Related papers: Endotrivial modules for infinite groups

Finding the number of maximal subgroups of infinite index of a finitely generated group is a natural problem that has been solved for several classes of `geometric' groups (linear groups, hyperbolic groups, mapping class groups, etc). Here…

We study the category of Sp-equivariant modules over the infinite variable polynomial ring, where Sp denotes the infinite symplectic group. We establish a number of results about this category: for instance, we show that every finitely…

These are notes from talks given at ICMS, Edinburgh, 4/2007 ("Geometry and Algorithms workshop") and at Bernoulli Center, Lausanne 5/2007 ("Limits of graphs in group theory and computer science"). We survey the following type of dichotomies…

This text contains lecture notes of the course taught to Ph.D. students of Jagiellonian University in Krakow on 25-28 November, 2013.

This is the written version of the supersymmetry lectures delivered at the 30th and 31st British Universities Summer Schools in Theoretical Elementary Particle Physics (BUSSTEPP) held in Oxford in September 2000 and in Manchester in…

We construct a well-behaved stable category of modules for a large class of infinite groups. We then consider its Picard group, which is the group of invertible (or endotrivial) modules. We show how this group can be calculated when the…

These are the notes of some lectures given by the author for a workshop held at TIFR, Mumbai in December, 2011, giving an exposition of the Deligne-Lusztig theory.

These are lecture notes on Floer and Rabinowitz-Floer homology written for a graduate course at UNICAMP August-December 2016 and a mini-course held at IMPA in August 2017.

We show how tools from computational group theory can be used to prove that a subgroup of matrices has infinite index.

In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…

This is the first of a three parts paper providing full details for our previous announcement in Pr\'epublications Orsay 2007-16, arXiv:0711.3579. Here we prove the results stated in the title.

While persistent homology has taken strides towards becoming a wide-spread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and…

We give new explicit formulas for the representations of the mapping class group of a genus one surface with one boundary component which arise from Integral TQFT. Our formulas allow one to compute the h-adic expansion of the TQFT-matrix…

This article focuses on the study of the group of units of incidence rings, which is a class of infinite matrix groups indexed by ordered sets, on a topological perspective. We first show when these groups can inherit the topological…

We introduce invariant rings for forms (homogeneous polynomials) and for d points on the projective space, from the point of view of representation theory. We discuss several examples, addressing some computational issues. We introduce the…

We describe recent links between two topics: geometric structures on manifolds in the sense of Ehresmann and Thurston, and dynamics "at infinity" for representations of discrete groups into Lie groups.

This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.

This survey article is intended as an introduction to the recent categorical classification theorems of the three authors, restricting to the special case of the category of modules for a finite group.

These are the expanded lecture notes from the author's mini-course during the graduate summer school of the Park City Math Institute in 2015. The main topics covered are: geometry of Springer fibers, affine Springer fibers and Hitchin…

Support $\tau$-tilting modules correspond to some classes of categorical objects bijectively, such as two-term tilting complexes for any finite dimensional symmetric algebra. This fact motivates us to classify support $\tau$-tilting modules…