ISBN 978-3-03719-102-6
DOI 10.4171/102
December 2011, 661 pages, hardcover, 16,5 x 23,5 cm.
EMS Textbooks in Mathematics
This is the first of two volumes which will provide a comprehensive introduction to the modern representation theory of Frobenius algebras. The first part of the book serves as a general introduction to basic results and techniques of the modern representation theory of finite dimensional associative algebras over fields, including the Morita theory of equivalences and dualities and the Auslander?Reiten theory of irreducible morphisms and almost split sequences.
The second part is devoted to fundamental classical and recent results concerning the Frobenius algebras and their module categories. Moreover, the prominent classes of Frobenius algebras, the Hecke algebras of Coxeter groups and the finite dimensional Hopf algebras over fields are exhibited.
This volume is self-contained and the only prerequisite is a basic knowledge of linear algebra. It includes complete proofs of all results presented and provides a rich supply of examples and exercises.
The text is primarily addressed to graduate students starting research in the representation theory of algebras as well mathematicians working in other fields.
ISBN 978-3-03719-100-2
January 2012, 146 pages, softcover, 17 x 24 cm.
Zurich Lectures in Advanced Mathematics
The goal of geometric numerical integration is the simulation of evolution equations possessing geometric properties over long times. Of particular importance are Hamiltonian partial differential equations typically arising in application fields such as quantum mechanics or wave propagation phenomena. They exhibit many important dynamical features such as energy preservation and conservation of adiabatic invariants over long time. In this setting, a natural question is how and to which extent the reproduction of such long time qualitative behavior can be ensured by numerical schemes.
Starting from numerical examples, these notes provide a detailed analysis of the Schrodinger equation in a simple setting (periodic boundary conditions, polynomial nonlinearities) approximated by symplectic splitting methods. Analysis of stability and instability phenomena induced by space and time discretization are given, and rigorous mathematical explanations for them.
The book grew out of a graduate level course and is of interest to researchers and students seeking an introduction to the subject matter.
ISBN 978-3-03719-075-3
January 2012, 377 pages, hardcover, 17 x 24 cm.
The QGM Master Class Series
There is an essentially “tinker-toy” model of a trivial bundle over the classical Teichmuller space of a punctured surface, called the decorated Teichmuller space, where the fiber over a point is the space of all tuples of horocycles, one about each puncture. This model leads to an extension of the classical mapping class groups called the Ptolemy groupoids and to certain matrix models solving related enumerative problems, each of which has proved useful both in mathematics and in theoretical physics. These spaces enjoy several related parametrizations leading to a rich and intricate algebro-geometric structure tied to the already elaborate combinatorial structure of the tinker-toy model. Indeed, the natural coordinates give the prototypical examples not only of cluster algebras but also of tropicalization. This interplay of combinatorics and coordinates admits further manifestations, for example, in a Lie theory for homeomorphisms of the circle, in the geometry underlying the Gauss product, in profinite and pronilpotent geometry, in the combinatorics underlying conformal and topological quantum field theories, and in the geometry and combinatorics of macromolecules.
This volume gives the story and wider context of these decorated Teichmuller spaces as developed by the author over the last two decades in a series of papers, some of them in collaboration. Sometimes correcting errors or typos, sometimes simplifying proofs and sometimes articulating more general formulations than the original research papers, this volume is self-contained and requires little formal background. Based on a master’s course at Aarhus University, it gives the first treatment of these works in monographic form.
Comme les precedents volumes de ce seminaire, qui compte maintenant plus de mille exposes, celui-ci contient quinze exposes de synthese sur des sujets d'actualite : cinq exposes concernant les groupes dans differents contextes, trois de physique mathematique, deux lies au programme de Langlands, deux de geometrie algebrique, un de geometrie differentielle, un sur les algebres amassees et un sur les matrices aleatoires
Bourbaki Seminar, volume 2009/2010, talks 1012-1026
As in the preceding volumes of this seminar, which now counts more than one thousand talks, one finds here fifteen survey lectures on topics of current interest : five lectures around group theory, three about mathematical physics, two related to Langlands' program, two on algebraic geometry, one about differential geometry, one on clusters algebras, and one about random matrices.
Keywords: -modules, -stability, -adic approximation, -adic fields, -adic Galois representations, -adic Hecke algebras, -adic Hodge theory, -completion, algebraic cycles, algebraic linear group, ammassed algebra, antisymmetrical systems, ascending chain condition, asymptotic group geometry, automorphism group, Bieri-Neumann-Strebel invariant, black hole, canonical base, carquois representation, Chow groups, classification, classifying spaces, compact Lie groups, conjugation, conservation laws, discrete dynamical system, ergodicity, extremal metric, finite index subgroups, free group, fundamental group, group action on trees, harmonic applications, Hecke curve, Kahler manifold, Langlands correspondence, Lie theory, log-canonical threshold, loop spaces, minimal model conjecture, Navier-Stokes equations, ordinary families, outer-space of de Culler-Vogtmann, Palais-Smale sequences, profinite groups, (pseudo-) reductive group, pseudo-reflection groups, random matrices, regularity, resolvable group, scalar restriction, Schwarzschild, Shokurov connectivity theorem, special linear group, stability, structure, surface group, Teichmuller space, toric manifold, total positivity, turbulence, vector field method, verbal subgroups, Willmore surfaces, word value, zero-cycles
ISBN : 978-2-85629-326-3
- A. J. de JONG, Xuha HE, and Jason Michael, STARR
Families of rationally simply connected varieties over surfaces and torsors for semisimple groups
p. 1-85
- Daniel GREB, Stefan KEBEKUS, Sandor J. KOVACS, and Thomas PETERNELL
Differential forms on log canonical spaces
p. 87-169
- Artur AVILA and Mikhail LYUBICH
The Full renormalization Horseshoe for unimodal maps of higher degree : exponential contraction along hybrid classes
p. 171-223