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Research talks;Partial Differential Equations;Geometry;Mathematical Physics

Polyakov’s formula expresses a difference of zeta-regularized determinants of Laplace operators, an anomaly of global quantities, in terms of simple local quantities. Such a formula is well known in the case of closed surfaces (Osgood, Philips, & Sarnak 1988) and surfaces with smooth boundary (Alvarez 1983). Due to the abstract nature of the definition of the zeta-regularized determinant of the Laplacian, it is typically impossible to compute an explicit formula. Nonetheless, Kokotov (genus one Kokotov & Klochko 2007, arbitrary genus Kokotov 2013) demonstrated such a formula for polyhedral surfaces ! I will discuss joint work with Clara Aldana concerning the zeta regularized determinant of the Laplacian on Euclidean domains with corners. We determine a Polyakov formula which expresses the dependence of the determinant on the opening angle at a corner. Our ultimate goal is to determine an explicit formula, in the spirit of Kokotov’s results, for the determinant on polygonal domains. Polyakov’s formula expresses a difference of zeta-regularized determinants of Laplace operators, an anomaly of global quantities, in terms of simple local quantities. Such a formula is well known in the case of closed surfaces (Osgood, Philips, & Sarnak 1988) and surfaces with smooth boundary (Alvarez 1983). Due to the abstract nature of the definition of the zeta-regularized determinant of the Laplacian, it is typically impossible to compute an ...

35K08 ; 58C40 ; 58J52

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- xix, 517 p.
ISBN 978-0-8218-4661-2

Mathematical surveys and monographs , 0163

Localisation : Collection 1er étage

géométrie différentielle globale # flot de Ricci # variétés de Riemann # entropie de Perelman

53C44 ; 53C25 ; 58J35 ; 35K55 ; 35K05 ; 35K10 ; 53C21 ; 35K08

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