AKLS Seminar on Modular Forms / Dutch Intercity Number Theory Seminar
What and When?
On 17 April 2009 the Aachen-(Bonn-)Koeln-Lille-Siegen(-Darmstadt-etc.) Seminar on Modular Forms will join forces with the Dutch Intercity Number Theory Seminar for a common activity at Utrecht University.
Programme
14:00-14:50 Matthias Schuett (University of Copenhagen)
K3 surfaces and modular forms
A classical construction of Shimura associates every Hecke eigenform of weight 2 with rational coefficients to an elliptic curve over Q. The converse statement that every elliptic curve over Q is modular, is the Taniyama-Shimura-Weil conjecture, proven by Wiles, Taylor et al. For higher weight, however, the opposite situation applies: Nowadays we know the modularity for wide classes of varieties, but it is an open problem whether all newforms of fixed weight with rational coefficients can be realised in a single class of varieties. I will present joint work with Noam Elkies that provides the first solution to the realisation problem in higher weight: We show that every newform of weight 3 with rational coefficients is associated to a singular K3 surface over Q.15:00-15:50 Gerard van der Geer (University of Amsterdam)
Siegel modular forms of low genera
The Eichler-Shimura theorem expresses elliptic modular forms in terms of cohomology of local systems. This theorem generalizes to higher genera. The cohomology of local systems can be explored by counting points over finite fields. We show how this can be succesfully applied to obtain a lot of information about Siegel modular forms of genus 2 and 3. This is joint work with Jonas Bergstroem and Carel Faber.16:00 Coffee/Tea
16:30-17:20 Don Zagier (MPIM Bonn/ CdF Paris)
On a U(3,1)-automorphic form of Ferapontov-Odesskii
We study an automorphic form from the paper "Integrable Lagrangians and modular forms" (arxiv:0707.3433) by E.V. Ferapontov and A.V. Odesskii on certains types of Lagrangians that are integrable by the method of hydrodynamic reductions.18:00 Dinner
Practical Information
- Talks will take place in room BBL 513 in the Buys Ballot Lab (BBL) at the North West Corner of Utrecht University Campus "de Uithof". The BBL, Minnaert, Geography and Mathematics (Wiskunde) buildings are connected by walking bridges. Room 513 is on the fifth floor of BBL. Please mind that reconstruction works are going on in other parts of the BBL building and you might not be able to take the direct route to the fifth floor. Information on how to reach "de Uithof" and the BBL building can be found here.
- If you need hotel at Utrecht, use the designated hotel websites, or contact the secretaries of the Mathematics Department at science.secr.mathinst at uu.nl.
- Send an email to science.secr.mathinst at uu.nl if you want to join for dinner, and indicate the number of persons (dinner - count on 30 euro - is at your own expenses unless you are a speaker, or another agreement has been made).