Seminar on Geometric Complex Analysis

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Date, time & place Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Kengo Hirachi, Shigeharu Takayama


10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Akira Kitaoka (The Univ. of Tokyo)
Analytic torsions associated with the Rumin complex on contact spheres (Japanese)
[ Abstract ]
The Rumin complex, which is defined on contact manifolds, is a resolution of the constant sheaf of $\mathbb{R}$ given by a subquotient of the de Rham complex. In this talk, we explicitly write down all eigenvalues of the Rumin Laplacian on the standard contact spheres, and express the analytic torsion functions associated with the Rumin complex in terms of the Riemann zeta function. In particular, we find that the functions vanish at the origin and determine the analytic torsions.