Homological Mirror Symmetry and applications

点击翻译按钮获取中文摘要

Homological Mirror Symmetry (HMS) was initially introduced by Kontsevichas a duality between Morse theory and de Rham theory.After many wonderful physics papers at the beginning (Vafa, Hori,Kapustin) many algebraic and symplectic Geometers have turned to thesubject. Rigorous mathematical proofs of HMS were given in several cases by D.Auroux, L. Katzarkov, P.Seidel, M. Kontsevich, D. Orlov,Y. Soibelman, K. Ueda. Bondal, Ruan, Abuzaid.This research will concentrate on some striking applications of HMS to birational geometry, Gromov -Witten theory, Symplectic Geometry as well as some rather promising connections with Hodge theory. The expected results will help streamlineclassical ideas of algebraic geometry in the new light ofcollaboration between Mathematicians and String Theorists.