Abstract
Floer defined Floer homology in two different cases. One is the case of Instanton Floer homology of 3 manifolds (homology sphere). The other uses pseudo-holomorphic curves. (The first Floer homology Floer defined using pseudo-holomorphic curves is Lagrangian Floer homology.) Atiyah-Floer conjecture says that those two coincide in certain situations. This is > 30 year old conjecture. I will explain several results around this conjecture including recent ones. My own research on this topic is a joint work with A. Daemi and M. Lipyanskiy.
Speaker
Kenji Fukaya became a permanent member of the Simons Center on April 1, 2013. He received his BA in Mathematics at the University of Tokyo in 1981, and continued graduate studies at the University of Tokyo, receiving his PhD in 1986. He was at the University of Tokyo from 1983 through 1990, where he was first a research assistant and then an Associate Professor. He was a Professor of Mathematics at Kyoto University in 1994 until coming to the Simons Center. Fukaya's recent work has been in symplectic geometry and in particular has centered around the study of Lagrangian submanifolds and the Floer homology related to intersections of these submanifolds. Fukaya developed and has studied extensively a theory in which the Lagrangian submanifolds of a given symplectic manifold are the objects of a generalized category, now called the Fukaya category, and the morphisms are the Floer homology groups. Fukaya was awarded the Japan Academy Award in 2003, Asahi prize in 2009, and Fujiwara prize in 2012. He is a member of the Japanese National Academy of Sciences.
