Mathematical Sciences Research Institute

Home » Workshop » Schedules » SYZ mirror symmetry in the complement of a divisor and regular functions on the mirror

SYZ mirror symmetry in the complement of a divisor and regular functions on the mirror

Hot Topics: Cluster algebras and wall-crossing March 28, 2016 - April 01, 2016

March 28, 2016 (10:00 AM PDT - 11:00 AM PDT)
Speaker(s): Denis Auroux (University of California, Berkeley)
Location: MSRI: Simons Auditorium
  • symplectic mirror symmetry

  • homological mirror symmetry

  • Fukaya category

  • Lagrangian Floer homology

  • sheaf cohomology

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



We will give an overview of the Strominger-Yau-Zaslow (SYZ) approach to mirror symmetry in the setting of non-compact Calabi-Yau varieties given by the complement U of an anticanonical divisor D in a projective variety X. Namely, U is expected to carry a Lagrangian torus fibration, and a mirror Calabi-Yau variety U' can then be

constructed as a (suitably corrected) moduli space of Lagrangian torus fibers equipped with local systems. (Partial) compactifications of U deform the symplectic geometry of these Lagrangian tori by introducing holomorphic discs; counting these discs yields distinguished regular functions on the mirror U'. The goal of the talk will be to illustrate these concepts on simple examples, such as the complement of a conic in C^2.

If time permits we will also try to explain the relation of this story to the symplectic cohomology of U and its product structure

25685?type=thumb Auroux Notes 467 KB application/pdf Download
Video/Audio Files


H.264 Video 14476.mp4 372 MB video/mp4 rtsp://videos.msri.org/data/000/025/616/original/14476.mp4 Download
Troubles with video?

Please report video problems to itsupport@msri.org.

See more of our Streaming videos on our main VMath Videos page.