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Explore the fundamental role of corks in studying exotic smooth structures on 4-manifolds in this lecture by Abhishek Mallick from Rutgers University. Delve into the use of Heegaard Floer homology as a method for detecting corks. Discover new examples of corks that address a question posed by Gompf, as presented in joint work with Irving Dai and Ian Zemke. Gain insights into this advanced topic in topology and its implications for understanding the complex nature of 4-dimensional manifolds.