Sommersemester 2009
28.04.2009  Hartwig Mayer (HU Berlin) 
Arithmetic selfintersection number of the dualizing sheaf on modular curves  
05.05.2009  Anna Posingies (HU Berlin) 
A Kronecker Limit Formula for Fermat Curves  
19.05.2009  Shabnam Akhtari (MPI Bonn) 
Representation of Integers by Binary Forms  
Abstract: Suppose F(x,y) is an irreducible binary form with integral coefficients, degree n >= 3 and discriminant D_F \neq 0. Let h be an integer. The equation F(x,y)=h has finitely many solutions in integers x and y. I shall discuss some different approaches to the problem of counting the number of integral solutions to such equations. I will give upper bounds upon the number of solutions to the Thue equation F(x,y)= h. These upper bounds are derived by combining methods from classical analysis and geometry of numbers. The theory of linear forms in logarithms plays an essential rule in this study.  
26.05.2009  Anil Aryasomayajula (HU Berlin) 
A fundamental identity of metrics on hyperbolic Riemann surfaces of finite volume  
02.06.2009  Ronald van Luijk (Leiden) 
Explicit twocoverings of Jacobians of genus two  
23.06.2009  Remke Nanne Kloosterman (HU Berlin) 
Average rank of elliptic nfolds  
Abstract:
For elliptic curves over number fields it is conjectured that
the half the curves have rank 1 and half the curves have rank 0.
Similarly, if C/F_q is a curve then it is conjectured the half the
elliptic curves over F_q(C) have rank 0 and half the curves have rank 1.
In this talk we show that the situation is different if one considers elliptic curves over F_q(V), with dim(V)>1. 

07.07.2009  Anna von Pippich (HU Berlin) 
The arithmetic of elliptic Eisenstein series  
14.07.2009  H. Shiga (Chiba University) 
A Jacobi type formula in two variables with application to a new AGM  
J. Estrada Sarlabous (Havana)  
Nonhyperelliptic curves of genus 3 and the DLP  
Abstract:
The index calculus algorithm of Gaudry, Thom$\acute{e}$,
Th$\acute{e}$riault, and Diem makes possible to solve the Discrete
Logarithm Problem (DLP) in the Jacobian varieties of hyperelliptic
curves of genus 3 over $F_q$ in $O(q^{4/3})$ group operations. On
the other hand, applied to Jacobian varieties of nonhyperelliptic
curves of genus 3 over $F_q$, the index calculus algorithm of Diem
requires only $O(q)$ group operations to solve the DLP.
This vulnerability to faster index calculus attacks of the nonhyperelliptic curves of genus 3 has discouraged the use of Jacobian varieties of nonhyperelliptic curves of genus 3 as a basis of DLPbased cryptosystems. A recent work of B. Smith introduces the idea of exploiting this vulnerability to faster index calculus attacks of the nonhyperelliptic curves of genus 3 to discard a nonnegligable subset of hyperelliptic curves of genus 3 over $F_q$. I would like to expose some highlights of this approach of B. Smith (the mathematical ingredients are nice: isogenies of Jacobian varieties, Recilla's trigonal construction, etc.) and to discuss the interest of studying nonhyperelliptic curves of genus 3 in the context of DLPbased cryptosystems. 
