# Prof Zoé Chatzidakis

(Département de Mathématiques et Applications, ENS Paris)

# A new invariant for difference fields

If $(K,f)$ is a difference field, and $a$ is a finite tuple in some difference field extending $K$, and such that $f(a)$ in $K(a)^{\mathrm{alg}}$, then we define $dd(a/K)=lim[K(f^k(a),a):K(a)]^{1/k}$, the distant degree of $a$ over $K$. This is an invariant of the difference field extension $K(a)^{\mathrm{alg}}/K$. We show that there is some $b$ in the difference field generated by $a$ over $K$, which is equi-algebraic with $a$ over $K$, and such that $dd(a/K)=[K(f(b),b):K(b)]$, i.e.: for every $k>0$, $f(b)$ in $K(b,f^k(b))$. Viewing $Aut(K(a)^{\mathrm{alg}}/K)$ as a locally compact group, this result is connected to results of Goerge Willis on scales of automorphisms of locally compact totally disconnected groups. I will explicit the correspondence between the two sets of results. (Joint with E. Hrushovski)

# Dr Laura Ciobanu

(Mathematical and Computer Sciences, Heriot-Watt University)

# Free group homomorphisms and the Post Correspondence Problem

he Post Correspondence Problem (PCP) is a classical problem in computer science that can be stated as: is it decidable whether given two morphisms $g$ and $h$ between two free semigroups $A$ and $B$, there is any nontrivial $x$ in $A$ such that $g(x)=h(x)$? This question can be phrased in terms of equalisers, asked in the context of free groups, and expanded: if the `equaliser' of $g$ and $h$ is defined to be the subgroup consisting of all $x$ where $g(x)=h(x)$, it is natural to wonder not only whether the equaliser is trivial, but what its rank or basis might be. While the PCP for semigroups is famously insoluble and acts as a source of undecidability in many areas of computer science, the PCP for free groups is open, as are the related questions about rank, basis, or further generalisations. However, in this talk we will show that there are links and surprising equivalences between these problems in free groups, and classes of maps for which we can give complete answers. This is joint work with Alan Logan.

# CARMA Colloquium

## Thursday, 22nd Apr 2021

SR118, SR Building (and online via Zoom)

Join via Zoom, or join us in person (max room capacity is 9 people).

3:30pm for pre-talk drinks + snacks, and 4pm for the talk

# Prof Ole Warnaar

(School of Mathematics and Physics, The University of Queensland)

# Cylindric Partitions and Rogers–Ramanujan Identities

Plane partitions are a two-dimensional analogue of integer partitions introduced by MacMahon in the 1890s. Various generating functions for plane partitions admit beautiful product forms, displaying an unexpected connection to the representation theory of classical groups and Lie algebras. Cylindric partitions, defined by Gessel and Krattenthaler in the 1990s, are an affine analogue of plane partitions.

In this talk I will explain what cylindric partitions are, discuss their connection with the representation theory of infinite dimensional Lie algebras, and describe some recent results on Rogers--Ramanujan-type identities arising from the study of cylindric partitions. No knowledge of representation theory will be assumed in this talk.

# CARMA Colloquium

## Thursday, 20th May 2021

(Location to be decided)

Joint presentation with AustMS/AMSI lunchtime seminar series

Join via Zoom

# Emma Zbarsky

(Wentworth Institute of Technology)

# Conversation as Assessment

As educators, we need to assess our students for a variety of reasons from the mundane requirement to submit ranked scores to the arcane desire to encourage and track learning. I have developed my approach to oral examinations for undergraduate students in an attempt to support collaborative analysis of my student's understanding, as well as an opportunity for growth and discovery right up to the final moments of a course. I will present my experiences using oral assessments both alone and in combination with written work in multivariable calculus with mid-level students, in partial differential equations with upper-level students, and in introductory calculus with first-year students.

# Indigenising University Mathematics

## Monday, 20th Sep 2021 — Tuesday, 21st Sep 2021

Birabahn building of the Wollotuka Institute

This national and international two-day symposium will address the pressing challenge of how to Indigenise mathematical practice at Universities, both in education and research. The methodology is of collaboration and sharing of knowledge and worldviews from within both Indigenous cultures and the cultures of mathematics and its allied disciplines.

The symposium will be organised around a collection of interconnected themes, each chaired by a partnership of Indigenous and non-Indigenous practitioners. These include: Indigenous Mathematics, Re-imagining the living present, Traditional Knowledge, Country, Language and Oral Traditions, and Love and Pedagogy. The symposium will also launch a call for contributions to a book on the same topic.

The physical location of this blended face to face and online symposium is significant. The Birabahn building of the Wollotuka Institute blends indoor and outdoor spaces, inviting new perspectives, whilst also having the capabilities for an international video-linked conference.

Speakers:

• Associate Professor Kathryn Butler of the Bundjalung and Worimi people, Director of the Wollotuka Institute, University of Newcastle
• Miss Tammy Small, student advancement manager, Wollotuka Institute, University of Newcastle
• Dr Henry Fowler of the Navajo people, Diné College, Tsaile, Arizona
• Associate Professor Edward Doolittle of the Mohawk people from Six Nations in southern Ontario, First Nations University of Canada
• Mr Dan Collins of the Worimi/Biripi nation, Yapug program convener, Wollotuka Institute, University of Newcastle
• Mr Nathan Towney of the Wiradjuri people from Wellington in NSW, Pro Vice Chancellor Indigenous Strategy and Leadership, University of Newcastle
• Dr Michael Donovan of the Gumbaynggir people, Macquarie University, Australia
• Mr Jade Kennedy, of the Yuin people of the Illawarra and South Coast of NSW, University of Wollongong
• Professor Rowena Ball, ANU
• Professor Mark Maclean, UBC
• Dr Veselin Jungic, Simon Fraser University
• Dr Naomi Borwein, Western Ontario University (ECR)
• Miss Jo-Ann Larkins, Federation University (ECR)
• Miss Amber Hughes, University of Newcastle (ECR)
• Dr Maureen Edwards, Wollongong University