Geometric group theory Lecture Notes∗

Lecture notes on Geometric Group Theory

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...

Geometric Complexity Theory: Introduction

Foreword These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author in the spring quarter, 2007. It gives introduction to the basic structure of GCT. Part II consists of the lecture notes for the course given by the...

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...

Groups in stable and simple theories

These are sketch notes for my lecture on the MALOA Introductory Day of the meeting ‘Geometric Model theory’, March 25–28 2010, Oxford. They were written after the lecture, but have not been carefully polished. The bibliography is not carefully put together. For an old but wonderful introduction to stable group theory, see [13]. For an update, often with results stated in great generality, see [...