## 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. |