Mirror Symmetry and Deformation Theory I

Yan Soibelman
Kansas State University

I plan to talk about categorical aspects
of Mirror Symmetry, mostly about
what is now called Homological Mirror Symmetry.
I am going to discuss the structure of
maximally degenerating
families of Calabi-Yau manifolds and its relation
to non-archimedean geometry.
I will formulate the Homological Mirror
Conjecture as a certain duality in the world
of non-commutative spaces and explain
its relation to deformation theory.

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