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Presented By: Department of Mathematics

Integrable Systems and Random Matrix Theory Seminar

Counting saddles in high dimensions

I will discuss the almost surely asymptotics of the number of saddles in the spherical p spin-glass model. Our main result confirms the almost surely existence of a layered structure of critical points of the energy landscape. I will then relate this computation to a detailed information about the landscape around the ground state energy and the structure of the Parisi measure at zero temperature. The proofs heavily use tools from random matrix theory, including large deviation principles and rigidity results.

Based on a joint work with Julian Gold (Northwestern University) and Yi Gu (Northwestern University). Speaker(s): Antonio Auffinger (Northwestern University)

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