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Hypoelliptic Laplacian and twisted trace formula

Abstract : In this thesis, we give an explicit geometric formula for the twisted semisimple orbital integrals associated with the heat kernel on symmetric spaces. For that purpose, we use the method of the hypoelliptic Laplacian developed by Bismut. We show that our results are compatible with classical results in local equivariant index theory. We also use this formula to evaluate the leading term of the asymptotics as d -> + ∞ of the equivariant Ray-Singer analytic torsion associated with a sequence of flat vector bundles Fd on a compact locally symmetric space. We show that the leading term can be evaluated in terms of the W-invariants constructed by Bismut-Ma-Zhang.
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https://tel.archives-ouvertes.fr/tel-01841334
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Submitted on : Tuesday, July 17, 2018 - 11:31:09 AM
Last modification on : Wednesday, September 16, 2020 - 5:29:39 PM
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Bingxiao Liu. Hypoelliptic Laplacian and twisted trace formula. Differential Geometry [math.DG]. Université Paris-Saclay, 2018. English. ⟨NNT : 2018SACLS165⟩. ⟨tel-01841334⟩

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