Mini Course: Smooth and symplectic 4-manifolds

We will study the existence and uniqueness questions of smooth and symplectic structures on closed, simply-connected 4-manifolds.
We will focus on several surgery operations (the knot surgery and the rational blowdown of Fintushel and Stern, the symplectic fiber sum, and Luttinger surgery) that have been useful in changing smooth and symplectic structures and the Seiberg-Witten invariants that allow us to distinguish them.
The last set of lectures will concentrate on more specialized topics such as the exotic smooth and symplectic structures on small 4-manifolds, the exotic Stein fillings, the symplectic Kodaira dimension, and the fake projective planes. Many open problems will be introduced and discussed.

Schedule:
1. Construction Tools
2. Seibert-Witten Invariants
3. Knot Surgery
4. Rational Blowdowns
5. Symplectic Fiber Sum and Luttinger Surgery
6. Exotic 4-Manifolds with Small Euler Characteristics
7. Classification via Symplectic Kodaira Dimension
8. Exotic Stein Fillings, Fake Homology CP2

Tuesday, 11-13 in room Y27H28
Wednesday, 15-17 in room Y27H28

First lecture on May, 6 th