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Aspects of Homological Mirror Symmetry, Oct 13-17 2014

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What
  • Summer Schools
When Oct 13, 2014 09:00 AM to
Oct 17, 2014 05:00 PM
Contact Name Katrin Wendland, Emanuel Scheidegger
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Date:

October 13 - 17, 2014

Organization

 

Speakers:

  • Paul S. Aspinwall (Duke)
  • Hubert Flenner (Bochum)
  • Siu-Cheong Lau (Harvard)

Topic

Homological mirror symmetry is an equivalence between the derived category of coherent sheaves on a Calabi-Yau threefold and the Fukaya category of the mirror Calabi-Yau threefold. This conjecture was put forward by Kontsevich in 1994 and has been proven for a large class of Calabi-Yau threefolds by Sheridan in 2012. Nevertheless there are many interesting open questions such an as explicit construction of the equivalence functors as well as a description of further structures of the categories. The focus of the school will lie on the A_\infty structures on both sides of the equivalence. On the side of the derived category this is related to deformation theory of coherent sheaves. On the side of the Fukaya category this is related to Lagrangian intersection theory. In physics, the structure is encoded in the spacetime effective superpotential. The goal of the school is give an introduction to these two aspects and the mirror relation between them.

Prerequisites

The school is intended for both mathematicians and string theorists with interest in mirror symmetry. Background knowledge about Calabi-Yau threefolds is required. Furthermore, some familiarity with coherent sheaves and with Floer theory is desired.

 

Organizers:

  • Katrin Wendland
  • Emanuel Scheidegger
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