Clara Stegehuis

Title: Detecting geometry in scale free networks

Abstract: Geometric network models formalize the natural idea that similar vertices are likely to connect. Therefore, geometric models capture many common structural properties of real-world networks. However, if one observes only the network connections, the presence of geometry is not always evident. Currently, triangle counts and clustering coefficients are the standard statistics to signal the presence of geometry. We show that triangle counts or clustering coefficients are insufficient because they fail to detect geometry induced by hyperbolic spaces, or in networks with power law degrees. We therefore introduce different statistics, based on weighted subgraph counts that can even detect geometry in the 'weak geometry' regime, where the geometric effects converge to zero.

David Belius

General talk

Title: The story of mean-field spin glasses

Abstract: Mean-field spin glasses are paradigmatic examples of complex systems. They involve a large (N->inf) number of simple “spin” variables, which are subject to disordered random interactions that cause highly complex and fascinating collective behavior. They were introduced in statistical physics to model disordered magnetic materials – subsequently models with very different origins but fundamentally similar behavior were discovered in theoretical computer science and theoretical statistics. All together these form a kind of universality class of mean-field spin glass models, that spans several areas of science.

This talk will consist of a high-level narrative retelling of the history of mean-field spin glasses, including original motivations, the remarkable description of their complex behavior discovered by Giorgio Parisi (Nobel Prize in Physics 2021), and the subsequent effort to put it on a mathematically rigorous footing.

Specialized talk

Title: The Thouless-Andersson-Palmer (TAP) approach to mean-field spin glasses

Abstract: The Thouless-Andersson-Palmer (TAP) approach to mean-field spin glasses provides a particularly attractive lens on the phenomena of the models, thanks to its geometric and potentially constructive nature. In the story of spin glasses the TAP approach has played an important, but ultimately supporting, role – in both physics and mathematics the main tools come from other very different approaches. This talk will be about ongoing efforts to turn the TAP approach into a self-contained mathematically rigorous theory of mean-field spin glasses, which is my main research interest in the area.