Graz Combinatorics Day 2026


The Graz Combinatorics Day 2026 — an SFB associated event — will take place at TU Graz on 20 November 2026 (Friday) in the seminar room STEG050 (AE06) on the ground floor (EG) of the Mathematics Building located at Steyrergasse 30, A-8010 Graz, on the Neue Technik Campus of TU Graz.

Directions to the Neue Technik Campus: Coming from the central station (Graz Hbf) one may take the tram (aka "Bim") number 6 (direction to St.Peter) until the station "Neue Technik" and walk around 3 minutes.


Speakers


Program

20 November seminar room AE06 at TU Graz, Steyrergasse 30/EG
10:00-12:00 Anna Geisler:  Percolation and Ising model on graphs with good expansion properties (PhD defence talk)
13:00-13:50 Refreshments and snacks
14:00-15:00 Michael Krivelevich:  Vertex sampling for graph theoretic problems
15:00-15:30 Coffee break
15:30-16:30 Matthew Kwan:  Counting things at criticality
16:40-17:40 Ronen Wdowinski:  Counting homomorphisms in a percolated setting

Abstracts

Anna Geisler: Percolation and Ising model on graphs with good expansion properties

Expansion properties of a graph facilitate the study of its properties under randomisation. The talk gives an introduction to the main themes of my dissertation, illustrating this phenomenon in three different settings. Firstly, we study the random graph process and show that the hitting times for k-connectedness and minimum degree k coincide with high probability on graphs with good edge-expansion. Secondly, we study an infection process called majority bootstrap percolation and show that under randomised initialisation a large class of high-dimensional graphs exhibits a sharp threshold for infection of the whole vertex set. Finally, we study independent sets in random subgraphs of bipartite, regular graphs with good vertex-expansion. Using connections to the Ising model from statistical physics we obtain an asymptotic expansion of the expected number of independent sets for a large regime of parameters.

Michael Krivelevich: Vertex sampling for graph theoretic problems

Based on the research experience of the speaker, we will showcase several quite diverse graph theoretic problems, where vertex percolation or more generally vertex sampling play a crucial role, despite their apparent irrelevance to the problem at hand.

Matthew Kwan: Counting things at criticality

How many graphs have $n$ vertices and $m$ edges, and no triangle? For a long time we have had a pretty good answer to this question except when m has order of magnitude $n^{3/2}$, which turns out to be a “critical regime” from the point of view of lower tail large deviations. We'll discuss some new methods to study this kind of problem. Joint work with Huy Tuan Pham.

Ronen Wdowinski: Counting homomorphisms in a percolated setting

For a graph $G$ and real $p \in [0,1]$, the random graph $G_p$ is obtained from $G$ by including each edge independently with probability $p$. For a fixed target graph $H$, we study the expected number of homomorphisms from $G_p$ to $H$ when $G$ is a $d$-regular bipartite graph and $d$ tends to infinity. Under a wide range of conditions on $G$ and $p$, even when $p$ tends to $0$ with $d$, we obtain precise asymptotics for the expected number of homomorphisms. This is done by studying the partition function of an associated positive-temperature discrete spin system on $G$ and applying the cluster expansion method from statistical physics. This generalizes previous works of Jenssen, Keevash, Kronenberg, and Spinka. Joint work with Anna Geisler and Mihyun Kang.


Local organisers


This is an associated event of the SFB "Discrete random structures: enumeration and scaling limits" and is supported in part by Austrian Science Fund (FWF) [10.55776/F1002] and NAWI Graz.