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, zzt. HU Berlin) 
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 
12.11.2014  kein Seminar 
19.11.2014  Michael Joswig (TU Berlin) 
Title: Moduli of Tropical Plane Curves  
Abstract: We study the moduli space of metric graphs that arise from tropical plane curves. There are far fewer such graphs than tropicalizations of classical plane curves. For fixed genus g, our moduli space is a stacky fan whose cones are indexed by regular unimodular triangulations of Newton polygons with g interior lattice points. It has dimension 2g+1 unless g≤3 or g=7. We compute these spaces explicitly for g≤5. Joint work with Sarah Brodsky, Ralph Morrison and Bernd Sturmfels.  
21.11.2014  Friday Complex Algebraic Geometry  A workshop on the occasion of Herbert Kurke's 75th birthday 
26.11.2014  Benjamin Bakker (HU Berlin) 
Title: Bounding torsion in geometric families of abelian varieties  
Abstract: A celebrated theorem of Mazur asserts that the order of the torsion part of the group of rational points of an elliptic curve over Q is absolutely bounded; it is conjectured that the same is true for abelian varieties over number fields K, though very little progress has been made in proving it. The natural geometric analog where K is replaced by the function field of a complex curve  known as the geometric torsion conjecture  is equivalent to the nonexistence of low genus curves in congruence towers of the moduli space of abelian varieties. In joint work with J. Tsimerman, we prove this conjecture for abelian varieties with real multiplication. We will discuss a general method for bounding the genera of curves in locally symmetric varieties using hyperbolic geometry to bound Seshadri constants and apply it to some related problems.  
03.12.2014  Mike Roth (Queens University, zzt. HU Berlin) 
Title: To be announced  
Abstract: To be announced.  
10.12.2014  Damiano Testa (University of Warwick) 
Title: To be announced  
Abstract: To be announced.  
17.12.2014  Andrew Kresch (Universität Zürich) 
Title: To be announced  
Abstract: To be announced.  
14.01.2015  Alessandro Verra (Università Roma Tre) 
Title: To be announced  
Abstract: To be announced.  