Theodore Voronov

The papers in this volume are based on talks given at the 2001 Manchester Meeting of the London Mathematical Society, which was followed by an international workshop on Quantization, Deformations, and New Homological and Categorical Methods in Mathematical Physics. Focus is on the topics suggested by the title: quantization in its various aspects, Poisson brackets and generalizations, and structures beyond'' this, including symplectic supermanifolds, operads, Lie groupoids and Lie (bi)algebroids, and algebras with $n$-ary operations. The book offers accounts of up-to-date results as well as accessible expositions aimed at a broad reading audience of researchers in differential geometry, algebraic topology and mathematical physics.

London Mathematical Society Regional Meeting and Workshop on Quantization, Deformantions, and New Homological and Categorical Methods in Mathematical Physics, July 6-13, 2001, University of Manchester Institute of Science and Technology, Manchester, United Kingdom

Quantization, Poisson Brackets and Beyond

The papers in this volume are based on talks given at the Manchester Meeting of the London Mathematical Society, which was followed by an international workshop on ``Quantization, Deformations, and New Homological and Categorical Methods in Mathematical Physics''. The focus is on the topics suggested by the title: Quantization in its various aspects, Poisson brackets and generalizations, and structures ``beyond'', including symplectic supermanifolds, operads, Lie groupoids and Lie (bi)algebroids and algebras with $n$-ary operations. This book offers accounts of new results as well as accessible expositions useful to a broad reading audience of researchers in differential geometry, algebraic topology and mathematical physics.

Quantization, Poisson Brackets, and Beyond

Martin Schlichenmaier

Piotr Kielanowski

S. Twareque Ali

Anatol Odzijewicz

Pierre Bieliavsky

This book features a selection of articles based on the XXXIV Białowieża Workshop on Geometric Methods in Physics, 2015. The articles presented are mathematically rigorous, include important physical implications and address the application of geometry in classical and quantum physics. Special attention deserves the session devoted to discussions of Gerard Emch's most important and lasting achievements in mathematical physics. The Białowieża workshops are among the most important meetings in the field and gather participants from mathematics and physics alike. Despite their long tradition, the Workshops remain at the cutting edge of ongoing research. For the past several years, the Białowieża Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented. The unique atmosphere of the Workshop and School is enhanced by the venue, framed by the natural beauty of the Białowieża forest in eastern Poland.

XXXIV Workshop, Białowieża, Poland, June 28 – July 4, 2015

Geometric Methods in Physics

The Białowieża workshops on Geometric Methods in Physics are among the most important meetings in the field. Every year some 80 to 100 participants from both mathematics and physics join to discuss new developments and to interchange ideas. This volume contains contributions by selected speakers at the XXX meeting in 2011 as well as additional review articles and shows that the workshop remains at the cutting edge of ongoing research. The 2011 workshop focussed on the works of the late Felix A. Berezin (1931–1980) on the occasion of his 80th anniversary as well as on Bogdan Mielnik and Stanisław Lech Woronowicz on their 75th and 70th birthday, respectively. The groundbreaking work of Berezin is discussed from today’s perspective by presenting an overview of his ideas and their impact on further developments. He was, among other fields, active in representation theory, general concepts of quantization and coherent states, supersymmetry and supermanifolds. Another focus lies on the accomplishments of Bogdan Mielnik and Stanisław Lech Woronowicz. Mielnik’s geometric approach to the description of quantum mixed states, the method of quantum state manipulation and their important implications for quantum computing and quantum entanglement are discussed as well as the intricacies of the quantum time operator. Woronowicz’ fruitful notion of a compact quantum group and related topics are also addressed.

Theodore Voronov

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