## 東京無限可積分系セミナー

開催情報 土曜日　13:30～16:00　数理科学研究科棟(駒場) 117号室 神保道夫、国場敦夫、山田裕二、武部尚志、高木太一郎、白石潤一 https://www.ms.u-tokyo.ac.jp/~takebe/iat/index-j.html

### 2006年06月06日(火)

13:30-14:30   数理科学研究科棟(駒場) 117号室
6月6日(火), 7日(水)の両日で行われます。
Leon Takhtajan 氏 (SUNY)
A local index theorem for families of $\\bar\\partial$-operators and moduli of parabolic vector bundles
[ 講演概要 ]
We extend our previous work on local index theorem for families of $\\bar\\partial$-operators on punctured Riemann surfaces (Comm. Math. Phys. 137 (1991), 399-426) and for families of $\\bar\\partial$-operators on endomorphism bundles of stable vector bundles over a compact Riemann surface (Math. USSR Izvestia 35 (1990), 83-100) to the case of stable parabolic vector bundles over a Riemann surface. The result is an explicit formula for the first Chern form of the canonical line bundle to the moduli space stable parabolic bundles with the Quillen's type metric. The derivation uses Mehta-Seshadri theorem and spectral theory of automorphic functions on the Lobatchevsky plane with the unitary representation. This is a joint work with P. Zograf.