MAT 6229: Geometric spectral theory

Lecturer: Iosif Polterovich

Description: The course will cover the fundamentals of geometric spectral theory as well as some recent developments in the area. Main topics include: spectral theorem for the Laplacian on Euclidean domains and Riemannian manifolds, geometric eigenvalue inequalities, nodal geometry of eigenfunctions, spectral invariants, "Can one hear the shape of a drum?", Steklov eigenvalue problem, spectral asymptotics.

Basic knowledge of PDEs and differential geometry will be assumed.

Syllabus

Schedule: Mondays and Thursdays, 10:00-12:00

Lectures:

Thursday, September 2, 2021: Lecture 1

Thursday, September 9, 2021: Lecture 2

Monday, September 20, 2021: Lecture 3

Thursday, September 23, 2021: Lecture 4

Monday, September 27, 2021: Lecture 5

Thursday, September 30, 2021: Lecture 6

Monday, October 4, 2021: Lecture 7

Thursday, October 7, 2021: Lecture 8

Thursday, October 14, 2021: Lecture 9