Related papers: Minicourse on Kac-Moody groups

In these lectures, we provide a toolkit to work with Chow-Witt groups, and more generally with the homology and cohomology of the Rost-Schmid complex associated to Milnor-Witt $K$-theory.

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

This paper surveys a few aspects of the global theory of wave equations. This material is structured around the contents of a minicourse given by the second author during the CMI/ETH Summer School on evolution equations during the Summer of…

These are the lecture notes for the LMS/EPSRC short course on strong approximation methods in linear groups organized by Dan Segal in Oxford in September 2007.

This note was prepared after the workshop on cdh descent and algebraic $K$-theory in Hara-mura, Japan (1 - 5 Sept. 2016), to complement the author's talk on the history and applications of pro cdh descent. In the final section pro cdh…

This paper introduces a new approach to the study of certain aspects of Galois module theory by combining ideas arising from the study of the Galois structure of torsors of finite group schemes with techniques coming from relative algebraic…

This document is the first iteration of an attempt to collate information about small-rank groups of Lie type over small fields, and their representation theory over the defining field. This information is important in the author's work on…

These are lecture notes on non-K\"ahler complex threefolds presented at the MATRIX program ``The geometry of moduli spaces in string theory''. We review some basics of Calabi-Yau geometry in Section 1, describe topological features of the…

In the past two decades there has been a great attention to Lie (super)algebras which are extensions of affine Kac-Moody Lie (super)algebras, in certain typical or axiomatic approaches. These Lie (super)algebras have been mostly studied…

These are expanded notes of some lectures given by the author for a workshop held at the Indian Statistical Institute, Bangalore in June, 2010, giving an exposition on the modular representations of finite groups of Lie type and $p$-adic…

The relationship between minimal algebraic Kac-Moody groups and twin buildings is well known as is the relationship between formal completions in one direction and affine buildings. Nevertheless, as the completion of a Kac-Moody group in…

This short expository text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists.

We describe the general framework for constructing collective--theory Hamiltonians whose hermicity requirements imply a Kac--Moody algebra of constraints on the associated Jacobian. We give explicit examples for the algebras $sl(2)_k$ and…

Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…

We propose a novel way to define imaginary root subgroups associated with (timelike) imaginary roots of hyperbolic Kac-Moody algebras. Using in an essential way the theory of unitary irreducible representation of covers of the group…

These are the lecture notes for a short course on tensor categories. The coverage in these notes is relatively non-technical, focussing on the essential ideas. They are meant to be accessible for beginners, but it is hoped that also some of…

Mickelsson defined a group 2-cocycle on the group of smooth maps from the closed unit 2-disk to a Lie group G and constructed a smooth central extension on a loop group of G, called the affine Kac-Moody central extension. We reformulate…

We give a rather informal introduction to the theory of mixed Hodge modules for young mathematicians.

These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…

These notes represent the transcript of three, 90 minute lectures given by the second author at the CRM in Barcelona in 2021 as part of the "Higher Structures and Operadic Calculus" workshop. The goal of the series was to introduce and…