Inbar Klang (VU Amsterdam): Configuration Spaces
(Tuesday 27 August)
Abstract
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Prerequisites
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Literature
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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.
