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Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their…

This is a brief introduction to the theories of Lie groups, algebraic groups and their discrete subgroups, which is based on a lecture series given during the Summer School held in the Banach Centre in Poland in Summer 2011.

These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT.

These are the lecture notes of a 2-hour mini-course on Lie groups over local fields presented at the "Workshop on Totally Disconnected Groups, Graphs and Geometry" at the Heinrich-Fabri-Institut Blaubeuren in May 2007. The goal of the notes…

Notes from lectures given at the Autumn School on Algebraic and Arithmetic Geometry at the Johannes Gutenberg-Universit\"at Mainz in October 2017.

This is a set of lecture notes for a course given at the 2005 Summer School in Poisson Geometry held at ICTP-Trieste.

These are notes of a graduate course on representations of non-compact semisimple Lie groups given by the author at MIT.

Lectures delivered at the 17th National Nuclear Physics Summer School 2005, Berkeley, CA, June 6-17, 2005.

This paper surveys results on the connections between the cohomology for algebraic groups, finite groups and Frobenius kernels that were presented at the Workshop and Summer School on Lie and Representation Theory at East China Normal…

These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…

These notes are based on a course given at the EPFL in May 2005. It is concerned with the representation theory of Hecke algebras in the non-semisimple case. We explain the role that these algebras play in the modular representation theory…

These are notes of a series of lectures on sieves, presented during the Special Activity in Analytic Number Theory, at the Max-Planck Institute for Mathematics in Bonn, during the period January--June 2002.

Lecture notes at a conference on Arithmetic Geometry, Goettingen, July/August 2006: Density of ordinary Hecke orbits and a conjecture by Grothendieck on deformations of p-divisible groups.

This is an expanded version of lectures given at a Summer School "Geometric methods in Representation Theory" (Grenoble, 2008).

These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.

The present notes contain the material of the lectures given by the author at the summer school on ``Modular Forms and their Applications'' at the Sophus Lie Conference Center in the summer of 2004.

These are lecture notes from Clay Summer School in Goettingen, in 2006; the lectures were an attempt at an elementary introduction to math.KT/0611623.

These notes grew out of a lecture series given at RIMS in the summer of 2001. The lecture series was aimed at a broad audience that included many graduate students. Its purpose lay in familiarizing the audience with the basics of 3-manifold…

These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous…

Notes of the lectures delivered in Les Houches during the Summer School on Complex Systems (July 2006).