# Giulio Zucal & Raffaella Mulas talk and discussions

### Description

The next Kutszem will be a double header. The first talk by Giulio Zucal is at 2pm (at Macis) and the second by Raffaella Mulas is at the usual 4.15pm at Macis.

Speaker: **Giulio Zucal** (Max Planck Institute for Mathematics in the Sciences, Leipzig)

Title: *Multi-linear action convergence for hypergraphs and tensors*

*Abstract*: The theory of graph limits considers the convergence of sequences of graphs with a diverging number of vertices. From an applied perspective, it aims to represent very large networks conveniently. Until recently, however, particular cases for graph limits have been investigated separately, while hypergraph limits are even less well-developed. In this talk, I will give a brief introduction to action convergence, a recent unified approach to graph limits based on functional analysis and measure theory. Moreover, I will present an extension of action convergence to multi-linear operators, investigate its properties and explain how this notion can be applied to sequences of hypergraphs and tensors.

Speaker:** Raffaella Mulas** (Vrije Universiteit Amsterdam & Max Planck Institutefor Mathematics in the Sciences, Leipzig)

Title: *Graphs and Hypergraphs: From spectral theory to extremal combinatorics*

*Abstract*: Spectral graph theory studies the qualitative properties of a graph that can be inferred from the eigenvalues and the eigenvectors of an associated operator. It has a long history, is widely used in applications, and the first part of this talk will focus on it. We will then consider a generalization of spectral graph theory to the case of hypergraphs, as well as an application to networks of genetic expression. Finally, in the last part of the talk, we will focus on a much more theoretical topic and we will talk about an extremal combinatorics problem for hypergraphs that was introduced by Paul Turán in 1941.