String Theory Seminar
Thursday, March 8, 2001, 4:00pm
Anton Kapustin (IAS Princeton)
Mirror Symmetry and
Noncommutative Geometry
I review the homological mirror symmetry conjecture of Kontsevich and its
relation with topological D-branes. This conjecture is nontrivial even for
tori, which allows one to perform some interesting
checks. It turns out that in the presence of a general B-field Kontsevich's
conjecture must be modified. In particular, on the B-side, coherent sheaves
on a Calabi-Yau must be replaced by coherent sheaves on a certain
`noncommutative deformation' of the Calabi-Yau. By contrast, an
algebraic description of the A-model branes, if it exists, should involve a
noncommutative algebra even for a vanishing B-field.
video
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