Homological Mirror Symmetry

I will discuss a construction of the homological mirror correspondence on algebraic integrable systems arising as moduli of flat bundles on curves. The focus will be on non-abelian Hodge theory as a tool for implementing hyper Kaehler rotations of...

I will discuss a construction of the homological mirror correspondence on algebraic integrable systems arising as moduli of flat bundles on curves. The focus will be on non-abelian Hodge theory as a tool for implementing hyper Kaehler rotations of...

Consider the Fukaya A8 algebra $E$ of $RP^{2m}$ in $CP^{2m}$ (with bulk and equivariant deformations, over the Novikov ring). On the one hand, elementary algebraic considerations show that E admis a rigid cyclic minimal model, whose structure...

The wrapped Fukaya category of an algebraic hypersurface $H$ in $(C*)^n$ is conjecturally related via homological mirror symmetry to the derived category of singularities of a toric Calabi-Yau manifold $X$, whose moment polytope is determined by the...

Homological mirror symmetry postulates a derived equivalence between the wrapped Fukaya category of an exact symplectic manifold and a category of coherent sheaves or matrix factorizations on a mirror space. This talk will provide an introduction to...

Abstract: In this talk we will report on joint work in progress with Mohammed Abouzaid concerning homological mirror symmetry for hypersurfaces in (C*)^n, namely, comparing the derived category of the hypersurface and the Fukaya category of the...

Abstract: Within an emerging approach to Fukaya categories via cohomology with categorical coefficients, I will outline a theory of a particularly nice class of nonconstant coefficient systems defined on Riemann surfaces. These are categorical...

Abstract: Mirror symmetry has led to deep conjectures regarding the geometry of Calabi-Yau manifolds. One of the most intriguing of these conjectures states that various geometric invariants, some classical and some more homological in nature, agree...

Abstract: In this talk we will combine classical mathematical structures and we will look at them from a new prospective. Applications to geometry will be considered.

Abstract: We study the effective BV quantization theory for chiral deformation of two dimensional conformal field theories. We establish an exact correspondence between renormalized quantum master equations for effective functionals and Maurer...