Related papers: On strong approximation for algebraic groups
These are the lecture notes for the LMS/EPSRC short course on strong approximation methods in linear groups organized by Dan Segal in Oxford in September 2007.
These notes were prepared for the MSRI hot topics workshop on superstrong approximation (2012). We give a brief overview of the developments in the theory, especially the fundamental expansion theorem. Applications to diophantine problems…
This paper is an overview of my recent work on abstract homomorphisms of algebraic groups. It is based on a talk given at the Conference on Group Actions and Applications in Geometry, Topology, and Analysis held in Kunming in July 2012.
This document is an expanded version of a lecture presented at a conference on "Thin Groups and Superstrong Approximation" held at the Mathematical Sciences Research Institute in February 2012. Superstrong approximation is a criterion on a…
Reproducing my talk at Algebra Symposium held at Hiroshima University, August 26--29, 2013, I review recent results on super algebraic groups, emphasizing results obtained by myself and my coauthors using Hopf algebraic techniques. The…
We investigate a slight weakening of the classical property of strong approximation, which we call almost strong approximation, for connected reductive algebraic groups over global fields with respect to special sets of valuations. While…
Surveying some of the recent developments on approximate subgroups and super-strong approximation for thin groups, we describe the Bourgain-Gamburd method for establishing spectral gaps for finite groups and the proof of the classification…
This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.
This is the expanded version of my talk at the workshop "Groups of Automorphisms in Birational and Affine Geometry", October 29--November 3, 2012, Levico Terme, Italy. The first section is focused on Jordan groups in abstract setting, the…
We show that strong approximate lattices in higher-rank semi-simple algebraic groups are arithmetic.
Let K be the function field of a curve over the complex field. Let X be a homogeneous space of a semisimple linear algebraic group. Strong approximation holds for X outside any finite nonempty set of places of K. Strong approximation fails…
This is an extended abstract of my talk at the Oberwolfach Workshop ''Cluster Algebras and Related Topics'' (December 8 - 14, 2013). It is based on a joint work with A. Zelevinsky (arXiv:1306.3495).
These are notes for a mini-course of 3 lectures given at the St. Petersburg School in Probability and Statistical Physics (June 2012). My aim was to explain, on the example of a particular model, how ideas from the representation theory of…
This is an extended abstract for the conference "Microlocal2011 : Microlocal Methods in Mathematical Physics and Global Analysis Universit\"at T\"ubingen, June 14 - 18, 2011"
This is an edited write-up of lecture notes of the 7-th Appalachian set theory workshop of the same title led by the first named author at the Cornell University on November 22, 2008. A draft version of the notes was prepared by the second…
This article is an expanded version of my talk at the Gathering for Gardner, 2012.
This survey is a slightly extended version of the lecture given by the author at the \emph{VI International Course of Mathematical Analysis in Andaluc\'\i a} (CIDAMA), in September 2014. Most results are contained (in a slightly less…
These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…
We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group $H \leq \mathrm{SL}(n,…
This paper is an extended version of four lectures at PIMS in Vancouver given June 27 - 30, 2016. The primary goal of these lectures was to publicize the author's recent efforts to extend to representations of linear algebraic groups the…