Related papers: Loop groups and string topology

These are notes for a five lecture series intended to uncover large-scale phenomena in the homotopy groups of spheres using the Adams-Novikov Spectral Sequence. The lectures were given in Strasbourg, May 7-11, 2007.

We determine the ranks of string C-group representations of the groups ${\rm PSp}(4,\mathbb{F}_q)\cong\Omega(5,\mathbb{F}_q)$, and comment on those of higher-dimensional symplectic and orthogonal groups.

Lecture notes of lectures delivered at the Hodge Theory Summer School in ICTP Trieste, June 2010.

This is a lecture note prepared for the SFT 9 workshop in Augsburg, Germany. The text describes a polyfold approach to the construction of symplectic field theory and focuses on the perturbation and transversality theory.

Talk given at the 7th Marcel Grossmann Meeting on General Relativity, Stanford University, July 24-30, 1994.

In this paper, we will present the author's interpretation and embellishment of five lectures on cluster theory given by Kiyoshi Igusa during the Spring semester of 2022 at Brandeis University. They are meant to be used as an introduction…

These are extended notes of a course given at Tulane University for the 2015 Clifford Lectures. Their aim is to present structure results for group schemes of finite type over a field, with applications to Picard varieties and automorphism…

This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.

This is the text of my habilitation thesis defended at the \'Ecole Normale Sup\'erieure. The topological string presents an arena in which many features of string theory proper, such as the interplay between worldsheet and target space…

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.

Notes used for a course held in 2016 in the School of Advances in Group Theory and Applications, for some lectures given in 2018 for the students of the Master in Mathematics of the Vrije Universiteit Brussels, a course for master and Ph.D.…

An overview of some of the developments in string theory over the past two years is given, focusing on four topics: realistic (standard model like) models from string theory, geometric engineering and theories with fluxes, the gauge…

These are (somewhat informal) lectures notes for the CIME summer school "Geometric Representation Theory and Gauge Theory" in June 2018. In these notes we review the results and constructions of a series of our joint papers with H.Nakajima…

The goal of these lectures is to present an informal but precise introduction to a body of concepts and methods of interest in number theory and string theory revolving around modular forms and their generalizations. Modular invariance lies…

This expository article introduces the topic of roots in a compact Lie group. Compared to the many other treatments of this standard topic, I intended for mine to be relatively elementary, example-driven, and free of unnecessary…

This article focuses on two related topics: unitary representations of the loop $ax+b$-group and their relation to a loop version of the $\Gamma$-function and the construction of continuous series for the…

\noindent 1. Generalities\hfil\break 2. Lie groups and Lie algebras\hfil\break 3. The unitary groups\hfil\break 4. Representations of the SU(n) groups (and of their algebras)\hfil\break 5. The tensor method for unitary groups, and\hb the…

We study and relate certain actions and extensions involving 2-groups.

Let G be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension $\G$ of G by a cyclic group of order n, under some mild tameness assumptions on n. In particular, we…

We analyze the structure of a large class of connected algebraic rings over an algebraically closed field of positive characteristic using Greenberg's perfectization functor. We then give applications to rigidity problems for…