Mirror Duality via G2 and Spin(7) Manifolds by Selman Akbulut and Sema Salur.-2-Gerbes and 2-Tate Spaces by Sergey Arkhipov and Kobi Kremnizer.-Towards Quantum Cohomology of Real Varieties by Özgür Ceyhan.-Weyl Modules and Opers without Monodromy by Edward Frenkel and Dennis Gaitsgory.-Differentiable Operad, Kuranishi Correspondence, and Foundation of Topological Field Theories Based on Pseudo-holomorphic Curve by Kenji Fukaya.-The Geometry of Partial Order on Contact Transformations of Prequantization Manifolds by Gabi Ben Simon.-Notes on the Self-reducibility of the Weil Representation and Quantum Chaos by Shamgar Gurevich and Ronny Hadani.-Notes on Canonical Quantization of Symplectic Vector Spaces over Finite Fields by Shamgar Gurevich and Ronny Hadani.-Noncommutative Geometry in the Framework of Differential Graded Categories by Snigdhayan Mahanta.-Multiplicative Renormalization and Hopf Algebras by Walter D. van Suijlekom.

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