Einstein Visiting Fellowship Rahul Pandharipande – Moduli of Curves, Bundles and K3 Surfaces

Building on well-documented existing ties, the proposal aims to integrate Rahul Pandharipande, the world's leading expert on moduli spaces in algebraic geometry, into the Berlin scientific landscape. Moduli spaces are parameter spaces for zero sets of polynomial equations in several variables (algebraic varieties). They play a central role in mathematics, especially in algebraic geometry, number theory, representation theory, and topology. The field uses insights and techniques with origins in both mathematics and physics. We propose to study moduli spaces of curves, sheaves, and K3 surfaces. While each of these moduli problems has independent roots in algebraic geometry, striking new relationships between them have been found in the past decade. Using these new perspectives, we plan to attack central questions concerning the cohomology (algebra of tautological classes) of the moduli space of curves, strata of abelian differentials over moduli, statistical properties of Hurwitz covers and the enumerative geometry of the moduli space of polarized K3 surfaces. All of the proposed directions are fundamental to the understanding of moduli spaces in mathematics and their interplay with topology, string theory, and classical algebraic geometry. These questions will be approached by a mix of new geometries and new techniques. The new geometries include log geometry and the moduli spaces of stable pairs introduced by Pandharipande, and the new techniques involve a combination of virtual localization, degeneration and birational geometry. At least four times a year, Pandharipande will visit Berlin for an extended period of time, will deliver intensive courses and various lectures. His research group will work closely with the group of Farkas at Humboldt Universität, but there will be further significant interaction, for instance with Altmann, Esnault and Schmitt at FU and with Kramer at HU.

Laufzeit

Projektstart: 01/2015

Projektende: 12/2019