Related papers: Algebraic tori - thirty years after
This book is a manual for the course of electrodynamics and theory of relativity. It is recommended primarily for students of mathematical departments. This defines its style: I use elements of vectorial and tensorial analysis, differential…
The objective of this paper is to describe the structure of Zariski closed algebras, which provide a useful generalization to finite dimensional algebras in the study of representable algebras over finite fields. Our results include a…
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.
In the present paper we define homogeneous algebraic systems. Particular cases of these systems are: semigroup (monoid, group) system. These algebraic systems were studied by J. Loday, A. Zhuchok, T. Pirashvili, N. Koreshkov. Quandle…
This is the Foreword to the book ``Explicit birational geometry of 3-folds'', edited by A. Corti and M. Reid, CUP Jun 2000, ISBN: 0 521 63641 8, with papers by K. Altmann, A. Corti, A.R. Iano-Fletcher, J. Koll\'ar, A.V. Pukhlikov and M.…
This article provides a conceptual and historical review of the evolution of integrable Hamiltonian systems from the Moscow School of A. T. Fomenko to the emerging Azarbaijan School of Geometric Dynamical Systems founded by the author.…
We provide a further analysis of the class of positive maps proposed ten years ago by Kossakowski. In particular we propose a new parametrization which reveals an elegant geometric structure and an interesting interplay between group theory…
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.
These are notes to accompany four lectures that I gave at the School on Additive Combinatorics, held in Montreal, Quebec between March 30th and April 5th 2006. My aim is to introduce ``quadratic fourier analysis'' in so far as we understand…
This paper is for the proceedings of the Chen-Chow Conference held in Tianjin, China in October 2000. The goal of the paper is to produce and survey evidence for a connection between Chen's work on iterated integrals on the one hand, and…
This paper answers a question raised by Grothendieck in 1970 on the "Grothendieck closure" of an integral linear group and proves a conjecture of the first author made in 1980. This is done by a detailed study of the congruence topology of…
This article is based on a talk given by the author at MSRI in the workshop "Connections for Women" in January 2013, while being a part of the program "Noncommutative Algebraic Geometry and Representation Theory" at MSRI. One purpose of the…
We prove a transcendence theorem concerning values of holomorphic maps from a disk to a quasi-projective variety over $\overline{\mathbf{Q}}$ that are integral curves of some algebraic vector field (defined over $\overline{\mathbf{Q}}$).…
In this paper we complete the results of Sullivant and Sturmfels proving that many of the algebraic group-based models for Markov processes on trees are pseudo-toric. We also show in which cases these varieties are normal. This is done by…
We extend the results by R.P. Langlands on representations of (connected) abelian algebraic groups. This is done by considering characters into any divisible abelian topological group. With this we can then prove what is known as the…
Algebraic computing in relativity and gravitation dates back more than thirty years, but only relatively recently has hardware of sufficient power to tackle large scale calculations become commonplace. Whereas it is generally understood…
This work is dedicated to a new completely algebraic approach to Arakelov geometry, which doesn't require the variety under consideration to be generically smooth or projective. In order to construct such an approach we develop a theory of…
This article is an extended version of the minicourse given by the second author at the summer school of the conference "Interactions of quantum affine algebras with cluster algebras, current algebras and categorification", held in June…
The text of the talk on Workshop on Topology of Algebraic Varieties in honour of Boris Moishezon, Bonn, MPI, Monday July 27, 1998.
We give a cohomological criterion for existence of outer automorphisms of a semisimple algebraic group over an arbitrary field. This criterion is then applied to the special case of groups of type D_2n over a global field, which completes…