Departement Mathematik

Number theory seminar

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Herbstsemester 2010

Datum / Zeit Referent:in Titel Ort
10. September 2010
14:15-15:15 		Prof. Dr. Bernhard Heim
MPI Bonn / German University of Technology, Oman
Details

Number Theory Seminar

Titel On the coincidence of Borcherds and Saito-Kurokawa lifts
Referent:in, Affiliation Prof. Dr. Bernhard Heim, MPI Bonn / German University of Technology, Oman
Datum, Zeit 10. September 2010, 14:15-15:15
Ort HG G 43
Abstract In this talk we consider lifts on the Siegel three fold. Motivated from physics, string theory, it is an interesting question to study these multiplicative (Borcherds lifts) and additive lifts (Saito-Kurokawa lifts, also called Maass Spezialschar) and their coincidence.
On the coincidence of Borcherds and Saito-Kurokawa liftsread_more
HG G 43
24. September 2010
14:15-15:15 		Prof. Dr. Emmanuel Kowalski
ETH Zurich, Switzerland
Details

Number Theory Seminar

Titel Spectral gaps and arithmetic geometry
Referent:in, Affiliation Prof. Dr. Emmanuel Kowalski, ETH Zurich, Switzerland
Datum, Zeit 24. September 2010, 14:15-15:15
Ort HG G 43
Spectral gaps and arithmetic geometry
HG G 43
22. Oktober 2010
14:15-15:15 		Prof. Dr. Patrick Tuen Wai Ng
University of Hong Kong
Details

Number Theory Seminar

Titel Smale's mean value conjecture and the amoebae
Referent:in, Affiliation Prof. Dr. Patrick Tuen Wai Ng, University of Hong Kong
Datum, Zeit 22. Oktober 2010, 14:15-15:15
Ort HG G 43
Abstract We introduce the theory of amoebae to the study of Smale's mean value conjecture and prove a necessary and sufficient condition for the conjecture to be true. By considering certain Max-Min and Min-Max problem on hypersurfaces in C^n, we lead to a dual mean value conjecture and prove the existence of an extremal polynomial for this dual conjecture.
Smale's mean value conjecture and the amoebaeread_more
HG G 43
29. Oktober 2010
14:15-15:15 		Dr. Abhishek Saha
ETH Zurich, Switzerland
Details

Number Theory Seminar

Titel Local spectral equidistribution for Siegel modular forms
Referent:in, Affiliation Dr. Abhishek Saha, ETH Zurich, Switzerland
Datum, Zeit 29. Oktober 2010, 14:15-15:15
Ort HG G 43
Abstract Fix a prime p and consider the eigenvalues (more generally the Satake parameters) of the pth Hecke operator acting upon the space of Siegel cusp forms of genus 2, level 1 and growing weight k. I will talk of my recent work, joint with Emmanuel Kowalski and Jacob Tsimerman, where we prove that these eigenvalues, weighted appropriately, get equidistributed with respect to a certain measure.
Local spectral equidistribution for Siegel modular formsread_more
HG G 43
19. November 2010
14:15-15:15 		Dr. Dimitar Petkov Jetchev
EPFL
Details

Number Theory Seminar

Titel New Upper Bounds on the Shafarevich-Tate Group of Elliptic Curves of Rank 1 Over Imaginary Quadratic Fields
Referent:in, Affiliation Dr. Dimitar Petkov Jetchev, EPFL
Datum, Zeit 19. November 2010, 14:15-15:15
Ort HG G 43
Abstract Using a refinement of Kolyvagin's Euler system methods, we obtain improved upper bounds on the order of the Shafarevich-Tate group as predicted by the Birch and Swinnerton-Dyer conjectural formula for elliptic curves of rank 1 over imaginary quadratic fields. Our approach makes use of certain reduction properties of Heegner points on the bad fibers of the Deligne-Rapoport (and more generally, Katz-Mazur) integral models of modular curves, as well as a combinatorial refinement of the Euler system arguments. Our approach leads to an alternative proof of a recent result of Ciperiani-Wiles on the existence of solvable points on genus one curves with local points everywhere. We also obtain new results about Selmer groups of elliptic curves of analytic rank 0 over Q and the Euler system of Kato. Finally, we state some open conjectures about elliptic curves of high analytic rank.
New Upper Bounds on the Shafarevich-Tate Group of Elliptic Curves of Rank 1 Over Imaginary Quadratic Fieldsread_more
HG G 43
3. Dezember 2010
14:15-15:15 		Prof. Dr. Winfried Kohnen
University of Heidelberg
Details

Number Theory Seminar

Titel Generalized modular functions
Referent:in, Affiliation Prof. Dr. Winfried Kohnen, University of Heidelberg
Datum, Zeit 3. Dezember 2010, 14:15-15:15
Ort HG G 43
Abstract Generalized modular functions (GMF) are holomorphic functions on the complex upper half-plane, meromorphic at the cusps, that satisfy the usual transformation formula of a modular function, however with the important exception that the character need not be of finite order or even unitary. The theory was partly motivated from CFT in Physics. In this talk I will report on recent results obtained jointly with G. Mason on the character and Fourier coefficients of a GMF.
Generalized modular functionsread_more
HG G 43
10. Dezember 2010
14:15-15:15 		Dr. Peter Jossen
University of Regensburg
Details

Number Theory Seminar

Titel The unipotent Mumford-Tate conjecture for 1-motives
Referent:in, Affiliation Dr. Peter Jossen, University of Regensburg
Datum, Zeit 10. Dezember 2010, 14:15-15:15
Ort HG G 43
Abstract Around 1975 A.Schinzel and P.Erdös raised the question whether or not every finitely generated subgroup of Q^* is characterised by its reduction modulo p for all but finitely prime numbers p. The question was answered by Schinzel: "Yes" for n=1 and "No" for n>1. In 2002 W.Gajda asked the analogous question for abelian varieties. Gajdas question was answered only recently by A.Perucca and myself: "Yes" for geometrically simple abelian varieties, and generally "No" for composite abelian varieties. At the heart of the proofs lies the computation of the image of the absolute Galois group in l-adic representations associated with 1-motives (I will explain what that is). A version of the Mumford-Tate conjecture predicts what that image is, up to finite index. I will show that the "unipotent part" of this conjecture holds true, and how it can be used for the local-global statements.
The unipotent Mumford-Tate conjecture for 1-motivesread_more
HG G 43
17. Dezember 2010
14:15-15:15 		Prof. Dr. Johannes Huisman
Université de Bretagne Occidentale
Details

Number Theory Seminar

Titel Real projective hypersurfaces and arrangements of pseudo-hyperplanes
Referent:in, Affiliation Prof. Dr. Johannes Huisman, Université de Bretagne Occidentale
Datum, Zeit 17. Dezember 2010, 14:15-15:15
Ort HG G 43
Abstract A pseudo-hyperplane is a topological submanifold of real projective space that is isotopic to a hyperplane. An irreducible real projective hypersurface of degree d can have at most d-2 pseudo-hyperplanes, if d is greater than or equal to 2. We study those hypersurfaces that have exactly d-2 pseudo-hyperplanes, and determine the arrangements of pseudo-hyperplanes they can have. (This is joint work with Nicolas Halter.)
Real projective hypersurfaces and arrangements of pseudo-hyperplanesread_more
HG G 43

Organisatoren:innen: Clemens Fuchs, Özlem Imamoglu, Emmanuel Kowalski, Richard Pink, Gisbert Wüstholz

Archiv: FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 FS 21 HS 20 FS 20 HS 19 FS 19 HS 18 FS 18 HS 17 FS 17 HS 16 FS 16 HS 15 FS 15 HS 14 FS 14 HS 13 FS 13 HS 12 FS 12 HS 11 FS 11 HS 10 FS 10 HS 09

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