Homological Mirror Symmetry

Thursday, September 1, 2016 (All day) to Sunday, April 30, 2017 (All day)

During the 2016-17 academic year, the School will have a special program on Homological Mirror Symmetry. Paul Seidel, from MIT, will be the Distinguished Visiting Professor. Maxim Kontsevich, from IHES, will be attending the program for one month during each of the fall and spring terms (from mid-October to mid-November, and for the month of February). Denis Auroux, from UC Berkeley, will be attending for the spring term.

Homological Mirror Symmetry (HMS) was initiated by Kontsevich. It benefits from a close relationship with string theory, and has developed into a powerful and versatile idea. During the program, we will consider the core conjectures of HMS, and its role as a framework within which wider questions from mirror symmetry and other parts of mathematics can be studied. This is still a developing subject, and the program is open to a variety of approaches and viewpoints.

The intention is that the fall term will have a greater focus on the core building blocks of HMS as currently understood: the A-model theory (Lagrangian submanifolds, holomorphic curves and their generalizations), the B-model theory (derived categories in algebraic geometry), and mathematical interpretations of the Strominger-Yau-Zaslow approach, including the Gross-Siebert program. Specific questions of interest include: the role of singular Lagrangian submanifolds (such as Lagrangian skeleta); the effect of instanton corrections on the construction of mirror manifolds; and the structure of wrapped Fukaya categories. We will also consider the interplay between the various algebraic notions that appear in HMS.

The spring term would widen the focus, allowing space for emerging interactions between HMS and other areas. Examples are the theory of Special Lagrangian submanifolds, tropical geometry, and non-archimedean analytic geometry, as well as sheaf-theoretic methods. We also intend to look at applications of ideas from homological mirror symmetry to specific classes of manifolds, such as complex symplectic manifolds and cluster varieties.

There will be two workshops during the special program. The term I workshop, "homological mirror symmetry: methods and structures," will be held November 7-11, 2016.  The term II workshop, "homological mirror symmetry: emerging developments and applications," will be held March 13-17, 2017.