Spring 2017

The Algebraic Geometry and Differential Topology group of the Alfréd Rényi Institute of Mathematics and the Geometry and its Interfaces group of IST Austria organize a joint seminar, alternatingly in Budapest and Vienna. All are welcome to attend.

Upcoming and past seminars

Friday 21 April 2017, Erwin Schrödinger-Institut, Boltzmanngasse 9a, Boltzmann Lecture Hall Map

  • 2:00--3:00 Yuri Tschinkel (Courant Institute, New York): Rational points and rational varieties

    I wil discuss connections between geometry and arithmetic, with implications for both sides.

  • 3:30--4:30 Anton Mellit (IST Austria): Cohomology of character varieties

    Character varieties are spaces that parametrize representations of fundamental groups of Riemann surfaces with punctures, with prescribed local monodromies around the punctures. Via Simpson's correspondence, they are diffeomorphic to moduli spaces of semistable Higgs bundles. A conjecture of Hausel, Letellier and Rodriguez-Villegas gives an explicit formula for the Betti numbers of these spaces, which hints on a connection with Hilbert schemes. In another development Gorsky, Oblomkov, Rasmussen and Shende conjecture a connection between Hilbert schemes and homological invariants of torus knots and links. The purpose of this talk is to show that certain cell decompositions of character varieties produce an explicit connection between the two conjectures, allows us to calculate the cohomologies in some examples, and implies the so-called curious hard Lefschetz property.

    Friday 10 March 2017, Rényi Institute, Main Lecture Hall

  • 2:00--3:00 Gábor Farkas (Humboldt-Universität Berlin): Compact moduli of holomorphic differentials

    The moduli space of holomorphic differentials (with prescribed zeros and poles) on nonsingular curves is not compact since the curve may degenerate. I will discuss a compactification of these strata in the moduli space of Deligne-Mumford stable pointed curves, which includes the space of canonical divisors as an open subset. The theory leads to geometric/combinatorial constraints on the closures of the strata of holomorphic differentials and as a consequence, one can determine the cohomology classes of the strata. This is joint work with Rahul Pandharipande.

  • 3:30--4:30 Tamás Szamuely (Rényi Institute): Homotopy groups of algebraic homogeneous spaces

    According to a classical theorem of Elie Cartan, compact Lie groups have trivial second homotopy. I shall explain the analogue of this result in algebraic geometry (in all characteristics). I shall also show how to compute low-degree homotopy groups of homogeneous spaces of algebraic groups in terms of invariants of the group and the stabilizer. This is joint work with Cyril Demarche.