Wintersemester 2010/11
19.10.2010  Vorbesprechung 
26.10.2010  Nahid Walji (HU Berlin) 
The Lang Trotter conjecture on average and congruence class bias  
02.11.2010  Anilatmaja Aryasomayajula (HU Berlin) 
Bounds on canonical Green's function  
09.11.2010  Stefan Keil (HU Berlin) 
The SatoTate Conjecture and the LFunction Method  
Abstract: In the last years Tayler et al. showed that the mth symmetric power of the Lfunctions of ladic Galoisrepresentations of an elliptic curve over QQ are potential automorphic. Therefore they fulfill certain meromorphic properties which are sufficient to use the so called Lfunction method to prove the SatoTate Conjecture (over QQ). We will talk in general about equidistribution and the Lfunction method and its application (e.g. the prove of Chebotarev's density theorem). We will explain why one can apply the Lfunction method for the SatoTate Conjecture. If there is time we will discuss the exceptional case of CMcurves.  
16.11.2010  Remke Kloosterman (HU Berlin) 
MordellWeil groups, Syzygies and BrillNoether theory  
Abstract:
For a particular class of elliptic threefolds with base P^2 we discuss
the relation between the rank of the MordellWeil group and the syzygies
of the singular locus of the discriminant curve of the elliptic fibration.
From this we deduce that for each high rank elliptic threefold we find examples of triples (g,k,n) such that the locus {[C] \in M_g  C admits a g^2_{6k} and the image of C has at least n cusps} has much bigger dimension than expected. 

23.11.2010  kein Seminar 
30.11.2010  Luis Dieulefait (Universitat de Barcelona) 
Modularity by propagation: Serre's conjecture and nonsolvable base change for GL(2)  
07.12.2010  Jose Ignacio Cogolludo (Zaragoza) 
On the connection between the topology of plane curves, the position of their singular points, and elliptic threefolds  
14.12.2010  Brendan Creutz (Univ. Bayreuth) 
Large TateShafarevich Groups  
Abstract: For an abelian variety A over a number field k, the TateShafarevich group of A/k parameterizes principal homogeneous spaces for A/k which have points over every completion of k. It is conjectured that this group is finite. However, there are several results in the literature which show that this group can be arbitrarily large. We will discuss some of these and show, in particular, that the ptorsion in the TateShafarevich group of any principally polarized abelian variety over k is unbounded as one ranges over extensions of k of degree O(p).  
04.01.2011  kein Seminar 
11.01.2011  Jens Funke (Univ. of Durham/BMS) 
On a theorem of Hirzebruch and Zagier  
18.01.2011  Jay Jorgenson (City College New York/BMS) 
Progress in bounds for Fourier coefficients of modular forms  
25.01.2011  Barbara Jung (HU Berlin) 
On the volume formula of the fundamental domain of the Siegel modular group  
01.02.2011  Jürg Kramer (HU Berlin) 
On a result of HoffsteinLockhart  
08.02.2011  Lejla Smajlović (Univ. of Sarajevo) 
On the distribution of the zeros of the derivative of the Selberg zeta function  
15.02.2011  AnnaMaria von Pippich (HU Berlin) 
The Weierstrass $\wp$function and transcendence questions  
Freitag  
18.03.2011  Alex Bartel (POSTECH, Pohang Univ., Korea) 
Some applications of integral group representations in number theory  
Abstract: Certain quotients of regulators of number fields or of abelian varieties can be interpreted as purely representation theoretic invariants. I will introduce a technique for analysing such invariants and will apply it to some questions on the arithmetic of number fields and of elliptic curves. One of the main results will be a curious identity linking the fine integral Galois module structure of certain units of number fields and of MordellWeil groups to sizes of class groups and of TateShafarevich groups, respectively. There will be plenty of examples along the way, and also some mystery and food for future thought. The talk will be accessible to graduate students with a very modest background in number theory and ordinary representation theory.  