Homological Mirror Symmetry and applications

同调镜面对称性(HMS)最初是由介于Morse理论和De Rham理论之间的Kontsevich提出的，在最初的许多精彩的物理论文(Vafa，Hori，Kapustin)之后，许多代数和辛几何工作者都转向了这个主题。D.Auroux，L.Katzarkov，P.Seidel，M.Kontsevich，D.Orlov，Y.Soibelman，K.Ueda在几种情况下给出了HMS的严格的数学证明。这项研究将集中在HMS在双曲几何、Gromov-Witten理论、辛几何以及与Hodge理论的一些很有前途的联系中的一些引人注目的应用。预期的结果将有助于在数学家和弦理论家之间合作的新视角下，简化代数几何的经典思想。

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.