**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