AbstractFloer 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 w...
课程介绍 / DescriptionIn his memoir of 1900, Henri Poincaré proposed a program to study the arithmetic properties of algebraic curves based on their geometric structures. This led to tremendous achievements in the 20th century, including the proof of the Mordell—Weil theorem (Mordell 1922, Weil 1928), the Mordell conjecture (Faltings 1983), and Fermat's last theorem (Wiles 1994).In this series...