Mathematical Aspects of Quantization
About this Title
Samuel Evens, University of Notre Dame, Notre Dame, IN, Michael Gekhtman, University of Notre Dame, Notre Dame, IN, Brian C. Hall, University of Notre Dame, Notre Dame, IN, Xiaobo Liu, University of Notre Dame, Notre Dame, IN and Claudia Polini, University of Notre Dame, Notre Dame, IN, Editors
Publication: Contemporary Mathematics
Publication Year 2012: Volume 583
ISBNs: 978-0-8218-7573-5 (print); 978-0-8218-9436-1 (online)
This book is a collection of expository articles from the Center of Mathematics at Notre Dame's 2011 program on quantization.
Included are lecture notes from a summer school on quantization on topics such as the Cherednik algebra, geometric quantization, detailed proofs of Willwacher's results on the Kontsevich graph complex, and group-valued moment maps.
This book also includes expository articles on quantization and automorphic forms, renormalization, Berezin–Toeplitz quantization in the complex setting, and the commutation of quantization with reduction, as well as an original article on derived Poisson brackets.
The primary goal of this volume is to make topics in quantization more accessible to graduate students and researchers.
Graduate students and research mathematicians interested in mathematical physics and quantization.
Table of Contents
- Yuri Berest and Peter Samuelson – Dunkl operators and quasi-invariants of complex reflection groups
- Vasily A. Dolgushev and Christopher L. Rogers – Notes on algebraic operads, graph complexes, and Willwacher’s construction
- Eugene Lerman – Geometric quantization; a crash course
- Eckhard Meinrenken – Lectures on group-valued moment maps and Verlinde formulas
- Tatyana Barron – Quantization and automorphic forms
- Yuri Berest, Xiaojun Chen, Farkhod Eshmatov and Ajay Ramadoss – Noncommutative Poisson structures, derived representation schemes and Calabi-Yau algebras
- Arnab Kar and S. G. Rajeev – Renormalization by any means necessary
- Martin Schlichenmaier – Berezin-Toeplitz quantization and star products for compact Kähler manifolds
- Jȩdrzej Śniatycki – Commutation of geometric quantization and algebraic reduction