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One more formula for the determinant of Laplacian on a compact Riemann surface

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Alexey Kokotov
Concordia University/MPI
Tue, 2017-10-17 14:00 - 15:00
MPIM Lecture Hall

Let $f$ be a meromorphic function on a compact Riemann surface $X$  and let $m$ be the standard round
metric of curvature $1$ on the Riemann sphere. Then the pullback $f^*m$ of $m$ under $f$ is a metric on
$X$ of curvature $1$ with conical singularities at the critical points of $f$. We study the $\zeta$-regularized
determinant of the Laplace operator on $X$ corresponding to the metric $f^*m$ as a functional on the moduli
space of pairs $(X, f)$  and derive an explicit formula for the functional. The talk is based on the joint work
with V. Kalvin (Concordia University).

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