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.
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
Monday, October 25, 2021: Lecture 10
Thursday, October 28, 2021: Lecture 11
Monday, November 1, 2021: Lecture 12
Thursday, November 4, 2021: Lecture 13
Monday, November 8, 2021: Lecture 14
Thursday, November 11, 2021: Lecture 15
Monday, November 15, 2021: Lecture 16
Thursday, November 18, 2021: Lecture 17
Monday, November 22, 2021: Lecture 18
Thursday, November 25, 2021: Lecture 19
Monday, November 29, 2021: Lecture 20