Inbar Klang (VU Amsterdam): Configuration Spaces
(Tuesday 27 August)
Abstract
Spaces of configurations of points in a manifold show up in many fields of mathematics, including algebraic topology, knot theory, and mathematical physics. We will introduce configuration spaces and study their topology. We will also explore how they appear in questions about manifold topology, as well as their connections to braid groups and to Eilenberg-Mac Lane spaces.
Prerequisites
Basic algebraic topology, including the fundamental group and the notions of homotopy and homotopy equivalence. Some knowledge about (co) homology and higher homotopy groups would be helpful, but the basics of these will be reviewed as necessary during the talks.
Maarten Solleveld (RU Nijmegen): p-adic groups
(Monday 26 August)
Abstract
P-adic groups are algebraic groups over a p-adic field. The archetypical example is GL_n (Q_p), where Q_p denotes the p-adic numbers. Such groups play an important role in algebraic geometry, representation theory and the Langlands program.
In this course we will discuss the structure of p-adic groups from several perspectives: number theory, topology and algebraic geometry. We will focus on split reductive p-adic groups, whose algebraic structure can be described with root systems and Weyl groups.This is quite similar to Lie groups. But many aspects of p-adic groups are completely different from Lie groups, for example the action on an affine building. As an example we will explain the action of GL_2 (Q_p) on a regular, infinite tree.
Prerequisites
Basic algebraic geometry and some knowledge of Lie groups and Lie algebras.
Literature
- Serre, “Local fields” (chapters 1 and 2)
- Springer, “Linear algebraic groups
- Borel, “Linear algebraic groups”
Michał Wrochna (Utrecht University): Geometric singular analysis
(Wednesday 28 August)
Abstract
The lectures will provide an introduction to geometric singular analysis, a framework for the study of partial differential equations on noncompact or singular spaces. In particular, I will introduce b-differential operators and discuss applications. This will include examples such as the Laplace operator on Euclidean space, possibly with a singular potential and the wave equation on Minkowski, de Sitter and anti-de Sitter spacetimes.
Prerequisites
functional analysis (Hilbert spaces), distribution theory or partial differential equations, Riemannian differential geometry (recommended but not mandatory)
Literature
Lecture notes on geometric singular by Peter Hintz + own notes.
