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.