Jean-Michel Bismut (Institut de Mathématique d'Orsay): A conversation with analytic torsion
Thursday, 05.09.2024 14:00 im Raum M3
In this survey talk, we will review aspects of analytic torsion in real and
complex geometry.
Analytic torsion was introduced by Ray and Singer as a spectral invariant
(a determinant) of the Hodge Laplacian in real and complex geometry. It
has been used to define metrics on certain line bundles, the determinants of
the cohomology.
In real geometry, Ray and Singer conjectured that analytic torsion coincides
with Reidemeister torsion, a combinatorial invariant. In 1978, the
conjecture was established by Cheeger and M¨uller.
In complex geometry, Ray and Singer computed explicitly the analytic
torsion of elliptic curves. Quillen used analytic torsion to define a metric
on the determinant of the cohomology of a holomorphic line bundle on a
Riemann surface, and proved the relevant curvature theorem.
These were the starting points of a considerable body of work, whose
scope is to make analytic torsion a natural object in suitable theories of
secondary invariants, and also to find applications of analytic torsion in
topology, number theory and dynamical systems.
The purpose of our talk will be to address some of the above questions.
Angelegt am 26.08.2024 von Carolin Gietz
Geändert am 26.08.2024 von Carolin Gietz
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