Graduate course by Prof. A. Tikhomirov

[Ugo Bruzzo]

Prof. A Tikhomirov (HSE Moscow) will give a graduate course on

GAUGE THEORY

starting April 4th, 2019. The lectures will take place in Room 136
on Thursdays and Fridays from 2 to 4 pm.

Summary: The course will provide an introduction to gauge theory on smooth 4-manifolds and
its applications to differential topology and algebraic geometry. The following topics are supposed to be
covered:

1. Principal Bundles and Connections
2. Curvature and Characteristic Classes
3. The Space of Connections
4. The ASD Equations and the Moduli Space
5. Compactness and Gluing Theorems
6. Definite intersection forms
7. The Donaldson polynomial invariants
8. The Connected Sum Theorem
9. The Kobayashi-Hitchin correspondence
10. Differentiable structures on complex algebraic surfaces

U. Bruzzo