Geometric Group Theory Notes

Lecture notes on Geometric Group Theory

Geometric group theory Lecture Notes∗

One of the main themes of geometric group theory is to study a (finitely generated) group G in terms of the geometric properties of the Cayley graph of G. These “geometric properties” come in the form of quasi-isometry invariants. Our goal this semester is to look as some specific quasiisometry invariants such as Dehn functions, hyperbolicity, growth functions, and amenabiliity and try to under...

Lecture Notes -stability Theory (math 414) Spring 2003

The aim of this course and these notes is to present an exposition of the basics of stability theory, stable group theory, and geometric stability theory. I will assume knowledge of my Autumn 2002 model theory lecture notes [1]. In fact the current notes are a natural continuation of the earlier ones. The model theory lecture notes ended with a proof of Morley’s Theorem. Stability theory develo...

Introduction to actions of algebraic groups

These notes present some fundamental results and examples in the theory of algebraic group actions, with special attention to the topics of geometric invariant theory and of spherical varieties. Their goal is to provide a self-contained introduction to more advanced lectures.

Notes on Algebraic Number Theory

1 Number Fields 2 1.1 Norm, Trace, and Discriminant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Algebraic Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Dedekind Rings 7 2.1 Fractional Ideals and Unique Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 The Ideal Class Group ...

Asymptotic Safety, and Quantum Einstein Gravity∗

These lecture notes provide a pedagogical introduction to a specific continuum implementation of the Wilsonian renormalization group, the effective average action. Its general properties and, in particular, its functional renormalization group equation are explained in a simple scalar setting. The approach is then applied to Quantum Einstein Gravity (QEG). The possibility of constructing a fund...