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Meet homological mirror symmetry. (English) Zbl 1155.14307

Yui, Noriko (ed.) et al., Modular forms and string duality. Proceedings of a workshop, Banff, Canada, June 3–8, 2006. Providence, RI: American Mathematical Society (AMS); Toronto: The Fields Institute for Research in Mathematical Sciences (ISBN 978-0-8218-4484-7/hbk). Fields Institute Communications 54, 191-224 (2008).
Summary: We introduce the interested reader to homological mirror symmetry. After recalling a little background knowledge, we tackle the simplest cases of homological mirror symmetry: curves of genus zero and one. We close by outlining the current state of the field and mentioning what homological mirror symmetry has to say about other aspects of mirror symmetry.
For the entire collection see [Zbl 1147.11005].

MSC:

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
18E30 Derived categories, triangulated categories (MSC2010)
53D40 Symplectic aspects of Floer homology and cohomology
53D35 Global theory of symplectic and contact manifolds
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