Dear colleagues,

this is a gentle reminder of today One World Probability Seminar, details below. The seminar will be held at 15:00 (italian time).

You can find the calendar for the upcoming seminars at this link (next dates: May 14, May 21).

We hope to see many of you online!

Luisa and Roger

---------- Forwarded message ---------

From: One World Probability <ow.probability@gmail.com>
Date: Sun, May 4, 2025 at 9:58 PM
Subject: Next OWPS this Wednesday
To: <owps@lists.bath.ac.uk>

The next OWPS will be on Wednesday, May 7, from 13:00 to 15:00 UTC time

Speakers: Matthew Kahle (Ohio State University), András Mészáros (Alfréd Rényi Institute of Mathematics)

Title, abstract and the zoom link are below the signature and can be found on the website https://www.owprobability.org/one-world-probability-seminar.

Upcoming seminars:

May 14: Matteo Quattropani (Roma Tre University), Federico Sau (University of Milan)

May 21: Eleanor Archer (Dauphine-PSL Paris), Anita Winter (Duisburg-Essen University)

-----------------------

Introduction to determinantal random hypertrees

Matthew Kahle (Ohio State University)

Abstract: A hypertree is a simplicial complex that serves as a higher-dimensional analogue of a tree. We will discuss a natural model of random hypertree, inspired by enumerative work of Kalai and probabilistic work of Lyons. This model is a higher-dimensional analogue of a uniform spanning tree on a complete graph.

In this talk, we will take some time to carefully motivate and define the model, and then to discuss some of its probabilistic properties. Finally, we will overview some results of Andrew Newman's and mine about the basic properties of 2-dimensional determinantal random hypertrees. In particular, we will discuss torsion in homology and hyperbolicity of the fundamental group. I will not assume any topological prerequisites, and will aim to make the talk as self contained as possible.

Determinantal hypertrees and graph limits

András Mészáros (Alfréd Rényi Institute of Mathematics)

Abstract: We discuss how graph limit theory can provide us with useful tools to understand random simplicial complexes.

Extendending the result of Grimmett on the local weak limit of uniform random spanning trees of complete graphs, we describe the local weak limit of determinantal hypertrees.

Relying on the large deviation principle for the Erdős–Rényi random graph by Chatterjee and Varadhan, we give an upper bound on the mod 2 homology of 2-dimensional determinantal hypertrees.

If time permits, we discuss conjectures on the distribution of the p-torsion of the first integral homology group of 2-dimensional determinantal hypertrees.

https://polimi-it.zoom.us/j/92945513591?pwd=zjtRwpHoO9kRyQuPPj4o186jXrvg1v.1

Meeting ID: 92945513591

Passcode: 131676