In recent decades, quantization has led to interesting applications in various mathematical branches. This volume, comprised of research and survey articles, discusses key topics, including symplectic and algebraic geometry, representation theory, quantum groups, the geometric Langlands program, quantum ergodicity, and non-commutative geometry. A wide range of topics related to quantization are covered, giving a glimpse of the broad subject. The articles are written by distinguished mathematicians in the field and reflect subsequent developments following the Arithmetic and Geometry around Quantization conference held in Istanbul.
List of Contributors:
S. Akbulut R. Hadani
S. Arkhipov K. Kremnizer
Ö. Ceyhan S. Mahanta
E. Frenkel S. Salur
K. Fukaya G. Ben Simon
D. Gaitsgory W. van Suijlekom
S. Gurevich
Author(s): Selman Akbulut, Sema Salur (auth.), Özgür Ceyhan, Yu. I. Manin, Matilde Marcolli (eds.)
Series: Progress in Mathematics 279
Edition: 1
Publisher: Birkhäuser Basel
Year: 2010
Language: English
Pages: 292
Tags: Geometry;Applications of Mathematics;Algebra;Mathematical Methods in Physics;Quantum Physics;Algebraic Geometry
Front Matter....Pages i-viii
Mirror Duality via G 2 and Spin (7) Manifolds....Pages 1-21
2-Gerbes and 2-Tate Spaces....Pages 23-35
The Geometry of Partial Order on Contact Transformations of Prequantization Manifolds....Pages 37-64
Towards Quantum Cohomology of Real Varieties....Pages 65-99
Weyl Modules and Opers without Monodromy....Pages 101-121
Differentiable Operads, the Kuranishi Correspondence, and Foundations of Topological Field Theories Based on Pseudo-Holomorphic Curves....Pages 123-200
Notes on the Self-Reducibility of the Weil Representation and Higher-Dimensional Quantum Chaos....Pages 201-232
Notes on Canonical Quantization of Symplectic Vector Spaces over Finite Fields....Pages 233-251
Noncommutative Geometry in the Framework of Differential Graded Categories....Pages 253-275
Multiplicative Renormalization and Hopf Algebras....Pages 277-292
