Titlebook: Homological Mirror Symmetry; New Developments and Karl-Georg Schlesinger,Maximilian Kreuzer,Anton Ka Book 2009 Springer-Verlag Berlin Heide

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,B-Type D-Branes in Toric Calabi–Yau Varieties,eneral paths in the Kähler moduli space. The most important finding is the grade restriction rule. It classifies Chan–Paton representations of the gauge group that are allowed when we cross the phase boundaries. Upon reduction to the chiral sector, we find equivalences of the derived categories on d

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,Notes on A∞-Algebras, A∞-Categories and Non-Commutative Geometry, spaces. The geometric approach clarifies several questions, e.g. the notion of homological unit or A-infinity structure on A-infinity functors. We discuss Hochschild complexes of A-infinity algebras from the geometric point of view. The chapter contains homological versions of the notions of proper

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On Non-Commutative Analytic Spaces Over Non-Archimedean Fields,urfaces and quantized locally analytic p-adic groups. In the latter case we found a quantization of the Schneider–Teitelbaum algebra of locally analytic distributions by using the ideas of representation theory of quantized function algebras.

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