Representations 3-manifold group, the Chern-Simons function and Floer homology

Time: 9:30 -- 11:00, July 17, 2024

Venue: Room 612, A6, Institute of Mathematics-VAST

Abstract: Starting in dimension 4 an arbitrary finitely presented group is the fundamental group of a compact n dimensional manifold.  Fundamental groups of 3-manifolds instead are restricted.  I’ll explain some of the questions and results about finding representations of three manifold fundamental groups and how such representations reflect the topology of the underlying manifold.  The focus will mainly be on those results  that use ideas from  gauge theory in particular the Chern-Simons function and Floer homology.

Professor Tomasz Mrowka is a leading expert in the field of geometry and gauge theory. In joint work with Professor Peter Kronheimer, Tomasz Mrowka settled many long-standing conjectures, three of which earned them the 2007 Oswald Veblen Prize from the AMS. In 1994 He was an invited speaker at the ICM in Zurich on Embedded surfaces and the structure of Donaldson's polynomial invariants. In 2018 He gave a plenary lecture at the ICM in Rio de Janeiro on Knots, three-manifolds and instantons. In 2023 He was awarded the Leroy P. Steele Prize for seminal contribution to research (jointly with Peter Kronheimer). In addition, He became a fellow of the American Academy of Arts & Sciences in 2007, and a member of the National Academy of Sciences in 2015.