# Probability and Mathematical Physics Seminar

#### Probability and the City seminar

**Speaker:**
Michael Aizenman (Princeton University), Daniel Stein (NYU) and Ivan Corwin (Columbia University)

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, March 8, 2024, 10 a.m.

**Notes:**

Michael Aizenman (10am)

Title: Stochastic geometry of correlations in statistical and quantum mechanics

Abstract: The talk will start by recalling some of the pivotal contributions made by Charles M. Newman and collaborators in their rigorous analyses of critical phenomena in statistical mechanic, in which non-perturbative results of fundamental interest were derived through a broad range of analytic and probabilistic methods. Among those are techniques enabled by percolation-type stochastic geometric representations of the spread of correlations in systems of local interactions. The discussion will expand into such methods which, when available, are enabled by local conditional symmetries. Their more recent applications include proofs of discontinuity, or its absence, in symmetry breaking phase transitions in some paradigmatic classical and quantum spin models, and bounds on the quantum entanglement in the ground states of related quantum spin arrays.

(Results mentioned will include also speaker’s joint works with S. Warzel and H. Duminil-Copin).

Daniel Stein (11am)

Title: The Thermodynamic Structure of Short-Range Spin Glasses

Abstract: The thermodynamics of classical spin glasses, and more generally the statistical mechanics of quenched disorder, is a problem of general interest to physicists and mathematicians and one to which Chuck has made numerous contributions. Its importance was recognized in 2021 with the awarding of the Nobel Prize in Physics to Giorgio Parisi for his replica symmetry breaking solution of the Sherrington-Kirkpatrick model (a mean-field model of spin glasses) and its application to other problems in complex systems.