Archive: Number Theory Seminar HS10
Time: Friday at 14.15
Place: HWZ (HG G43)
Autumn Semester 2010
| Date |
Speaker |
Title |
Time |
Location |
| 10-sep-2010 (fri) |
Bernhard Heim
|
On the coincidence of Borcherds and Saito-Kurokawa lifts
|
14:15-15:15 |
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. |
| Speakers: |
Prof. Dr. Bernhard Heim
(MPI Bonn / German University of Technology, Oman)
Invited by: Ö. Imamoglu
|
|
| 24-sep-2010 (fri) |
Emmanuel Kowalski
|
Spectral gaps and arithmetic geometry
|
14:15-15:15 |
HG G 43 |
| Speakers: |
Prof. Dr. Emmanuel Kowalski
(ETH Zürich, Switzerland)
E-Mail:
|
|
| 22-oct-2010 (fri) |
Patrick Tuen Wai Ng
|
Smale's mean value conjecture and the amoebae
|
14:15-15:15 |
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. |
| Speakers: |
Prof. Dr. Patrick Tuen Wai Ng
(University of Hong Kong)
Invited by: G. Wüstholz
E-Mail:
|
|
| 29-oct-2010 (fri) |
Abhishek Saha
|
Local spectral equidistribution for Siegel modular forms
|
14:15-15:15 |
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. |
| Speakers: |
Dr. Abhishek Saha
(ETH Zürich, Switzerland)
E-Mail:
|
|
| 19-nov-2010 (fri) |
Dimitar Petkov Jetchev
|
New Upper Bounds on the Shafarevich-Tate Group of Elliptic Curves of Rank 1 Over Imaginary Quadratic Fields
|
14:15-15:15 |
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. |
| Speakers: |
Dr. Dimitar Petkov Jetchev
(EPFL)
Invited by: E. Kowalski
|
|
| 3-dec-2010 (fri) |
Winfried Kohnen
|
Generalized modular functions
|
14:15-15:15 |
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. |
| Speakers: |
Prof. Dr. Winfried Kohnen
(University of Heidelberg)
Invited by: G. Wüstholz
|
|
| 10-dec-2010 (fri) |
Peter Jossen
|
The unipotent Mumford-Tate conjecture for 1-motives
|
14:15-15:15 |
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. |
| Speakers: |
Dr. Peter Jossen
(University of Regensburg)
Invited by: G. Wüstholz
|
|
| 17-dec-2010 (fri) |
Johannes Huisman
|
Real projective hypersurfaces and arrangements of pseudo-hyperplanes
|
14:15-15:15 |
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.) |
| Speakers: |
Prof. Dr. Johannes Huisman
(Université de Bretagne Occidentale)
Invited by: G. Wüstholz
|
|
The seminar is organized by G. Wüstholz, R. Pink, Ö. Imamoglu, E. Kowalski and C. Fuchs. If you have any questions send an email to one of the organizers.
