Organizers : Jeff Kahn, Bhargav Narayanan, Swee Hong Chan, and Natalya Ter-Saakov
Date: March 9, 2026 at 2:00pm
Speaker: Ian Jauslin (Rutgers)
Title: The liquid-vapor phase transition in a system with a finite but coarse-grained attraction
Abstract: The standard approach to studying the liquid-vapor phase transition uses the Maxwell double-tangent construction. Whereas this construction is easily justified physically, deriving it mathematically has proved to be more difficult. In 1966, Lebowitz and Penrose proved the Maxwell construction in a mean field model, where the particles interact via a hard-core repulsion, and an infinite range, infinitely weak attraction. Generalizing their result to finite pair attractions remains an open problem.
In this talk, I will discuss a proof of the existence of a liquid-vapor phase transition in a system with an attraction that is finite, but is also coarse-grained. More precisely, we split up space into mesoscopic boxes, and define an attraction that ignores the location of the particles within each box. Defined in this way, our model is reflection positive, which allows us to prove the existence of a liquid-vapor phase transition.
This is joint work with Qidong He, Joel L. Lebowitz, and Ron Peled.
Date: March 2, 2026 at 2:00pm
Speaker: Yuval Wigderson (ETHZurich)
Title: Triangle-free graphs and the odd Hadwiger conjecture
Abstract: Hadwiger's conjecture, first formulated in 1943, is a vast generalization of the four-color theorem, and remains one of the central open problems in graph theory. An even stronger statement, known as the odd Hadwiger conjecture, was proposed in 1993 by Gerards and Seymour. For many decades, progress on one problem was quickly followed by progress on the other, and recent developments indicate that Hadwiger's conjecture and its odd variant are very closely linked.
However, as it turns out, the odd Hadwiger conjecture is false. The key ingredient to the counterexamples is a new random model of triangle-free graphs, which arose in the recent breakthrough work of Hefty et al. on off-diagonal Ramsey numbers. In this talk, I will describe this construction, and sketch how it can be used to disprove the odd Hadwiger conjecture.
Based on joint work with Marcus Kühn, Lisa Sauermann, and Raphael Steiner.
Date: February 16, 2026 at 2:00pm
Speaker: Ferdinand Ihringer (SUSTech)
Title: The Structure of Large Intersecting Families in Vector Spaces
Abstract: The classical EKR theorem states that the largest intersecting family of k-uniform subsets of an n-element set consists of all k-sets through a fixed element. More generally, it is known that large intersecting families are locally concentrated. So far such characterization results are missing for intersecting families of subspaces in vector. We will describe ongoing work which closes this gap in the literature. Joint work with Andrey Kupavskii.
Date: February 9, 2026 at 2:00pm
Speaker: Maya Sankar (IAS)
Title: The Turán Density of Tight Cycles
Abstract: I will discuss several recent results on the Turán density of long cycle-like hypergraphs. These results (due to Kamčev–Letzter–Pokrovskiy, Balogh–Luo, and myself) all follow a similar framework, and I will outline a general strategy to prove Turán-type results for tight cycles in larger uniformities or for other "cycle-like" hypergraphs.
One key ingredient in this framework, which I hope to prove in full, is a hypergraph analogue of the statement that a graph has no odd closed walks if and only if it is bipartite. More precisely, for various classes C of "cycle-like" r-uniform hypergraphs — including, for any k, the family of tight cycles of length k modulo r — we equiivalently characterize C-hom-free hypergraphs as those admitting a certain type of coloring of (r-1)-tuples of vertices. This provides a common generalization of results due to Kamčev–Letzter–Pokrovskiy and Balogh–Luo.