Related papers: Schr\"oder e la Teoria dei Gruppi

This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the study of higher versions of Grothendieck…

This article explains basic constructions and results on group algebras and their cohomology, starting from the point of view of commutative algebra. It provides the background necessary for a novice in this subject to begin reading Dave…

How does the spectrum of a Schr\"odinger operator vary if the corresponding geometry and dynamics change? Is it possible to define approximations of the spectrum of such operators by defining approximations of the underlying structures? In…

We present some recent results on the existence of solutions of the Schr\"odinger flows, and pose some problems for further research.

The general theory of Grothendieck categories is presented. We systemize the principle methods and results of the theory, showing how these results can be used for studying rings and modules.

These are lecture notes of a mini-course given by the first author in Moscow in July 2019, taken by the second author and then edited and expanded by the first author. They were also a basis of the lectures given by the first author at the…

This is a survey article on the Springer correspondence for symmetric spaces. We discuss various generalization of the theory of the Springer correspondence for reductive groups to symmetric spaces and exotic symmetric spaces associated to…

This is a series of lecture notes explaining topos theory and its application in physics.

In this article, we determine the derivation algebra and the automorphism group of the twisted Schr\"{o}dinger-Virasoro algebra.

We present a diagram surveying equivalence or strict implication for properties of different nature (algebraic, model theoretic, topological, etc.) about groups definable in o-minimal structures. All results are well-known and an extensive…

An objective of the theory of combinatorial groupoids is to introduce concepts like "holonomy", "parallel transport", "bundles", "combinatorial curvature" etc. in the context of simplicial (polyhedral) complexes, posets, graphs, polytopes,…

In this article we survey, and make a few new observations about, the surprising connection between sub-monoids of mapping class groups and interesting geometry and topology in low-dimensions.

We suggest a generalization of \pi_0 for topological groupoids, which encodes incidence relations among the strata of the associated quotient object, and argue for its utility by example, starting from the orbit categories of the theory of…

This is a survey of the spectral theory of tensors.

This paper gives a self-contained group-theoretic proof of a dual version of a theorem of Ore on distributive intervals of finite groups. We deduce a bridge between combinatorics and representations in finite group theory.

This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.

This paper is devoted to the investigation of the property of order separability for free products of groups.

In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as sets with operations that satisfy the group axioms "up to…

This is an overview (in french) of the Theory of Species for a general audience. Basic notions are introduced in a non too technical manner, with an explanation of why should one approach the notion of discrete structures in this particular…

Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.