Murray Elder (University Technology Sydney)

Tony Martin (Australian National University)

Adam Piggott (Australian National University)

Kane Townsend (Australian National University)

Vandit Trivedi (Australian National University)

Invited Speakers

• Ilaria Castellano (Heinrich-Heine-Universität Düsseldorf)

  Title: Totally disconnected locally compact groups, accessibility and Euler-Poincaré characteristic.

  In the first part of the talk I will illustrate how the classical notion of accessibility for finitely generated groups carries over to the realm of compactly generated totally disconnected locally compact (= t.d.l.c.) groups. Then, by means of a new notion of Euler-Poincaré characteristic, I will discuss an accessibility result in the t.d.l.c. framework, under the assumption of rational discrete cohomological dimension = 1.

• James East (University of Western Sydney)

  Title: Transformation representations of diagram monoids

  We obtain formulae for the minimum transformation degrees of the most well-studied families of finite diagram monoids, including the partition, Brauer, Temperley--Lieb and Motzkin monoids. For example, the partition monoid the partition monoid $\mathcal P_n$ has degree $1 + \frac{B(n+2)-B(n+1)+B(n)}2$ for $n\geq2$, where these are Bell numbers. The proofs involve constructing explicit faithful representations of the minimum degree, many of which can be realised as (partial) actions on projections. This is joint work with Reinis Cirpons and James Mitchell (both from St Andrews).

• Uri Onn (Australian National University)

  Title: Representation growth of arithmetic groups

  A group is said to have polynomial representation growth if the sequence enumerating the isomorphism classes of finite dimensional irreducible representations according to their dimension is polynomially bounded. The representation zeta function of such group is the associated Dirichlet generating series. In this talk I will focus on representation zeta functions of arithmetic groups and their properties. I will explain the ideas behind a proof of a variant of the Larsen--Lubotzky conjecture on the representation growth of arithmetic lattices in high rank semisimple Lie groups (joint with Nir Avni, Benjamin Klopsch and Christopher Voll) and analogous results for arithmetic groups of type A_2 in positive characteristic (joint with Amritanshu Prasad and Pooja Singla).

• Anne Thomas (University of Sydney)

  Title: Divergence in Coxeter groups

  Abstract: The divergence of a pair of geodesic rays is a classical notion, which measures how fast these rays move away from each other. In the 1990s, Gersten used this idea to formulate a large-scale invariant of finitely generated groups, also called divergence. We survey the results obtained over the last decade for divergence in right-angled Coxeter groups, and begin the investigation of divergence in arbitrary Coxeter groups.  This is joint work with Pallavi Dani, Yusra Naqvi and Ignat Soroko.

Talk title and abstract submissions

We welcome submissions from all participants.   The conference has a proud tradition of encouraging talks by students: typically about one-third of the talks are presented by students. The conference aims to provide graduate students in algebra with the opportunity to give their first public presentation in a relaxed and supportive environment. Each conference, the most outstanding student talk is awarded the Gordon Preston Prize.  To submit a title and abstract for consideration, please use the link below. Talks successful will be 20 minutes in length with 10 minutes for questions.

Submit

Registration

AAG Members = $15.00AUD

Students = Free (Participant support is available and is subject to registration and panel review)

AustMS members (who are not AAG members) = $40.00AUD

Non-members off AustMS = $50.00AUD

Reception and Conference Dinner

There will be a reception on the first night of the conference Wed 27 Nov 2024.

The conference dinner will be held at the Civic Pub on Lonsdale Street in Braddon, Canberra Thu 28 Nov 2024.

The conference will end with the MSI End of Year Party on 29 Nov 2024. If you would like to attend this event, please register.  No payment is required, but a donation on the day is appreciated.

General information for visitors

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