Related papers: An introduction to hyperlinear and sofic groups
These notes are an introduction to symplectic groupoids and the double structures associated with them. The treatment is intended to lie about midway between the original account of Coste, Dazord and Weinstein, which relied on effective use…
These notes combine material from short lecture courses given in Paris, France, in July 2001 and in Srni, the Czech Republic, in January 2003. They discuss groups of symplectomorphisms of closed symplectic manifolds (M,\om) from various…
These notes correspond roughly to the two minicourses prepared by the authors for the workshop on Analytic Microlocal Analysis, held at Northwestern University in May 2013. The first part of the text gives an elementary introduction to some…
This text is an extended version of the lecture notes for a course on representation theory of finite groups that was given by the authors during several years for graduate and postgraduate students of Novosibirsk State University and…
These notes grew out of lectures given at the LMS-EPSRC Short Course on Asymptotic Methods in Infinite Group Theory, University of Oxford, 9-14 September 2007, organised by Dan Segal.
This is an expository article on the theory of formal group laws in homotopy theory, with the goal of leading to the connection with higher-dimensional abelian varieties and automorphic forms. These are roughly based on a talk at the…
These are expanded notes of a seminar held in Columbia university during the Spring and Fall of 2024 about the theory of analytic stacks of Clausen and Scholze, with a focus in the theory of solid mathematics. The seminar is inspired from…
These notes are based on Appalachian Set Theory lectures given by M. Malliaris on November 5, 2016 with D. Casey as the official scribe. The aim of the lectures was to present the setup and some key arguments of "Cofinality spectrum…
In this paper we study categorical properties of the category of abelian hypergroups that leads to the notion of hyper (almost) preadditive and hyper (almost) abelian categories. Our goal is to create a path towards a general theory of…
This thesis aims to serve as an introduction to the theory of quasitilings for amenable groups. In order to showcase the power of this theory, we focus on the study of the Sofic L\"uck Approximation Conjecture, which can be proven for…
These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT.
Summary talk at the Lepton-Photon Symposium, Cornell University, Aug. 10-15, 1993.
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…
These are the notes of five lectures given at the Summer School {\em Geometric and Topological Methods for Quantum Field Theory}, held in Villa de Leyva (Colombia), July 2--20, 2007. The lectures are meant for graduate or almost graduate…
These lecture notes provide an introduction to automorphism groups of graphs. Some special families of graphs are then discussed, especially the families of Cayley graphs generated by transposition sets.
A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations. A group is sofic if it admits a sofic approximation. Sofic…
A personal and subjective recollection, concerning mainly Wilson's lectures delivered over the spring of 1972 at Princeton University (summary of a talk at Cornell University on November 16, 2013 at the occasion of the memorial Kenneth G.…
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…
These are Notes prepared for nine lectures given at the Mathematical Sciences Research Institute, MSRI, Berkeley during the period January--March 1995. It is a pleasant duty to record here my gratitude to MSRI, and its staff, for making…
This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…