Humboldt Universität zu Berlin
Mathem.-Naturwissenschaftliche Fakultät
Institut für Mathematik

Forschungsseminar "Arithmetische Geometrie"

Wintersemester 2016/17

Das Forschungsseminar findet dienstags in der Zeit von 13:15 - 15:00 Uhr in der Rudower Chaussee 25, 12489 Berlin-Adlershof, Raum 3.006 (Haus 3, Erdgeschoss), statt.

18.10.2016 Vorbesprechung
25.10.2016 kein Seminar
01.11.2016 Antareep Mandal (HU Berlin)
Title: Uniform sup-norm bound for the average over an orthonormal basis of Siegel cusp forms
Abstract: This talk updates our progress towards obtaining the optimal sup-norm bound for the average over an orthonormal basis of Siegel cusp forms by relating it to the discrete spectrum of the heat kernel of the Siegel-Maass Laplacian. In particular, we study Maass operators and generalize the relation between the cusp forms and the Maass forms in higher dimensions along with presenting an interesting trick to obtain the heat kernel corresponding to the Maass Laplacians by adapting the "method of images" used to obtain the heat kernel corresponding to the Laplace-Beltrami operator.
08.11.2016 Erik Visse (University of Leiden)
Title: tba
Abstract: tba
15.11.2016 kein Seminar
22.11.2016 Remke Kloosterman (University of Padova)
Title: Monomial deformations of Delsarte Hypersurfaces and Arithmetic Mirror Symmetry
Abstract: In a recent preprint Doran, Kelly, Salerno, Sperber, Voight and Whitcher study for five distinct quartic Delsarte surfaces a one-parameter monomial deformation. Using character sums they find a remarkable similarity between the zeta functions of general members of each of the families.
In this talk we present another approach to prove these results. Moreover, we give a necessary and sufficient combinational criterion to check for a pair of monomial deformations of Delsarte hypersurfaces whether their zeta functions are essentially the same or not.


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