Explore the intricacies of exotic phenomena in 4-dimensional topology through this Mathematics Department Colloquium lecture delivered by Anubhav Mukherjee from Princeton University at Stony Brook University. Delve into the fundamental problem of identifying exotic phenomena that persist after stabilizations, a concept introduced by Wall in the 1960s. Learn about the construction of exotic embeddings of submanifolds, including surfaces and 3-manifolds, in 4-manifolds that can withstand multiple stabilizations. Gain insights into the fascinating world of topological category versus smooth category distinctions and their implications for understanding 4-dimensional manifolds.