Humboldt-Universität zu Berlin
Mathem.-Naturwissenschaftliche Fakultät
Institut für Mathematik

Forschungsseminar "Algebraische Geometrie"

Wintersemester 2017/18

Das Forschungsseminar findet mittwochs in der Zeit von 13:00 - 15:00 Uhr in der Rudower Chaussee 25, 12489 Berlin-Adlershof, Raum 1.114, statt.

Seminar: Algebraic Geometry an der FU

18.10.2017 Frank Gounelas (HU Berlin)
Title: Measures of irrationality

Abstract: In this talk I will begin by introducing and discussing basic properties of various invariants associated to an arbitrary projective variety, that aim to measure how far it is from being rational, rationally connected or uniruled respectively. In the second part of the talk I will discuss recent work with Alexis Kouvidakis computing these invariants for the Fano scheme of lines of a cubic threefold, which is a general type surface classically studied by Fano, Clemens-Griffiths and others.
08.11.2017 Ariyan Javanpeykar (Uni Mainz)
Title: Hyperbolicity of moduli spaces

Abstract: The moduli space of curves of genus at least two is hyperbolic (in any reasonable sense of the word hyperbolic). I will explain what this means precisely, and what one could expect in higher dimensions.
15.11.2017 kein Seminar wegen der NoGAGS 2017 (s. u.)
16. - 17.11.2017 NoGAGS 2017 - North German Algebraic Geometry Seminar 2017
22.11.2017 Michael Gröchenig (FU Berlin)
Title: Rigid local systems

Abstract: An irreducible representation of an abstract group is called rigid, if it gives rise to an isolated point in the moduli space of all representations. Complex rigid representations are always defined over a number field. According to a conjecture by Simpson, for fundamental groups of smooth projective varieties one should expect furthermore integrality. I will report on joint work with H. Esnault where we prove this for so-called cohomologically rigid representations. Our argument is mostly arithmetic and passes through fields of positive characteristic and the p-adic numbers.
29.11.2017 Marc Levine (Uni Duisburg-Essen)
Title: A calculus of characteristic classes in Witt cohomology

Abstract: As part of a program to develop an enumerative geometry with values in quadratic forms, we would like to have a practical calculus for suitable characteristic classes of vector bundles. One promising setting is via the theory of Pontryagin/Euler classes the cohomology of the sheaf of Witt groups. We describe the main points of this calculus: the SL_2-splitting principle of Ananyevskiy, an extension to a splliting principle for reduction to the normaliser of the torus in SL_2, and the computation of Pontryagin/Euler classes of symmetric powers of SL_2-bundles. As an application, we compute the quadratic form ``counting’’ the lines on a smooth hypersurface of degree 2d-1 in P^{d+1}.
17.01.2018 13:00 - 14:00 Filippo Viviani (Uni Roma Tre)
Title: Tba

Abstract: Tba
14:30 - 15:30 Alexis Kouvidakis (Uni of Crete)
Title: Tba

Abstract: Tba
31.01.2018 Margherita Lelli-Chiesa (Universita de L'Aquila)
Title: To be announced.

Abstract: To be announced.
01.02.2018 (DONNERSTAG) Einstein Lectures in Algebraic Geometry: Rahul Pandharipande (ETH Zürich), Johannes Schmitt (ETH Zürich) und Jason van Zelm (Liverpool/HU Berlin)
Ort: Raum 021, IRIS-Haus, Zum Großen Windkanal 6, 12489 Berlin
11:00, Johannes Schmitt: Tba

Abstract: Tba
14:00, Rahul Pandharipande: Tba

Abstract: Tba
15:30, Jason van Zelm: Tba

Abstract: Tba
14.02.2018 Francesco Russo (Università Catania Italia)
Title: To be announced.

Abstract: To be announced.


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