Mirror Duality via G 2 and Spin(7) Manifolds -- 2-Gerbes and 2-Tate Spaces -- The Geometry of Partial Order on Contact Transformations of Prequantization Manifolds -- Towards Quantum Cohomology of Real Varieties -- Weyl Modules and Opers without Monodromy -- Differentiable Operads, the Kuranishi Correspondence, and Foundations of Topological Field Theories Based on Pseudo-Holomorphic Curves -- Notes on the Self-Reducibility of the Weil Representation and Higher-Dimensional Quantum Chaos -- Notes on Canonical Quantization of Symplectic Vector Spaces over Finite Fields -- Noncommutative Geometry in the Framework of Differential Graded Categories -- Multiplicative Renormalization and Hopf Algebras.

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