Related papers: Endotrivial modules for infinite groups
This article is a revised version of the talk I gave at the conference ``Beauville Surfaces and groups'' held in Newcastle in June 2012. It presents some group theoretical methods to give bounds on the number of connected components of the…
Given a finite group scheme $\cG$ over an algebraically closed field $k$ of characteristic $\Char(k)=p>0$, we introduce new invariants for a $\cG$-module $M$ by associating certain morphisms $\deg^j_M : U_M \lra \Gr_d(M) \ \…
These are extended notes for my lectures at the workshop ``Reconstructing the Gravitational Hologram'' held at Galileo-Galilei Institute, Florence, in June 2022.
This paper is an extended version of a series of lectures on polar spaces given during the workshop and conference 'Groups and Geometries', held at the Indian Statistical Institute in Bangalore in December 2012. The aim of this paper is to…
This is a survey of vanishing and positivity theorems for Hodge modules, and their recent applications to birational and complex geometry, expanding on my lecture at the 2015 AMS Summer Institute.
These are the notes for an eponymous course given by the authors at the summer school on p-adic arithmetic geometry in Hangzhou.
We survey variety theory for modules of finite dimensional Hopf algebras, recalling some definitions and basic properties of support and rank varieties where they are known. We focus specifically on properties known for classes of examples…
The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…
These notes are an expanded version of the lectures held in Tromso, in May 2025 at the "Lie-Stormer Summer School : Invariant Theory from classics to modern developments", in the framework of TiME events. We emphasize the analogy between…
We use differential forms on loop spaces to prove that the fundamental group of certain geometric transformation groups is infinite. Examples include both finite and infinite dimensional Lie groups. The finite dimensional examples are the…
This note surveys some classical results and recent developments on the interplay between lower curvature bounds and the isoperimetric problem. It is based on mini-courses given at the European Doctorate School of Differential Geometry…
Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation…
This survey paper is based on my IMPANGA lectures given in the Banach Center, Warsaw in January 2011. We study the moduli of holomorphic map germs from the complex line into complex compact manifolds with applications in global singularity…
We construct the irreducible unipotent modules of the finite general linear groups using tableaux. Our construction is analogous to that of James (1976) for the symmetric groups, answering an open question as to whether such a construction…
This is an expanded version of my talk given at the workshop "Hot Topics: Thin Groups and Super-strong Approximation" (MSRI, Berkeley, February 6-10, 2012).
This note summarizes in an informal way some geometric properties of Anosov representations into the symplectic group, which were presented in a talk at the conference What is Next. The mathematical legacy of Bill Thurston, held in June…
We characterize the modules of infinite projective dimension over the endomorphism algebras of Opperman-Thomas cluster tilting objects $X$ in $(n+2)$-angulated categories $(\mathcal C,\Sigma^n,\Theta)$. For an indecomposable object $M$ of…
These are notes from the 2003 C.I.M.E. summer school "symplectic 4-manifolds and algebraic surfaces". They cover the same material as the author's (by now ancient) Ph.D. thesis.
We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…
This is a survey on old and new results as well as an introduction to various related basic notions and concepts, based on two talks given at the International Workshop on Geometry and Analysis in Kemerovo (Sobolev Institute of Mathematics,…