Kac-Moody algebras and derived algebraic geometry
Dienstag, 9.1.18, 09:15-10:15, SR 119, Eckerstr. 1
Kac-Moody algebras are usually used in physics to describe\nsome 2-dimensional conformal field theories. In this talk, we will introduce a new version of Kac-Moody algebras supposed to describe some physical phenomenons in higher dimensions.\n\nThose new algebras are in fact Lie algebras up to homotopy and we will study them using tools from algebraic topology and derived algebraic geometry.
Adelic formal neighborhoods and chiral modules with support
Donnerstag, 11.1.18, 09:15-10:15, SR 119, Eckerstr. 1
In this talk I will explain how one can use Ind-Pro objects\nto consider the restriction to formal and punctured formal\nneighborhoods of a subvariety Z in a variety X. This restriction functor can then be applied to give a description of modules for a chiral algebra over X supported at Z in terms of modules for an associative algebra object over Z. This is work in progress.\n\n\n(no worries, the speaker will explain what a "chiral algebra" is...)
Unlikely intersections between isogeny orbits and curves
Freitag, 19.1.18, 10:15-11:15, Hörsaal FRIAS, Albertsstr. 19
In the spirit of the Mordell-Lang conjecture, we consider the intersection of a curve in a family of abelian varieties with the images of a finite-rank subgroup of a fixed abelian variety A0 under all isogenies between A0 and some member of the family. After excluding certain degenerate cases, we can prove that this intersection is finite. This proves the so-called André-Pink-Zannier conjecture in the case of curves. We can even allow translates of the finite-rank subgroup by abelian subvarieties of controlled dimension if we strengthen the degeneracy hypotheses suitably. In my talk, I will try to explain the motivation for this problem and give an outline of the proof, which follows a strategy due to Pila-Zannier.
On the motivic Tamagawa number of number fields
Donnerstag, 25.1.18, 10:30-11:30, Hörsaal FRIAS, Albertstr. 19
The Tamagawa number of a linear algebraic group is a classical arithmetic invariant.\nIt was computed and related to special values of L-functions in the second half of the 20th century.\nIn 1990 Bloch and Kato proposed a Tamagawa number of a (certain kind of) motive, related it to special L-values of motives and stated a conjecture on their value in the spirit of the classical case. We will discuss motivic Tamagawa numbers for the (seemingly easiest) unknown case, namely the twisted motive of a number field. I will present precise formulas relating these two notions of Tamagawa numbers to one another and to Borel regulators.
The Koszul duality between D-modules and Omega-modules
Freitag, 26.1.18, 10:30-11:30, Hörsaal FRIAS, Albertstr. 19
Koszul duality between D-modules and Omega-modules (dg modules over the algebraic de Rham complex) has first been studied by Kapranov, and subsequently by various authors including Beilinson-Drinfeld and Positselski. In this talk, I will report on work in progress (joint with Dmitri Pavlov) on a refinement of Koszul duality. An application of this refinement is a presentation of the derived pushforward and pullback functors for D-modules which avoids the usual mixing of right and left adjoints.
Cohomological properties of OT manifolds
Dienstag, 30.1.18, 11:00-12:00, SR 119