Mathematics 790M - Mirror Symmetry

This course will study the mirror symmetry phenomenon of theoretical physics from a mathematical perspective. We will study the homological mirror symmetry conjecture of Kontsevich (1994) and the related Strominger?Yau?Zaslow conjecture (1996). We will develop the necessary mathematical background as needed, including derived categories of coherent sheaves on complex manifolds and Fukaya categories of symplectic manifolds. We will rigorously establish instructive special cases of the homological mirror symmetry conjecture.