Infinite Analysis Seminar Tokyo

Seminar information archive ~12/01Next seminarFuture seminars 12/02~

Date, time & place Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.)


13:30-14:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Leon Takhtajan (SUNY)
A local index theorem for families of $\\bar\\partial$-operators and moduli of parabolic vector bundles
[ Abstract ]
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.