Related papers: Arithmetic groups
This is the "preprint" for a paper that came out in 1998 but for some reason wasn't posted then. Abstract:These lectures are for novices to lattice QCD. They introduce a set of simple ideas and numerical techniques that can be implemented…
These are the notes for an eponymous course given by the authors at the summer school on p-adic arithmetic geometry in Hangzhou.
We use recurrence relations to derive explicit formulas for counting the number of subgroups of given order (or index) in rank 3 finite abelian p-groups and use these to derive similar formulas in few cases for rank 4. As a consequence, we…
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.
We prove that, under mild assumptions, a lattice in a product of semi-simple Lie group and a totally disconnected locally compact group is, in a certain sense, arithmetic. We do not assume the lattice to be finitely generated or the ambient…
This is a survey article on the theory of finite complex reflection groups. No proofs are given but numerous references are included.
In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].
These lecture notes from a first course in algebraic topology use the fundamental group and orbit categories to classify covering spaces.
Notes to lectures on the epsilon calculus, covering axioms, semantics, completeness, and the first epsilon theorem.
This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint work with Dustin Clausen. This is intended as a stable citable…
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
The paper is devoted to the study of the lattice of subgroups of the Lamplighter type groups and to the relative gradient rank.
An introduction to quantum groups and non-commutative differential calculus (Lecture at the III Workshop on Differential Geometry, Granada, September 1994)
It is a working version of a lecture on the theory of enlargement of filtration, given at the African Mathematic School in Marrakech, October 19-23, 2015.
These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and Hamiltonian systems. They are based on a series of lectures given by the author at Universit\`a degli Studi di Napoli "Federico II" (April 2009), at…
This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.
These are partial lecture notes from the fifteen Ess\'en Lectures for graduate students at Uppsala University given (in four days!) in June 2013.
This book provides a gentle introduction to the study of arithmetic subgroups of semisimple Lie groups. This means that the goal is to understand the group SL(n,Z) and certain of its subgroups. Among the major results discussed in the later…
This is an expanded version of my talk given at the workshop "Hot Topics: Thin Groups and Super-strong Approximation" (MSRI, Berkeley, February 6-10, 2012).