ALT UCI Math Department Special Colloquium: Why Can Kontsevich's Invariants Detect Exotic Phenomena? Presented by Junior Fellow Xujia Chen of the Harvard Society of Fellows at Room 1201 of Natural Sciences II on January 19, 2024. How to understand the role smooth structure plays in Kontsevich's invariants? The difference between the category of smooth manifolds and the category of topological manifolds has always been a delicate and intriguing problem, called the "exotic phenomena". Kontsevich's invariants, defined by Kontsevich in the early 1990s from perturbative Chern-Simons theory, are invariants of (certain) 3-manifolds / fiber bundles / knots and links (it is the same argument in different settings). The recent work of Watanabe (2018) uses Kontsevich's invariants to show that the group of diffeomorphisms of the 4-dimensional ball, as a topological group, has non-trivial homotopy type. In contrast, the group of homeomorphisms of the 4-dimensional ball is contractible. This implies tha