Homological Mirror Symmetry Events Institute For Advanced Study What's in the book. this monograph is an introduction to the mathematics of mirror symmetry, with a special emphasis on its algebro geometric aspects. topics covered include the quintic threefold, toric geometry, hodge theory, complex and kähler moduli, gromov witten invariants, quantum cohomology, localization in equivariant cohomology, and. Msc: primary 14; secondary 81. mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four dimensional projective space. understanding the mathematics behind these predictions has been a substantial challenge.
Mirror Symmetry And Algebraic Geometry The mirror symmetry leads the physicists to do important predictions about the rational curves on the quintic threefold, which were partially proved very late by people from algebraic geometry. the prediction about gromov–witten invariants given by the mirror symmetry is now proved mathematically in several cases. In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called calabi–yau manifolds. the term refers to a situation where two calabi–yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory. Algebraic geometry could prove at the time. for this reason the paper [3] became a challenge for mathematicians to understand mirror symmetry and to nd a math ematically rigorous proof of the predictions made by physicists. the process of creating a rigorous mathematical foundation for mirror symmetry is still far from being nished. Homological mirror symmetry and algebraic cycles. l. katzarkov. mathematics, physics. 2009. in this chapter we outline some applications of homological mirror symmetry to classical problems in algebraic geometry, like rationality of algebraic varieties and the study of algebraic cycles.…. expand.
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