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Institute for the Physics and Mathematics of the UniverseWPI

IPMU Seminar on Mathematical Physics

Date: Monday, December 10 17:00 - 18:30
Place: Room 002, Mathematical Sciences Building Komaba Campus, The University of Tokyo
Lecturer: Dmitry Kaledin (Steklov Institute and Univ. of Tokyo)
Title: Deligne conjecture and the Drinfeld double
Abstract: Deligne conjecture describes the structure which exists on the Hochschild cohomology $HH(A)$ of an associative algebra $A$. Several proofs exists, but they all combinatorial to a certain extent. I will present another proof which is more categorical in nature (in particular, the input data are not the algebra $A$, but rather, the tensor category of $A$-bimodules). Combinatorics is still there, but now it looks more natural -- in particular, the action of the Gerstenhaber operad, which is know to consist of homology of pure braid groups, is induced by the action of the braid groups themselves on the so-called "Drinfeld double" of the category $A$-bimod.
If time permits, I will also discuss what additional structures appear in the Calabi-Yau case, and what one needs to impose to insure Hodge-to-de Rham degeneration.