# CARMA Special Semester

*Special Year on Mathematical Communication*

## Wednesday, 1^{st} Jan 2020 — Thursday, 31^{st} Dec 2020

2020 is a Special Year in Mathematics Communication, hosted by the Mathematical Education Research Group in CARMA.

Upcoming events include:

- MISG: 28 Jan – 1 Feb
- MathsCraft: 5 – 7 Mar
- Writing Mathematics proposals for the ARC workshop: TBA
- EVIMS: TBA
- MESIG: December

as well as regular seminars during the teaching semesters. Events and seminars will address the increasing importance of mathematics communication for and amongst a wide range of contexts and audiences, including across disciplines and industries, with the general public, and in education from kindergarten to PhD.

Further information and details of events will appear on the MathsComm web page.

# Public Lecture

*Learning and Engagement at the Intersection of Mathematics and Computing: A Conversation with Celia Hoyles and Richard Noss*

## 5:00 pm — 7:00 pm

## Thursday, 27^{th} Feb 2020

**Harold Lobb Concert Hall, Newcastle Conservatorium**[Newcastle, NSW]

A major change in the educational policy landscape in many countries has been the introduction of computing into the school curriculum, either as part of Mathematics or as a separate subject. This has often happened alongside the establishment of ‘Coding’ in out-of school clubs. In this talk, we will reflect on the situation in England where computing has been a compulsory subject since 2014 for all students from age 7 to 16 years. We will describe the research project, UCL ScratchMaths, designed to introduce students, aged 9-11 years, to both core computational and mathematical ideas. We will discuss the findings of the project, the challenges faced in its implementation and the exciting next steps in the computing/mathematics initiative from a more international perspective.

Please visit the lecture's Eventbrite page for more information **and to register for this free event**.

# Symmetry in Newcastle

## 10:00 am — 4:30 pm

## Friday, 6^{th} Mar 2020

**(Location to be decided)**

**Schedule:**

10.00-11.00: Waltraud Lederle

11.00-11.30: Morning Tea

11.30-12.30: Mark Pengitore

12.30-14.00: Lunch

14.00-15.00: Jeroen Schillewaert

15.00-15.30: Afternoon Tea

15.30-16.00: François Thilmany

10.00-11.00: Waltraud Lederle

11.00-11.30: Morning Tea

11.30-12.30: Mark Pengitore

12.30-14.00: Lunch

14.00-15.00: Jeroen Schillewaert

15.00-15.30: Afternoon Tea

15.30-16.00: François Thilmany

## Senior Lecturer Jeroen Schillewaert

(Department of Mathematics, The University of Auckland)*Fixed points for group actions on $2$-dimensional affine buildings*

We prove a local-to-global result for fixed points of groups acting on $2$-dimensional affine buildings (possibly non-discrete, and not of type $\tilde{G}_{2}$). In the discrete case, our theorem establishes two conjectures by Marquis. (joint work with Koen Struyve and Anne Thomas)

## Dr François Thilmany

(UC Louvain)*Lattices of minimal covolume in $\mathrm{SL}_n$*

A classical result of Siegel asserts that the (2,3,7)-triangle group attains the smallest covolume among lattices of $\mathrm{SL}_2(\mathbb{R})$. In general, given a semisimple Lie group $G$ over some local field $F$, one may ask which lattices in $G$ attain the smallest covolume. A complete answer to this question seems out of reach at the moment; nevertheless, many steps have been made in the last decades. Inspired by Siegel's result, Lubotzky determined that a lattice of minimal covolume in $\mathrm{SL}_2(F)$ with $F=\mathbb{F}_q((t))$ is given by the so-called characteristic $p$ modular group $\mathrm{SL}_2(\mathbb{F}_q[1/t])$. He noted that, in contrast with Siegel’s lattice, the quotient by $\mathrm{SL}_2(\mathbb{F}_q[1/t])$ was not compact, and asked what the typical situation should be: "for a semisimple Lie group over a local field, is a lattice of minimal covolume a cocompact or nonuniform lattice?".

In the talk, we will review some of the known results, and then discuss the case of $\mathrm{SL}_n(\mathbb{R})$ for $n > 2$. It turns out that, up to automorphism, the unique lattice of minimal covolume in $\mathrm{SL}_n(\mathbb{R})$ ($n > 2$) is $\mathrm{SL}_n(\mathbb{Z})$. In particular, it is not uniform, giving a partial answer to Lubotzky’s question in this case.

## Dr Waltraud Lederle

(UC Louvain)*Conjugacy and dynamics in the almost automorphism group of a tree*

We define the almost automorphism group of a regular tree, also known as Neretin's group, and determine when two elements are conjugate. (joint work with Gil Goffer)

## Assistant Prof Mark Pengitore

(Ohio State University)*Translation-like actions on nilpotent groups*

Whyte introduced translation-like actions of groups as a geometric generalization of subgroup containment. He then proved a geometric reformulation of the von Neumann conjecture by demonstrating that a finitely generated group is non amenable if and only it admits a translation-like action by a non-abelian free group. This provides motivation for the study of what groups can act translation-like on other groups. As a consequence of Gromov’s polynomial growth theorem, virtually nilpotent groups can act translation-like on other nilpotent groups. We demonstrate that if two nilpotent groups have the same growth, but non-isomorphic Carnot completions, then they can't act translation-like on each other. (joint work with David Cohen)