Related papers: On strong approximation for algebraic groups
Let $K$ be a number field, let $X$ be a smooth integral variety over $K$, and assume that there exists a finite set of finite places $S$ of $K$ such that the $S$-integral points on $X$ are dense. Then the combined conjectures of Campana and…
In this talk, I will survey recent progress made on the classification of von Neumann algebras arising from countable groups and their actions on probability spaces. In particular, I will present the first results which provide classes of…
This report is a combined version of two talks presented by the authors at the Edinburgh $b$-physics Workshop, December 1991. It presents the ideas of heavy quark symmetry and gives an introduction to some applications. The references…
We extend Borel's theorem on the dominance of word maps from semisimple algebraic groups to some perfect groups. In another direction, we generalize Borel's theorem to some words with constants. We also consider the surjectivity problem for…
We prove that the approximation conjecture of Luck holds for all amenable groups in the complex group algebra case. This result was previously proved by Dodziuk, Linnell, Mathai, Schick and Yates under the assumption that the group is…
This is a write-up of the lectures given by the author during the Master Class "Categorification" at {\AA}rhus University, Denmark in October 2010.
This is an expanded version of my Shaw Prize Lecture delivered at the Chinese University of Hong Kong.
Talk given at NATO ARW in Kiev (September 2000) "Non-commutative Structures in Mathematics and Physics".
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…
This talk reviews progress in the (semi-) analytic calculations of the thermodynamics of the quark-gluon plasma. I shall explain how weak coupling techniques can allow us, through appropriate resummations, to deal with particular non…
This paper gathers four lectures, based on a mini-course at IMA in 2014, whose aim was to discuss the structure of approximate subgroups of an arbitrary group, following the works of Hrushovski and of Green, Tao and the author. Along the…
This article contains a slightly expanded version of the lectures given by the author at the summer school "Algebraic stacks and related topics" in Mainz, Germany from August 31 to September 4, 2015. The content of these lectures is purely…
This is a summary of the material for 3 lectures on geometrically finite and infinite Kleinian groups delivered by the author at a workshop held at Tata Institute of Fundamental Research in April 2014.
This is an expanded version of my talk given at the International Conference ``Algebra and Number Theory'' dedicated to the 80th anniversary of V. E. Voskresenskii, which was held at the Samara State University in May 2007. The goal is to…
This is a brief introduction to the theories of Lie groups, algebraic groups and their discrete subgroups, which is based on a lecture series given during the Summer School held in the Banach Centre in Poland in Summer 2011.
Those notes rest on the Samuel Eilenberg Lectures I gave at Columbia University, NY, in the fall 2022. I thank all the mathematicians who participated in their elaboration, directly or indirectly. They are meant to be published as a…
This is an introduction to the finite groups, with focus on the groups of permutations and reflections, and more generally, on the finite groups of unitary matrices. We first discuss the basics of group theory, featuring the cyclic,…
Strong approximation with Brauer-Manin obstruction is established for smooth varieties containing a connected linear algebraic group with a compatible action.
Below are the problems that I formulated at Open Problems Session of {\it Workshop on Group Actions on Rational Varieties}, McGill University and University of Montreal, Canada, March 2002. To appear in: "Affine Algebraic Geometry"…
In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general…