Critical points of high-dimensional random functions

Series
Job Candidate Talk
Time
Tuesday, December 5, 2023 - 4:30pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Benjamin McKenna – Harvard University – bmckenna@fas.harvard.eduhttps://www.benjaminmckenna.com
Organizer
Christian Houdré

How many critical points does a random function from R^N to R have for large N? Such functions appear naturally in probability, data science, and mathematical physics. Questions like this one, which have attracted longstanding interest from both physicists and mathematicians, can help explain both physical phase transitions and algorithmic thresholds. I will give an overview of this "landscape complexity" program, its motivations, and recent progress coming from random matrices.