Alpine Perspectives on Algebraic Topology
Alpine Perspectives on Algebraic Topology

Author: Christian Ausoni

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 274

ISBN-13: 0821848399

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Contains the proceedings of the Third Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, on August 18-24, 2008. This title includes research papers on stable homotopy theory, the theory of operads, localization and algebraic K-theory, as well as survey papers on the Witten genus and localization techniques.

An Alpine Expedition through Algebraic Topology
An Alpine Expedition through Algebraic Topology

Author: Christian Ausoni

Publisher: American Mathematical Soc.

Published: 2014-06-09

Total Pages: 314

ISBN-13: 0821891456

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This volume contains the proceedings of the Fourth Arolla Conference on Algebraic Topology, which took place in Arolla, Switzerland, from August 20-25, 2012. The papers in this volume cover topics such as category theory and homological algebra, functor homology, algebraic -theory, cobordism categories, group theory, generalized cohomology theories and multiplicative structures, the theory of iterated loop spaces, Smith-Toda complexes, and topological modular forms.

An Alpine Bouquet of Algebraic Topology
An Alpine Bouquet of Algebraic Topology

Author: Jérôme Scherer

Publisher: American Mathematical Soc.

Published: 2018-05-30

Total Pages: 322

ISBN-13: 147042911X

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This volume contains the proceedings of the Alpine Algebraic and Applied Topology Conference, held from August 15–21, 2016, in Saas-Almagell, Switzerland. The papers cover a broad range of topics in modern algebraic topology, including the theory of highly structured ring spectra, infinity-categories and Segal spaces, equivariant homotopy theory, algebraic -theory and topological cyclic, periodic, or Hochschild homology, intersection cohomology, and symplectic topology.

Building Bridges Between Algebra and Topology
Building Bridges Between Algebra and Topology

Author: Wojciech Chachólski

Publisher: Birkhäuser

Published: 2018-03-31

Total Pages: 235

ISBN-13: 3319701576

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This volume presents an elaborated version of lecture notes for two advanced courses: (Re)Emerging methods in Commutative Algebra and Representation Theory and Building Bridges Between Algebra and Topology, held at the CRM in the spring of 2015. Homological algebra is a rich and ubiquitous area; it is both an active field of research and a widespread toolbox for many mathematicians. Together, these notes introduce recent applications and interactions of homological methods in commutative algebra, representation theory and topology, narrowing the gap between specialists from different areas wishing to acquaint themselves with a rapidly growing field. The covered topics range from a fresh introduction to the growing area of support theory for triangulated categories to the striking consequences of the formulation in the homotopy theory of classical concepts in commutative algebra. Moreover, they also include a higher categories view of Hall algebras and an introduction to the use of idempotent functors in algebra and topology.

Mathematical Foundations of Quantum Field Theory and Perturbative String Theory
Mathematical Foundations of Quantum Field Theory and Perturbative String Theory

Author: Hisham Sati

Publisher: American Mathematical Soc.

Published: 2011-12-07

Total Pages: 370

ISBN-13: 0821851950

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Conceptual progress in fundamental theoretical physics is linked with the search for the suitable mathematical structures that model the physical systems. Quantum field theory (QFT) has proven to be a rich source of ideas for mathematics for a long time. However, fundamental questions such as ``What is a QFT?'' did not have satisfactory mathematical answers, especially on spaces with arbitrary topology, fundamental for the formulation of perturbative string theory. This book contains a collection of papers highlighting the mathematical foundations of QFT and its relevance to perturbative string theory as well as the deep techniques that have been emerging in the last few years. The papers are organized under three main chapters: Foundations for Quantum Field Theory, Quantization of Field Theories, and Two-Dimensional Quantum Field Theories. An introduction, written by the editors, provides an overview of the main underlying themes that bind together the papers in the volume.

Groups, Modules, and Model Theory - Surveys and Recent Developments
Groups, Modules, and Model Theory - Surveys and Recent Developments

Author: Manfred Droste

Publisher: Springer

Published: 2017-06-02

Total Pages: 493

ISBN-13: 331951718X

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This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.

Set Theory and Its Applications
Set Theory and Its Applications

Author: Liljana Babinkostova

Publisher: American Mathematical Soc.

Published: 2011

Total Pages: 346

ISBN-13: 0821848127

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This book consists of several survey and research papers covering a wide range of topics in active areas of set theory and set theoretic topology. Some of the articles present, for the first time in print, knowledge that has been around for several years and known intimately to only a few experts. The surveys bring the reader up to date on the latest information in several areas that have been surveyed a decade or more ago. Topics covered in the volume include combinatorial and descriptive set theory, determinacy, iterated forcing, Ramsey theory, selection principles, set-theoretic topology, and universality, among others. Graduate students and researchers in logic, especially set theory, descriptive set theory, and set-theoretic topology, will find this book to be a very valuable reference.

Spectral and Scattering Theory for Quantum Magnetic Systems
Spectral and Scattering Theory for Quantum Magnetic Systems

Author: Philippe Briet

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 202

ISBN-13: 0821847449

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Contains the proceedings of the conference on Spectral and Scattering Theory for Quantum Magnetic Systems, which took place at CIRM, Luminy, France, in July 2008. This volume includes original results presented by some of the invited speakers and surveys on advances in the mathematical theory of quantum magnetic Hamiltonians.

Dynamical Numbers: Interplay between Dynamical Systems and Number Theory
Dynamical Numbers: Interplay between Dynamical Systems and Number Theory

Author: S. F. Koli︠a︡da

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 258

ISBN-13: 0821849581

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This volume contains papers from the special program and international conference on Dynamical Numbers which were held at the Max-Planck Institute in Bonn, Germany in 2009. These papers reflect the extraordinary range and depth of the interactions between ergodic theory and dynamical systems and number theory. Topics covered in the book include stationary measures, systems of enumeration, geometrical methods, spectral methods, and algebraic dynamical systems.

Symplectic Topology and Measure Preserving Dynamical Systems
Symplectic Topology and Measure Preserving Dynamical Systems

Author: Albert Fathi

Publisher: American Mathematical Soc.

Published: 2010-04-09

Total Pages: 192

ISBN-13: 0821848925

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The papers in this volume were presented at the AMS-IMS-SIAM Joint Summer Research Conference on Symplectic Topology and Measure Preserving Dynamical Systems held in Snowbird, Utah in July 2007. The aim of the conference was to bring together specialists of symplectic topology and of measure preserving dynamics to try to connect these two subjects. One of the motivating conjectures at the interface of these two fields is the question of whether the group of area preserving homeomorphisms of the 2-disc is or is not simple. For diffeomorphisms it was known that the kernel of the Calabi invariant is a normal proper subgroup, so the group of area preserving diffeomorphisms is not simple. Most articles are related to understanding these and related questions in the framework of modern symplectic topology.