# Felix Klein Lectures 2023

## Families of higher dimensional varieties

## János Kollár (Princeton University)

Dates:

Lecture 1: HIM, Tuesday, Oct 17, 15:00--16:00

Lecture 2: HIM, Wednesday, Oct 18, 15:00--16:00

Lecture 3: HIM, Thursday, Oct 19, 15:00--16:00

Lecture 4: HIM, Tuesday, Oct 24, 15:00--16:00

Lecture 5: HIM, Wednesday, Oct 25, 15:00--16:00

Lecture 6: HIM, Thursday, Oct 26, 15:00--16:00 (tbc)

Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn

### Abstract:

The moduli space of smooth projective curves, and its compactification by nodal curves, turned out to be some of the most studied varieties in mathematics and string theory. The analogous theory for the moduli of higher dimensional varieties was completed recently, after 30 years of work by many mathematicians. The aim of the lectures is to outline this theory.

Lecture 1 will focus on examples that show unexpected features of the higher dimensional theory. The main definitions and theorems will be explained in lecture 2. The remaining lectures will be independent of each other, each treating a topic in moduli theory with connections to other questions in mathematics.

# Video Recordings

Lecture 1, October 17

Lecture 2, October 18

Lecture 3, October 19

Lecture 4, October 24

Lecture 5, October 25

Lecture 6, October 26