CCMS Colloquium: Morse theory, Floer homology, and string topology (Ko Honda, UCLA)

CCMS Colloquium invites you to a talk by Professor Ko Honda, Professor of Mathematics at UCLA.

Title: Morse theory, Floer homology, and string topology

Abstract: One of the most important theories in geometry/topology is Floer homology, which can be viewed as a Morse theory of a loop space of a manifold (a generalization of a surface to higher dimensions).  The aim of this talk is to give a gentle pictorial introduction to Morse theory for surfaces and then upgrade it in two steps: to Morse theory of loop spaces (e.g., of the 2-dimensional sphere) and then to “multiloops” (collections of many loops).  The last upgrade is intimately related to a mathematical model for string theory called “string topology”, due to Chas-Sullivan, and to quantum topology via the HOMFLY polynomial of knots/links.

Speaker Bio: Ko Honda is an entirely American-trained mathematician, receiving his BA and MA from Harvard University in 1992 and PhD from Princeton University in 1997.  After postdocs/visiting positions at Duke, the University of Georgia, the American Institute of Mathematics, and IHES, he arrived in LA in 2001, was a faculty member at USC for 12.5 years, and then moved across town to UCLA, where he has been for the last 11.5 years.  Sometime during his postdoc at Duke, he discovered/invented an object called a “bypass” in contact geometry, which allowed him to simplify the analysis of 3-dimensional contact manifolds and solve several open problems in that area, some in joint work with Colin, Etnyre, and Giroux.  He has been working on contact and symplectic geometry ever since, gradually branching out into adjacent areas (e.g., low-dimensional topology, Floer theory, and quantum topology) in the intervening years.