UHH > Fakultäten > MIN-Fakultät > Mathematik > Moduli spaces › Program

Hilfe - Suche

Schedule Monday, August 12 Tuesday, August 13 Wednesday, August 14 Thursday, August 15 Friday, August 16 9:00-9:30: Registration 9:30--10:30: Flenner I Donagi II Grushevsky II Farkas I Dolgachev III Coffee break/Reg. Coffee break Coffee break Coffee break Coffee break 11:00-12:00 Aspinwall I Flenner III Donagi III Flenner IV Farkas III 12:15-13:15 Grushevsky I Dolgachev I Aspinwall III Dolgachev II Grushevsky III Lunch break Lunch break Lunch break Lunch break Lunch break 15:00-16:00: Donagi I Pandharipande I Pandharipande II Pandharipande III Coffee break Coffee break Coffee break 16:30-17:30: Flenner II Aspinwall II Farkas II 16:30-18:45: Boat trip 19:00-??: Conference dinner Abstracts: The moduli space of complexified Kähler forms and mirror symmetry Paul Aspinwall (Duke University) Abstract: The moduli space of complexified Kähler forms on a Calabi-Yau threefold, which is given as a hypersurface in a toric variety, is reviewed. A natural model of the compactified moduli space is given in terms of toric geometry and the "secondary fan". We will discuss some interpretations of this compactified moduli space and examine associated monodromy on categories in homological mirror symmetry. These lectures will hopefully be self-contained requiring no previous knowledge of toric geometry or derived categories. Moduli of K3 surfaces (with emphasis on families of K3's with Picard number 19 and more) Igor Dolgachev (University of Michigan) Abstract: In my lectures I will try to explain the main features of the theory of periods of lattice polarized K3 surfaces with emphasis on the periods of families of K3 surfaces with Picard number at least 19. The mirror duality relates these families with the families of K3 surfaces with a fixed polarization class. I will also explain an idea of toroidal compactification of the moduli space of K3 surfaces. Moduli spaces of super Riemann surfaces and perturbative super string theory Ron Donagi (University of Pennsylvania) Abstract: These talks will outline some of superstring perturbation theory, focusing attention on the purely mathematical subjects of supermanifolds, super Riemann surfaces, and super moduli spaces. In particular, we will discuss recent results on non splitness and non projectedness of supermoduli spaces. Moduli of spin curves Gavril Farkas (Humboldt-Universität Berlin) Abstract: I will discuss various aspects of the global geometry of the moduli spaces of even and odd spin curves. Topics will include, compactifications, Kodaira dimension and the construction of concrete birational models of these spaces in small genus. Deformation theory Hubert Flenner (Ruhr Universität Bochum) Abstract: Remark on my lectures. Some of the material can be found in a very preliminary manuscript of R.O. Buchweitz and myself. The pdf-file is here. Abstract for Lecture 1: We give an introduction into some basic notions of moduli theory. In particular the notion of coarse and fine moduli space is explained. We present Riemann's heuristic argument for the count of the moduli of Riemann surfaces and without proof some results on the existence of moduli spaces. We also show that one cannot expect moduli spaces in general. Abstract for Lecture 2: Starting with Kodaira Spencer's fundamental paper in 1958 deformation theory developed in the framework of complex analysis. We explain the basic notion of deformation of manifolds and more generally complex spaces. The universal objects are replaced by versal deformations. We study and describe infinitesimal deformations and automorphisms of deformations and state some of the basic existence theorems for versal deformations without proof. Abstract for Lecture 3: We study obstructions for extending deformations. As an important tool we introduce the Kodaira Spencer sequence of a deformation. We apply this to the problem to decide when the base space of a deformation is smooth and discuss in particular the Theorem of Bogomolov-Tian-Todorov. Abstract for Lecture 4: The main topic is Openness of Versality, which can be derived from the Kodaira Spencer sequence. This was first proved by M. Artin in the algebraic context. We show that one can use this result to paste local deformations in order to get a global moduli space. This idea is in the algebraic context due to Artin who used this technique to construct the Hilbert and Picard moduli space in the relative case. We give an indication how to proceed in the analytic case. Moduli of abelian varieties, Siegel modular forms, and string scattering amplitudes Samuel Grushevsky (Stony Brook University) Abstract: We will discuss the mathematical framework for computing perturbatively the string scattering amplitudes. Lecture 1 will focus on the bosonic case and moduli of curves. Lecture 2 will be devoted to the details of the superstring framework for genus 1 and 2. In lecture 3 we will discuss further directions and questions on moduli of spin curves and super Riemann surfaces. Relations in the cohomology of the moduli space of stable curves Rahul Pandharipande (ETH Zürich) Abstract: The moduli space of curve carries tautological cohomology classes. I will discuss the study of relations amongst these classes starting with ideas of Mumford in 1980s. The subject advanced in the 1990s with conjectures of Faber and Faber-Zagier. I will explain the current state of affairs based on Pixton's conjectures related to cohomological field theories.

Impressum

geändert am 07.08.2013 von P. Sosna