## Kavli IPMU Komaba Seminar

開催情報 月曜日　16:30～18:00　数理科学研究科棟(駒場) 002号室 河野 俊丈

### 2007年12月10日(月)

17:00-18:30   数理科学研究科棟(駒場) 002号室
Dmitry Kaledin 氏 (Steklov Institute and The University of Tokyo)
Deligne conjecture and the Drinfeld double.
[ 講演概要 ]
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.