**Date:** Friday: 12-14

**First day of class:** Friday Apr 12, 2021

**Note: No Class on Friday May 7 !**

**Location: ** Online. Whenever the university allows it, we will switch to hybrid lectures.

Zoom Meeting ID: 981 0791 2608

Passcode: 3780

**Emails:** If you want to receive emails about the class, please sign up at eCampus.

**Overview:**The target of the course is to learn about the Gromov-Witten theory of hyperkaehler varieties, one of the main classes of Calabi-Yau varieties. We start with introducing some basics about virtual classes and Gromov-Witten invariants, and then discuss them for elliptic curves, K3 surfaces, and later Hilbert schemes of points on K3 surfaces, which is the main example of hyperkaehler varieties in higher dimension. The structure of the GW invariants of all of these spaces is quite beautiful. We will particular focus on the connection to modular forms. I plan to write lecture notes for most of the course.

**Prerequisites:** Basic knowledge of Algebraic Geometry. Some Intersection Theory (First few sections of Fulton's book on Intersection theory). A little bit about Stacks (Functorial Approach, M_g as a stack).

**Some references**:

- Lecture Notes (later)

**Files for the class:**

**Oral Exam:** July 23 afternoon, and Sep 24, 2021