Humboldt Universität zu Berlin
Mathem.Naturwissenschaftliche Fakultät
Institut für Mathematik
Wintersemester 2014/15
Das Forschungsseminar findet mittwochs in der Zeit von 15:00  17:00 Uhr in der Rudower Chaussee 25, 12489 BerlinAdlershof, Raum 2.006 (Haus 2, Erdgeschoss), statt.
Seminar: Algebraic Geometry an der FU
15.10.2014  Mike Roth (Queen's University) 
Title: Roth’s theorem for arbitrary varieties  
Abstract: If X is a variety of general type defined over a number field k, then the BombieriLang conjecture predicts that the krational points of X are not Zariski dense. The conjecture is a prediction that a global condition on the canonical bundle (that it is ''generically positive'') implies a global condition about rational points. By the localglobal philosophy in geometry we should look for local influence of positivity on the accumulation of rational points. To do that we need measures of both these local phenomena. Let L be an ample line bundle on X, and x an algebraic point. The central theme of the talk is the interrelations between α_{x}(L), an invariant measuring the accumulation of rational points around x as gauged by L, and the Seshadri constant ε_{x}(L), measuring the local positivity of L near x. In particular, the classic approximation theorem of K. F. Roth on P^{1} generalizes as an inequality between α_{x} and ε_{x} valid for all projective varieties. 

22.10.2014  Thomas Krämer (Universität Heidelberg) 
Title: Generic vanishing theory, cubic threefolds and the monodromy of the Gauss map  
Abstract: To any closed subvariety of an abelian variety one may attach a reductive algebraic group in a natural way, using the Tannakian formalism. The arising groups are new invariants with interesting applications to the moduli of abelian varieties and the Schottky problem, but their proper geometric interpretation remains mysterious. After a motivated introduction to the Tannakian framework via a generalization of the GreenLazarsfeld vanishing theorems, I will show that for the theta divisor on the intermediate Jacobian of a smooth cubic threefold the Tannaka group is an exceptional group of type E_{6}. This is the first known exceptional case, and it suggests a surprising connection with the monodromy of the Gauss map and the FourierMukai transform for Higgs bundles.  
29.10.2014  Jarod Alper (Australian National University, zzt. HU Berlin) 
Title: A Luna etale slice theorem for algebraic stacks  
Abstract: Quotient stacks are a distinguished class of algebraic stacks which provide key intuition for studying the geometry of general algebraic stacks. It has long been believed that certain algebraic stacks are in some sense "locally" quotient stacks. In this talk, we will prove that this expectation holds by providing a description of the etale local structure of algebraic stacks near points with linearly reductive stabilizer. We will then discuss a number of striking applications of this result. This is joint work with Jack Hall and David Rydh.  
05.11.2014  kein Seminar 
19.11.2014  Michael Joswig (TU Berlin) 
Title: To be announced  
Abstract: To be announced.  