Affine manifolds and Mirror Symmetry

April 25 - 27, 2008

University of Michigan
Ann Arbor, Michigan

Outside Participants


Slides for Andrey's talk

Andrey's notes on Affine Geometry



Ann Arbor

University of Michigan

Mathematics Department

Airport shuttle number:


(reserve 24h in advance)



Renzo Cavalieri
Hannah Markwig


For website problems, contact webmaster


This year the goal of the workshop is to try and get a grasp of the circle of ideas contained in recent work of Mark Gross and Bernd Siebert:

The Gross-Siebert mirror symmetry program, inspired by the Strominger-Yau-Zaslow conjecture, builds on the idea that the fundamental objects controllingmirror symmetry are integral affine manifolds: real manifolds with transition maps being integral affine transformations. In toy situations,
given such a manifold B without singularities, one obtains easily from it two manifolds: one symplectic and one complex. These form a mirror pair.
However, this leads to few interesting examples, and B must be allowed to have singularities where the affine structure is not defined in order to get interesting examples of mirror symmetry, such as for hypersurfaces in toric varieties.

The Gross-Siebert program then is an approach for dealing with this singular case, and at its heart lies a reconstruction theorem, stating that given some additional combinatorial structure and assumptions on B, it is possible to construct a family of degenerating Calabi-Yau varieties over the spectrum of a complete local ring. The goal of this seminar is to understand the motivation for this result and some of the ideas behind the proof, which appears in ``From Real Affine Geometry to Complex Geometry.'' This paper gives a very explicit description of the family using tropical data on B, hinting at a tropical description of the B-model side (complex structure side) of mirror symmetry.

Mark Gross has kindly agreed to participate and help out find a path among the vast amount of material involved. We intend this workshop as an occasion to bring toghether people from various areas of algebraic geometry (and mathematics in general). For this reason, the assumed background will be minimal. In the spirit of a "learning-seminar", most of the talks will be given by non-experts.

The first talks will be accessible to graduate students in algebraic geometry and related fields.

Arend Bayer U. Utah The SYZ conjectures and homological mirror symmetry
Dan Budreau UCSD Batyrev's contruction
Renzo Cavalieri U. Michigan Overview
Mark Gross UCSD Everything is illuminated
Hannah Markwig U. Michigan Tropical curves
Andrey Novoseltsev U. Washington Affine geometry and the Legendre transform
Nick Proudfoot U.Oregon Toric degenerations and the dual intersection complex
Helge Ruddat U. Freiburg The various Hodge numbers
David Speyer CLAY Log geometry in the G-S program



all talks - and refreshments - will be in EH 4088



Speaker or Event

April 25 th


  • 9:00 am
  • 10:00 -11:00 am
  • 11:00 - 12:00 pm
  • 2:00 - 3:00 pm
  • 3:30 - 4:30 pm



  • Coffee and munchies
  • Renzo Cavalieri
  • Arend Bayer
  • Andrey Novoseltsev
  • Dan Budreau

Apr 26 th

  • 9:00 am
  • 10:00 -11:00 am
  • 11:00 - 12:00 pm
  • 2:00 - 3:00 pm
  • 3:30 - 4:30 pm
  • 6:30 pm



  • Coffee and munchies
  • Nick Proudfoot
  • David Speyer
  • Hannah Markwig
  • Helge Ruddat
  • Workshop dinner.
Apr 27 th

 (Mark’s day)

  • 9:00 am
  • 9:30 - 12:30 am (with breaks)


  • Coffee and munchies
  • Mark Gross


Some funding may be available for outside participants, through the department's NSF RTG grant. Contact Hannah Markwig or Renzo Cavalieri for information.


Department of Mathematics  |  2074 East Hall  | 530 Church Street  
Ann Arbor, MI 48109-1043
Phone: 734.764-0335  |  Fax: 734.763-0937

Site errors should be directed to