Algebraic geometry and moduli seminar

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Autumn Semester 2013

Note: The highlighted event marks the next occurring event and events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

Date / Time Speaker Title Location
* 20 September 2013
ETH-ITS Mathematical physics meeting HG G 43 
27 September 2013
Dr. Alexandr Buryak
ETH Zürich
Dubrovin-Zhang hierarchy for Hodge integrals  HG G 43 
Abstract: In the talk I will explain that the generating series of the Hodge integrals over the moduli space of stable curves is a solution of a certain deformation of the KdV hierarchy. This hierarchy is constructed in the framework of the Dubrovin-Zhang theory of the hierarchies of the topological type.
4 October 2013
Iman Setayesh
IPM, Tehran
The combinatoriality of the kappa ring  HG G 43 
Abstract: In this talk I will discuss some results about the structure of the kappa ring of \bar{M}_{g,n}, and also some evidence for the combinatoriality of the kappa ring.
* 11 October 2013
FIM conference: Moduli space of curves HG G 43 
18 October 2013
Prof. Dr. Joseph Ayoub
Universität Zürich
Foliated cohomology HG G 43 
* 22 October 2013
Prof. Dr. Bernd Sturmfels
UC Berkeley and MPI Bonn
Tropicalization of Classical Moduli Spaces  HG G 19.2 
Abstract: Algebraic geometry is the study of solutions sets to polynomial equations. Solutions that depend on an infinitesimal parameter are studied combinatorially by tropical geometry. Tropicalization works especially well for varieties that are parametrized by monomials in linear forms. Many classical moduli spaces (for curves of low genus and few points in the plane) admit such a representation, and we here explore their tropical geometry. Examples to be discussed include the Segre cubic, the Igusa quartic, the Burkhardt quartic, and moduli spaces of marked del Pezzo surfaces. Matroids, hyperplane arrangements, and Weyl groups play a prominent role. Our favorites are E6, E7 and G32. This is joint work with Qingchun Ren and Steven Sam.
* 22 October 2013
Dr. Noah Giansiracusa
UC Berkeley
A non-reductive GIT approach to the effective cone of \M_{0,n}  HG G 19.2 
Abstract: I'll discuss joint work with Brent Doran and Dave Jensen in which we introduce a method for systematically studying the effective cone of \bar{M}_{0,n}. An "algebraic uniformization" of this space that we previously constructed translates information about all effective divisors (i.e. the Cox ring) into equivariant information about affine space, and to study effectivity of the rays spanned by divisor classes (i.e. the effective cone) translates naturally into non-reductive GIT stability analysis for this group action on affine space. We see in particular that there are numerous counterexamples to the Castravet-Tevelev hypertree conjecture on Eff(M_{0,n}) and that for all n \ge 7 a surprising discrepancy between the Cox ring and the effective cone emerges.
1 November 2013
Prof. Dr. Ivan Smith
Cambridge University
Quadratic differentials as stability conditions  HG G 43 
Abstract: We will explain why moduli spaces of meromorphic quadratic differentials on Riemann surfaces arise as spaces of stability conditions on triangulated categories. This talk reports on joint work with Tom Bridgeland.
15 November 2013
Prof. Dr. Stefan Kebekus
Université de Fribourg
Differential forms on singular spaces  HG G 43 
Abstract: The talk is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Applications will be discussed in some detail.
22 November 2013
Dr. Victoria Hoskins
Universität Zürich
Symplectic methods for non-reductive group actions  HG G 43 
Abstract: For complex reductive group actions, the geometric invariant theory quotient is often identified with the symplectic reduction for the associated maximal compact group via the Kempf-Ness Theorem. For non-reductive groups, one can ask whether there is an analogous symplectic picture. In this talk, we describe an approach for certain non-linear actions of the complex additive group on affine spaces. This is joint work in progress with Brent Doran.
29 November 2013
Prof. Dr. Bernd Siebert
Universität Hamburg
Generalized theta functions  HG G 43 
Abstract: The reconstruction theorem provides canonical maximal degenerations of polarized varieties with effective anticanonical divisor. The starting data is purely combinatorial, a cell complex of integral polyhedra along with charts for the affine structure at the vertices. The construction can be viewed as a non-linear generalization of toric geometry. In the talk I will explain how such degenerations come with a canonical basis of the homogeneous coordinate ring, which in the case of degenerations of abelian varieties agree with classical theta functions. I will also discuss why I believe that these generalized theta functions are the key to understanding many properties of varieties admitting maximal degenerations, including all of the properties relevant to mirror symmetry.
6 December 2013
Arend Bayer
University of Edinburgh
Birational geometry of moduli of sheaves on K3s via wall-crossing  HG G 43 
Abstract: A basic question about moduli spaces is to understand its birational geometry and relate it to the geometry of the underlying moduli problem. For moduli spaces of sheaves on K3 surfaces, this can be done completely systematically in terms of wall-crossing for deformations of Bridgeland stability conditions: any minimal model of the moduli space appears as a moduli space of Bridgeland-stable objects in some chamber. As applications, we can answer several open questions on these moduli spaces, e.g. we determine their nef cones, and we prove a conjecture on existence of Lagrangian fibrations. This is based on joint work with E. Macri.
13 December 2013
Dr. Christian Böhning
Universität Hamburg
Rationality problems: a bird's eye view HG G 43 

Organizers: Rahul Pandharipande 

Archive: SS 17  AS 16  SS 16  AS 15  SS 15  AS 14  SS 14  AS 13  SS 13  AS 12  SS 12  AS 11 

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Sat Jun 24 14:23:16 CEST 2017
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