Homological Mirror Symmetry [electronic resource] : New Developments and Perspectives / edited by Karl-Georg Schlesinger, Maximilian Kreuzer, Anton Kapustin.

The Symplectic Geometry of Cotangent Bundles from a Categorical Viewpoint -- B-Type D-Branes in Toric Calabi–Yau Varieties -- Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions -- Gauge Theory, Mirror Symmetry, and the Geometric Langlands Program -- Homological Mirror Symmetry and Algebraic Cycles -- Notes on A∞-Algebras, A∞-Categories and Non-Commutative Geometry -- On Non-Commutative Analytic Spaces Over Non-Archimedean Fields -- Derived Categories and Stacks in Physics.

Homological Mirror Symmetry, the study of dualities of certain quantum field theories in a mathematically rigorous form, has developed into a flourishing subject on its own over the past years. The present volume bridges a gap in the literature by providing a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives. With contributions by K. Fukaya, M. Herbst, K. Hori, M. Huang, A. Kapustin, L. Katzarkov, A. Klemm, M. Kontsevich, D. Page, S. Quackenbush, E. Sharpe, P. Seidel, I. Smith and Y. Soibelman, this volume will be a reference on the topic for everyone starting to work or actively working on mathematical aspects of quantum field theory.