Forschungsseminar "Arithmetische Geometrie"

Sommersemester 2010


13.04.2010 Vorbesprechung
20.04.2010  Anna von Pippich (HU Berlin)
Kronecker Limit Formula
27.04.2010 Alessandro Verra (Univ. Roma 3) (FS Algebraische Geometrie)
K3 surfaces and some moduli spaces related to curves
04.05.2010 Moritz Minzlaff (TU Berlin)
p-adic Cohomology of Curves and the Calculation of Zeta Functions
11.05.2010 Aaron Greicius (HU Berlin)
Abelian varieties with large adelic image of Galois
18.05.2010 Hartwig Mayer (HU Berlin)
Arakelov Theory on X_1(N)
25.05.2010 Hartwig Mayer (HU Berlin)
Arakelov theory on the modular curve X_1(N) (Part II)
01.06.2010 Stefan Müller-Stach (Univ. Mainz)
Numerical characterizations of Shimura subvarieties
08.06.2010 Andreas Stein (Univ. Oldenburg)
Elliptic Curves and Cryptography - Some (new) attacks to the elliptic curve discrete logarithm problem
Abstract: In recent years, elliptic curves have become objects of intense investigation because of their significance to public-key cryptography. The major advantage of ECC is that the cryptographic security is believed to grow exponentially with the length of the input parameters. This implies short parameters, short digital signatures, and fast computations. We provide a survey of elliptic curves over finite fields and their interactions with algorithmic number theory. Our main focus will be the discussion of various interesting attacks to the so-called elliptic curve discrete logarithm problem (ECDLP) and their mathematical background as well as their important impact on public-key cryptography. For several attacks, results on algebraic curves, especially hyperelliptic curves, are needed.
15.06.2010 Frank Monheim (Univ Tübingen)
Iterierte Integrale automorpher Formen
22.06.2010 kein Seminar
29.06.2010 Gérard Freixas (Univ. Paris 6)
Generalizing analytic torsion
06.07.2010 Morten Risager (Univ. Kopenhagen)
Non-vanishing of Fourier coefficients, Poincaré series, and central values of L-functions.
Abstract: We discuss Fourier coefficients of modular forms at cusps and non-cuspidal values. We show, without to much effort, that "generically" these coefficients are all non-vanishing. Yet it is highly non-trivial to prove that for a specific point z_0 the coefficients are non-vanishing. In the simplest case of the discriminant function the non-vanishing of Fourier coefficients at infinity is an old conjecture of Lehmer's. We show how the non-cuspidal analogue of this conjecture is true for certain CM-points. We then discuss how this has applications to non-vanishing of certain Poincaré series and to non-vanishing of certain central values of L-functions. This is joint work with Cormac O'Sullivan.
13.07.2010 kein Seminar