathematics Building**

# (CARMA, The University of Newcastle)

# CARMA OANT Seminar

## 4:00 pm

## Monday, 27^{th} 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

## 10:00 am

## Tuesday, 28^{th} 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

## 10:00 am

## Wednesday, 29^{th} Oct 2014

**V205, Mathematics Building**

# Dr Dzmitry Badziahin

(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.

# Tools for Mathematical Computation

## 10:00 am

## Tuesday, 4^{th} 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.

# AMSI Event

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

## 9:00 am

## Friday, 21^{st} 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.

Visit the conference website for more information.

# Mathematical Sciences Institute Conference

*New Directions in Fractal Geometry*

## 9:00 am

## Sunday, 23^{rd} 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.

# External Event

*2014 ANZAMP annual meeting*

## 9:00 am

## Monday, 8^{th} 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.

# AMSI Event

*AMSI Summer School in the Mathematical Sciences*

## 9:00 am

## Saturday, 3^{rd} Jan 2015

Details will be available later.

# AMSI Event

*2015 AMSI Summer School*

## 9:00 am

## Monday, 5^{th} 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.

# CARMA Workshop

*HMEC: Hunter Maths Educators Conference*

## 9:00 am

## Friday, 6^{th} Feb 2015

**Mathematics Building**

Details will be available on the conference webpage.

# CARMA and UniSA Conference

*SPCOM 2015: South Pacific Continuous Optimization Meeting*

## 9:00 am

## Sunday, 8^{th} 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.

# External Event

*Spring School on Variational Analysis VI*

## 9:00 am

## Sunday, 19^{th} Apr 2015

[Paseky nad Jizerou]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.

# CARMA Conference

*ANZAMP 2015*

## 9:00 am

## Wednesday, 9^{th} Dec 2015

More details will be added closer to the event.

# CARMA Workshop

*ANZAMP Satellite Meeting*

## 9:00 am

## Saturday, 12^{th} Dec 2015

More details will be added closer to the event.