Welcome! The CMSA seminar aims to bring together combinatorialists from Australasia and around the world.
The seminar is held roughly every two weeks during spring and autumn, usually at either 11am or 5pm AEDT.
Subscribe: In order to subscribe mail t.lesgourgues@unsw.edu.au and ask to be added to the list. We send announcements and zoom details before every talk.
Current organiser: Thomas Lesgourgues.
Please email with your feedback and suggestions.
Previous talks:
2020
2021
2022
2023
2024
2025
2026 talks:
|
1 April 2026, 11am AEDT
Natasha Morrison (University of Victoria)
|
|
Spanning Trees in Pseudorandom Graphs via Sorting Networks
|
| Abstract:
We show that (n, d, λ)-graphs with λ = O(d/ log^3 n) are universal with respect to all bounded degree spanning trees. This significantly improves upon the previous best bound due to Han and Yang of the form λ = d/ exp (O(√log n)), and makes progress towards a problem of Alon, Krivelevich, and Sudakov from 2007.
Our proof relies on the existence of sorting networks of logarithmic depth, as given by a celebrated construction of Ajtai, Komlós and Szemerédi. Using this construction, we show that the classical vertex-disjoint paths problem can be solved for a set of vertices fixed in advance.
|
|
6 May 2026, 5pm AEDT
Sahar Diskin (ETH Zürich)
|
|
Supercritical sharpness of percolation
|
| Abstract:
Given an infinite transitive graph (such as the standard lattice Z^d), build a random subgraph by independently including each edge with probability p.
This model undergoes a phase transition as p varies across the critical value p_c marking the emergence of an infinite component.
A fundamental result is that for any fixed p < p_c, the probability that a given vertex is in a component of size at least n decays exponentially with n.
We will prove the analogous result for the supercritical regime, p>p_c. Based on a joint work with Easo, Ramanan-Radhakrishnan, Sudakov, and Tassion.
|
|
27 May 2026, 5pm ASDT
Bertille Granet (University of Warwick)
|
|
On 2-factors of Hamiltonian graphs
|
| Abstract:
Let k ≥ 2. We show that, for a sufficiently small ε > 0, any sufficiently large n-vertex Hamiltonian
graph of minimum degree at least n^(1−ε) contains a 2-factor consisting of exactly k cycles. This is the first
minimum-degree condition which is polynomially smaller than linear. Our methods yield an analogous
result when the host graph is not required to contain a Hamilton cycle, but only a 2-factor consisting of
at most k cycles; this answers a question of Bucić, Jahn, Pokrovskiy and Sudakov. This is joint work with
Alberto Espuny Díaz, António Girão, and Gal Kronenberg.
|
|
30 September 2026, 5pm AEST
Julia wolf (University of Cambridge)
|
|
The structure of sets of bounded VC_2-dimension
|
| Abstract:
VC-dimension is a classical measure of combinatorial tameness, widely used across model theory, statistics, combinatorics, and theoretical computer science since its inception in the 1970s. A higher-dimensional analogue, known as VC_2-dimension, was introduced by Shelah in 2014 but has thus far received comparatively little attention.
In 2018, Alon, Fox and Zhao, and independently Sisask, showed that any subset of bounded VC-dimension in a high-dimensional vector space over a finite field is well approximated by a union of cosets of a large subspace. In joint work with Caroline Terry, we proved an analogous (but necessarily more sophisticated) structure theorem for the larger class of subsets of bounded VC_2-dimension. This has refined our understanding of the quantitative aspects of quadratic Fourier analysis, as developed by Green and Tao in this setting.
The talk aims to be accessible to graduate students across a variety of mathematical disciplines.
|