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Superschool on derived categories and D-branes, Edmonton, Canada, July 17–23, 2016. (English) Zbl 1402.18001

Springer Proceedings in Mathematics & Statistics 240. Cham: Springer; Vancouver: Pacific Institute for the Mathematical Sciences (ISBN 978-3-319-91625-5/hbk; 978-3-319-91626-2/ebook). ix, 260 p. (2018).

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Publisher’s description: This book consists of a series of introductory lectures on mirror symmetry and its surrounding topics. These lectures were provided by participants in the PIMS Superschool for Derived Categories and D-branes in July 2016. Together, they form a comprehensive introduction to the field that integrates perspectives from mathematicians and physicists alike.
These proceedings provide a pleasant and broad introduction into modern research topics surrounding string theory and mirror symmetry that is approachable to readers new to the subjects. These topics include constructions of various mirror pairs, approaches to mirror symmetry, connections to homological algebra, and physical motivations. Of particular interest is the connection between GLSMs, D-branes, birational geometry, and derived categories, which is explained both from a physical and mathematical perspective. The introductory lectures provided herein highlight many features of this emerging field and give concrete connections between the physics and the math.
Mathematical readers will come away with a broader perspective on this field and a bit of physical intuition, while physicists will gain an introductory overview of the developing mathematical realization of physical predictions.
The articles of this volume will be reviewed individually.
Indexed articles:
Hanratty, Chantelle, Abelian and triangulated categories, 3-16 [Zbl 1405.18019]
Chidambaram, Nitin Kumar, Derived categories and derived functors, 17-27 [Zbl 1405.18018]
Chinen, Minako, Introduction to quivers, 29-34 [Zbl 1402.16007]
Liu, Yijia, Semi-orthogonal decompositions of derived categories, 35-48 [Zbl 1405.18021]
Tramel, Rebecca, Introduction to stability conditions, 49-56 [Zbl 1406.14014]
Grieve, Nathan, A brief introduction to geometric invariant theory, 57-75 [Zbl 1405.14118]
Diemer, Colin, Birational geometry and derived categories, 77-92 [Zbl 1405.14038]
Derryberry, Richard, Introduction to mirror symmetry, 95-102 [Zbl 1405.14102]
Talpo, Mattia, Batyrev mirror symmetry, 103-113 [Zbl 1405.14105]
Takeda, Alex A., Introduction to differential graded categories, 115-128 [Zbl 1442.18001]
Zhang, Alex Zhongyi, Introduction to symplectic geometry and Fukaya category, 129-137 [Zbl 1407.53001]
Harder, Andrew, Introduction to homological mirror symmetry, 139-161 [Zbl 1405.14103]
Bejleri, Dori, The SYZ conjecture via homological mirror symmetry, 163-182 [Zbl 1405.14101]
Pietromonaco, Stephen, The derived category of coherent sheaves and B-model topological string theory, 185-208 [Zbl 1406.81078]
Osuga, Kento, Introduction to topological string theories, 209-227 [Zbl 1406.81077]
Ishtiaque, Nafiz, An overview of B-branes in gauged linear sigma models, 229-260 [Zbl 1406.81074]

MSC:

18-06 Proceedings, conferences, collections, etc. pertaining to category theory
81-06 Proceedings, conferences, collections, etc. pertaining to quantum theory
18E30 Derived categories, triangulated categories (MSC2010)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T45 Topological field theories in quantum mechanics
53D37 Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category
00B25 Proceedings of conferences of miscellaneous specific interest
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