# CARMA Retreat

## 9:00 am — 6:00 pm

## Saturday, 5^{th} Sep 2015

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

# PhD Confirmation Seminar

## 12:00 pm

## Monday, 7^{th} Sep 2015

**V205, Mathematics Building**

# Dushyant Tanna

(School of Mathematical and Physical Sciences, The University of Newcastle)*Graph Labeling and Applications*

**Supervisors:** Mirka Miller, Joe Ryan and Andrea Semanicova-Fenovcikova

We give some background to the labeling schemes like *graceful*, *harmonious*, *magic*, *antimagic* and *irregular total labeling*. Then we will describe why study of graph labeling is important by narrating some applications of graph labeling. Next we will briefly describe the methodology like Robert's construction to obtain completing separating systems (CSS) which will help us to determine the antimagic labeling of graphs and Alon's Combinatorial Nullstellensatz. We will illustrate an example from many applications of graphs labelling. Finally we will introduce reflexive irregular total labelling and explain its importance. To conclude, we add research plan and time line during candidature of research.

# CARMA Colloquium

## 4:00 pm

## Thursday, 10^{th} Sep 2015

**V205, Mathematics Building**

# Alan Haynes

(University of York)*Quasicrystals and Diophantine approximation*

In this talk we will begin with a brief history of the mathematics of aperiodic tilings of Euclidean space, highlighting their relevance to the theory of quasicrystals. Next we will focus on an important collection of point sets, cut and project sets, which come from a dynamical construction and provide us with a mathematical model for quasicrystals. After giving definitions and examples of these sets, we will discuss their relationship with Diophantine approximation, and show how the interplay between these two subjects has recently led to new results in both of them.

# CARMA Seminar

## 2:00 pm

## Monday, 14^{th} Sep 2015

**V205, Mathematics Building**

# Prof Richard Brent

(CARMA, The University of Newcastle)*Some Identities involving Products of Gamma Functions: a Case Study in Experimental Mathematics*

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

# The Undergraduate Talks in Mathematics

## 9:00 am

## Tuesday, 15^{th} Sep 2015

**,**

# Mr Matthew Tam

(School of Mathematical and Physical Sciences, The University of Newcastle)*How to Differentiate Non-Differentiable Functions*

# CARMA and AMSI Conference

*Number Theory Down Under*

## Friday, 18^{th} Sep 2015 — Saturday, 19^{th} Sep 2015

**VG01, Mathematics Building**

For more information, please visit the conference website.

# CARMA Seminar

## 4:00 pm

## Thursday, 24^{th} Sep 2015

**V205, Mathematics Building**

# Dr Björn Rüffer

(CARMA, The University of Newcastle)*tba*

# CARMA Number Theory Seminar

## 3:00 pm

## Tuesday, 20^{th} Oct 2015

**V205, Mathematics Building**

Details to be confirmed.

# Dr Faustin Adiceam

(University of York)*Rational approximation and arithmetic progressions*

We discuss problems of approximation of an irrational by rationals whose numerators and denominators lie in prescribed arithmetic progressions. Results are both, on the one hand, from a metrical and a non-metrical point of view, and on the other, from an asymptotic and also a uniform point of view. The principal novelty of this theory is a Khintchine-type theorem for uniform approximation in this setup. Time permitting some applications of this work will be discussed.

# CARMA Colloquium

## 4:00 pm

## Thursday, 22^{nd} Oct 2015

**V205, Mathematics Building**

# Dr Faustin Adiceam

(University of York)*How far can you see in a forest?*

We will be answering the following question raised by Christopher Bishop:

'Suppose we stand in a forest with tree trunks of radius $r > 0$ and no two trees centered closer than unit distance apart. Can the trees be arranged so that we can never see further than some distance $V < \infty$, no matter where we stand and what direction we look in? What is the size of $V$ in terms of $r$?'

The methods used to study this problem involve Fourier analysis and sharp estimates of exponential sums.

# CARMA Seminar

## 4:00 pm

## Friday, 23^{rd} Oct 2015

**V205, Mathematics Building**

# Michael Schonlein

(Universität Würzburg)*tba*

# CARMA Workshop

*ANZAMP Satellite Meeting: Tony Guttman at 70*

## Monday, 7^{th} Dec 2015 — Tuesday, 8^{th} Dec 2015

**Noah's On the Beach**[Newcastle, NSW]

Information about this meeting is available at www.guttmann2015.org.

# CARMA Conference

*ANZAMP 2015*

## Wednesday, 9^{th} Dec 2015 — Friday, 11^{th} Dec 2015

**Noah's On the Beach**[Newcastle, NSW]

Information about the meeting is available on the meeting website.