What is Mirror Symmetry?

Abstract: Mirror symmetry predicts that a Kähler manifold X (near a certain scaling limit) admits a dual space X^ so that symplectic invariants of X are equal to algebraic invariants of X^. We will begin by reviewing the Fukaya category of Lagrangian submanifolds of X, focusing on the case when X is a Stein manifold, and then describe the homological mirror symmetry conjecture that the Fukaya category of X is equal to the category of coherent sheaves on X^. If time permits, we will explain how to prove this conjecture.

algebraic geometrycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: learners

What is ...? Seminar

Series comments: The ``What is ... ? Seminar'' (WiSe) is a weekly Zoom mathematics seminar. The goal is to explain interesting things to each other in a casual manner. The name is inspired by the What is ...? column of the Notices of the American Mathematical Society. See the website for more details. If you want to receive the zoom link for the talks please fill out the form linked on the website or contact Anna at a.puskas@uq.edu.au.