Operads: Proceedings of Renaissance Conferences
| Author | : Jean-Louis Loday |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 458 |
| Release | : 1997 |
| Genre | : |
| ISBN | : 0821805134 |
Operads Proceedings Of Renaissance Conferences
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Operads
| Author | : Jean-Louis Loday |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 460 |
| Release | : 1996-12-13 |
| Genre | : Mathematics |
| ISBN | : 9780821855386 |
``Operads'' are mathematical devices which model many sorts of algebras (such as associative, commutative, Lie, Poisson, alternative, Leibniz, etc., including those defined up to homotopy, such as $A_{\infty}$-algebras). Since the notion of an operad appeared in the seventies in algebraic topology, there has been a renaissance of this theory due to the discovery of relationships with graph cohomology, Koszul duality, representation theory, combinatorics, cyclic cohomology, moduli spaces, knot theory, and quantum field theory. This renaissance was recognized at a special session ``Moduli Spaces, Operads, and Representation Theory'' of the AMS meeting in Hartford, CT (March 1995), and at a conference ``Operades et Algebre Homotopique'' held at the Centre International de Rencontres Mathematiques at Luminy, France (May-June 1995). Both meetings drew a diverse group of researchers. The authors have arranged the contributions so as to emphasize certain themes around which the renaissance of operads took place: homotopy algebra, algebraic topology, polyhedra and combinatorics, and applications to physics.
Operads And Universal Algebra - Proceedings Of The International Conference
| Author | : Chengming Bai |
| Publisher | : World Scientific |
| Total Pages | : 318 |
| Release | : 2012-02-23 |
| Genre | : Mathematics |
| ISBN | : 9814458333 |
The book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working in universal algebra (primarily the Chinese team), and to exchange problems, methods and techniques from these two subject areas.
Homotopy of Operads and Grothendieck-Teichmuller Groups
| Author | : Benoit Fresse |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 743 |
| Release | : 2017-05-22 |
| Genre | : Mathematics |
| ISBN | : 1470434822 |
The ultimate goal of this book is to explain that the Grothendieck–Teichmüller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this result, the applications of methods of algebraic topology to operads must be developed. This volume is devoted primarily to this subject, with the main objective of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and of general methods of homotopy theory. The definition of the Sullivan model for the rational homotopy of spaces is revisited, and the definition of models for the rational homotopy of operads is then explained. The applications of spectral sequence methods to compute homotopy automorphism spaces associated to operads are also explained. This approach is used to get a topological interpretation of the Grothendieck–Teichmüller group in the case of the little 2-disc operad. This volume is intended for graduate students and researchers interested in the applications of homotopy theory methods in operad theory. It is accessible to readers with a minimal background in classical algebraic topology and operad theory.
Operads in Algebra, Topology and Physics
| Author | : Martin Markl |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821843621 |
Operads are mathematical devices which describe algebraic structures of many varieties and in various categories. From their beginnings in the 1960s, they have developed to encompass such areas as combinatorics, knot theory, moduli spaces, string field theory and deformation quantization.
Cyclic Cohomology and Noncommutative Geometry
| Author | : Joachim J. R. Cuntz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 202 |
| Release | : 1997-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780821871249 |
Noncommutative geometry is a new field that is among the great challenges of present-day mathematics. Its methods allow one to treat noncommutative algebras - such as algebras of pseudodifferential operators, group algebras, or algebras arising from quantum field theory - on the same footing as commutative algebras, that is, as spaces. Applications range over many fields of mathematics and mathematical physics. This volume contains the proceedings of the workshop on "Cyclic Cohomology and Noncommutative Geometry" held at The Fields Institute (Waterloo, ON) in June 1995. The workshop was part of the program for the special year on operator algebras and its applications.
Tel Aviv Topology Conference: Rothenberg Festschrift
| Author | : Melvin Rothenberg |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 334 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 0821813625 |
This volume presents the proceedings of the Tel Aviv International Topology Conference held during the Special Topology Program at Tel Aviv University. The book is dedicated to Professor Mel Rothenberg on the occasion of his 65th birthday. His contributions to topology are well known-from the early work on triangulations to numerous papers on transformation groups and on geometric and analytic aspects of torsion theory. Current research related to those contributions are reported in this book. Coverage is included on the following topics: vanishing theorems for the Dirac operator, the theory of Reidemeister torsion (including infinite dimensional flat bundles), Nobikov-Shubin invariants of manifolds, topology of group actions, Lusternik-Schnirelman theory for closed 1-forms, finite type invariants of links and 3-manifolds, equivariant cobordisms, equivariant orientations and Thom isomorphisms, and more.
Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory
| Author | : Paul Gregory Goerss |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 520 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0821832859 |
As part of its series of Emphasis Years in Mathematics, Northwestern University hosted an International Conference on Algebraic Topology. The purpose of the conference was to develop new connections between homotopy theory and other areas of mathematics. This proceedings volume grew out of that event. Topics discussed include algebraic geometry, cohomology of groups, algebraic $K$-theory, and $\mathbb{A 1$ homotopy theory. Among the contributors to the volume were Alejandro Adem,Ralph L. Cohen, Jean-Louis Loday, and many others. The book is suitable for graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.
Homotopy Invariant Algebraic Structures
| Author | : Jean-Pierre Meyer |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 392 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 082181057X |
This volume presents the proceedings of the conference held in honor of J. Michael Boardman's 60th birthday. It brings into print his classic work on conditionally convergent spectral sequences. Over the past 30 years, it has become evident that some of the deepest questions in algebra are best understood against the background of homotopy theory. Boardman and Vogt's theory of homotopy-theoretic algebraic structures and the theory of spectra, for example, were two benchmark breakthroughs underlying the development of algebraic $K$-theory and the recent advances in the theory of motives. The volume begins with short notes by Mac Lane, May, Stasheff, and others on the early and recent history of the subject. But the bulk of the volume consists of research papers on topics that have been strongly influenced by Boardman's work. Articles give readers a vivid sense of the current state of the theory of "homotopy-invariant algebraic structures". Also included are two major foundational papers by Goerss and Strickland on applications of methods of algebra (i.e., Dieudonné modules and formal schemes) to problems of topology. Boardman is known for the depth and wit of his ideas. This volume is intended to reflect and to celebrate those fine characteristics.
Graphs and Patterns in Mathematics and Theoretical Physics
| Author | : Mikhail Lyubich |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 443 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821836668 |
The Stony Brook Conference, "Graphs and Patterns in Mathematics and Theoretical Physics", was dedicated to Dennis Sullivan in honor of his sixtieth birthday. The event's scientific content, which was suggested by Sullivan, was largely based on mini-courses and survey lectures. The main idea was to help researchers and graduate students in mathematics and theoretical physics who encounter graphs in their research to overcome conceptual barriers. The collection begins with Sullivan's paper, "Sigma models and string topology," which describes a background algebraic structure for the sigma model based on algebraic topology and transversality. Other contributions to the volume were organized into five sections: Feynman Diagrams, Algebraic Structures, Manifolds: Invariants and Mirror Symmetry, Combinatorial Aspects of Dynamics, and Physics. These sections, along with more research-oriented articles, contain the following surveys: "Feynman diagrams for pedestrians and mathematicians" by M. Polyak, "Notes on universal algebra" by A. Voronov, "Unimodal maps and hierarchical models" by M. Yampolsky, and "Quantum geometry in action: big bang and black holes" by A. Ashtekar. This comprehensive volume is suitable for graduate students and research mathematicians interested in graph theory and its applications in mathematics and physics.
