Humboldt Universität zu Berlin
Mathem.Naturwissenschaftliche Fakultät
Institut für Mathematik
Sommersemester 2018
Das Forschungsseminar findet dienstags in der Zeit von 13:15  15:00 Uhr in der Rudower Chaussee 25, 12489 BerlinAdlershof, Raum 3.006 (Haus 3, Erdgeschoss), statt.
24.04.2018  Ulf Kühn (Uni Hamburg) 
Title: Multiple qzeta values and period polynomials Abstract: We present a class of qanalogues of multiple zeta values given by certain formal qseries with rational coefficients. After introducing a notion of weight and depth for these qanalogues of multiple zeta values we will state a dimension conjecture for the spaces of their weight and depthgraded parts, which have a similar shape as the conjectures of Zagier and Broadhurst Kreimer for multiple zeta values. 

08.05.2018  Emre Sertöz (MPI Leipzig) 
Title: Computing and using periods of hypersurfaces Abstract: The periods of a complex projective manifold X are complex numbers, typically expressed as integrals, which give an explicit representation of the Hodge structure on the cohomology of X. Although they provide great insight, periods are often very hard to compute. In the past 20 years, an algorithm for computing the periods existed only for plane curves. We will give a different algorithm which can compute the periods of any smooth projective hypersurface and can do so with much higher precision. As an application, we will demonstrate how to reliably guess the Picard rank of quartic K3 surfaces and the Hodge rank of cubic fourfolds from their periods. 

15.05.2018  Robin de Jong (Uni Leiden) 
Title: To be announced Abstract: Tba 

22.05.2018  Roberto Laface (TU München) 
Title: Picard numbers of abelian varieties in all characteristics Abstract: I will talk about the Picard numbers of abelian varieties over C (joint work with Klaus Hulek) and over fields of positive characteristic. After providing an algorithm for computing the Picard number, we show that the set R_{g} of Picard numbers of gdimensional abelian varieties is not complete if g ≥ 2, that is there esist gaps in the sequence of Picard numbers seen as a sequence of integers. We will also study which Picard numbers can or cannot occur, and we will deduce structure results for abelian varieties with large Picard number. In characteristic zero we are able to give a complete and satisfactory description of the overall picture, while in positive characteristic there are several pathologies and open questions yet to be answered. 

12.06.2018  Giuseppe Ancona (Uni Strasbourg) 
Title: On the standard conjecture of Hodge type for abelian fourfolds Abstract: Let S be a surface and V be the Qvector space of divisors on S modulo numerical equivalence. The intersection product defines a non degenerate quadratic form on V. We know since the Thirties that it is of signature (1,d1), where d is the dimension of V. In the Sixties Grothendieck conjectured a generalization of this statement to cycles of any codimension on a variety of any dimension. In characteristic zero this conjecture is an easy consequence of Hodge theory but in positive characteristic almost nothing is known. Instead of studying these quadratic forms at the archimedean place we will study them at padic places. It turns out that this question is more tractable. Moreover, using a classical product formula on quadratic forms, the padic result will give us nontrivial informations on the archimedean place. For instance, we will prove the original conjecture for abelian fourfolds. 

17.07.2018  Javier Fresán (École Polytechnique) 
Title: To be announced Abstract: Tba 
Wintersemester 2007/08
