The world of 4-manifolds is very interesting in many senses. For example, a closed topological n-manifold $X^n$ has exactly one smooth structure if $n \leq 3$ and has at most finitely many smooth structures if $n > 4$. However, there are many simply-connected closed 4-manifolds which admit infinitely many smooth structures. Also, classification problems for smooth, simply connected 4-manifolds have still not fully been understood. For example, the generalized Poincaré conjecture is still open for dimension 4. In this talk, we will talk about the construction of symplectic 4-manifolds homeomorphic but not diffeomorphic to some well-known manifolds with given topological invariants. We will mostly focus on the simply-connected symplectic 4-manifolds, describe the topological invariants, and give examples.

Link to the seminar is:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1622891637112?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d