Related papers: Arithmetic groups
These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…
We establish an error estimate for counting lattice points in Euclidean norm balls (associated to an arbitrary irreducible linear representation) for lattices in simple Lie groups of real rank at least two. Our approach utilizes refined…
These are notes for a summer course given at the PIMS Summer School on Geometric and Topological Aspects of the Representation Theory of Finite Groups in Vancouver, July 27-30 2016.
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.
A short proof of a theorem of M.H. Albert, and its application to lattices.
This is the written version of a set of introductory lectures on string theory.
Expanded lecture notes. Preliminary version, comments are welcome.
These are extended notes of a course given at Tulane University for the 2015 Clifford Lectures. Their aim is to present structure results for group schemes of finite type over a field, with applications to Picard varieties and automorphism…
These notes are meant to provide a rapid introduction to triangulated categories. We start with the definition of an additive category and end with a glimps of tilting theory. Some exercises are included.
This text is the preprint version of the concluding chapter for the book New Directions in Locally Compact Groups published by Cambridge University Press in the series Lecture Notes of the LMS. The recent progress on locally compact groups…
In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.
We present an accessible introduction to basic results on groups of intermediate growth.
Notes for a course at the H.-C. R. I., Allahabad, 15 August 2008 -- 26 January 2009
This is the author's PhD thesis, published at the Universit\"at M\"unster, Germany in 2010. It contains a detailed description of the results of arXiv:0903.1989, arXiv:0905.0071 and arXiv:0908.2713.
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.
We establish an arithmeticity vs. non-linearity alternative for irreducible lattices in suitable product groups, such as for instance products of topologically simple groups. This applies notably to a (large class of) Kac-Moody groups. The…
This is an expository article on recent developments in the theory of group relaxations in integer programming from an algebraic perspective.
Lecture notes at a conference on Arithmetic Geometry, Goettingen, July/August 2006: Density of ordinary Hecke orbits and a conjecture by Grothendieck on deformations of p-divisible groups.
Here we briefly discuss lattices in Euclidean spaces and spaces of lattices, which are basic objects that can be described in terms of matrices and are important settings in classical analysis.
Arithmetical properties of a finite group are properties of the group which are defined by its arithmetical parameters such as the order of the group, the element orders and so on. In this paper, we discuss a number of results on…