Past Kinderseminar

2 December 2009
11:30
Matthew Clarke
Abstract
This talk is about the ordinary representation theory of finite groups of Lie type. I will begin by carefully reviewing algebraic groups and finite groups of Lie type and the construction and properties of (ordinary) Gelfand--Graev characters. I will then introduce generalized Gelfand--Graev characters, which are constructed using the Lie algebra of the ambient algebraic group. Towards the end I hope to give an idea of how generalized Gelfand--Graev characters can and have been used to attack Lusztig's conjecture and the role this plays in the determination of the character tables of finite groups of Lie type.
4 November 2009
11:30
Tobias Barthel
Abstract
We will present different ideas leading to and evolving around geometry over the field with one element. After a brief summary of the so-called numbers-functions correspondence we will discuss some aspects of Weil's proof of the Riemann hypothesis for function fields. We will see then how lambda geometry can be thought of as a model for geometry over $\mathbb{F}_\mathrm{un}$ and what some familiar objects should look like there. If time permits, we will explain a link with stable homotopy theory.

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