# CARMA OANT Seminar

## Monday, 27th Apr 2015

V205, Mathematics Building

# Assoc Prof Regina Burachik

(University of South Australia)

# An additive subfamily of enlargements of a maximally monotone Operator

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).

# The Undergraduate Talks in Mathematics

## Tuesday, 28th Apr 2015

V104, Mathematics Building

# Dr Murray Elder

(CARMA, The University of Newcastle)

# Solving Equations in Free Groups

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.

# Honours Seminars

## Thursday, 30th Apr 2015

V205, Mathematics Building

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. Speakers: Geoff Lee, Riordan Dose, Milutin Brankovic.

# Newcastle Maths Educators Conference

## Friday, 1st May 2015

The Great Hall, The University of Newcastle

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.

# CARMA RHD Meeting

## Tuesday, 5th May 2015

V205, Mathematics Building

# Mr Daniel Sutherland

(CARMA, The University of Newcastle)

# Arithmetic Applications of Hankel Determinants

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.

# Mathematical Logic and Philosophy

## Friday, 8th May 2015

V206, Mathematics Building

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.

[SeeVogh]

# CARMA RHD Meeting

## Tuesday, 12th May 2015

V205, Mathematics Building

# Laureate Prof Jon Borwein

(CARMA, The University of Newcastle)

# Mathematical Logic and Philosophy

## Friday, 15th May 2015

V206, Mathematics Building

Four lectures by Professor Jeremy Avigad (Department of Philosophy and the Department of Mathematical Sciences, Carnegie Mellon University). This is the third lecture.

[SeeVogh]

# CARMA RHD Meeting

## Tuesday, 19th May 2015

V205, Mathematics Building

# Mathematical Logic and Philosophy

## Friday, 22nd May 2015

V206, Mathematics Building

Four lectures by Professor Jeremy Avigad (Department of Philosophy and the Department of Mathematical Sciences, Carnegie Mellon University). This is the fourth lecture.

[SeeVogh]

# CARMA RHD Meeting

## Tuesday, 26th May 2015

V205, Mathematics Building

# CARMA RHD Meeting

## Tuesday, 2nd Jun 2015

V205, Mathematics Building

# CARMA RHD Meeting

## Tuesday, 9th Jun 2015

V205, Mathematics Building

# CARMA RHD Meeting

## Tuesday, 16th Jun 2015

V205, Mathematics Building

# Mathematics and Computation

## Friday, 19th Jun 2015 — Sunday, 21st Jun 2015

V205, Mathematics Building

# CARMA RHD Meeting

## Tuesday, 23rd Jun 2015

V205, Mathematics Building

# CARMA RHD Meeting

## Tuesday, 30th Jun 2015

V205, Mathematics Building

# Celebration for Brailey Sims

## Friday, 21st Aug 2015

CARMA, Mathematics Building

For more details please visit the workshop website.

# Number Theory Down Under

## Friday, 18th Sep 2015 — Saturday, 19th Sep 2015

VG01, Mathematics Building

# ANZAMP 2015

## Wednesday, 9th Dec 2015 — Friday, 11th Dec 2015

(Location to be decided)

More details will be added closer to the event.