Critical points of high-dimensional random functions

Job Candidate Talk
Tuesday, December 5, 2023 - 4:30pm for 1 hour (actually 50 minutes)
Skiles 006
Benjamin McKenna – Harvard University – bmckenna@fas.harvard.edu
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.