Seminars & Events for Joint PU/IAS Symplectic Geometry Seminar

October 9, 2017
4:45pm - 5:45pm
Wrapped Floer theory and Homological mirror symmetry for toric Calabi-Yau manifolds

Abstract: Consider a Lagrangian torus fibration a la SYZ over a non compact base. Using techniques from arXiv:1510.04265, I will discuss the construction of wrapped Floer theory in this setting. Note that this setting is generally not exact even near infinity. The construction allows the formulation of a version of the homological mirror symmetry conjecture for open manifolds which are not exact near infinity. According to time constraints, I will apply this to prove homological mirror symmetry in the case where the A-model is the complement of an anti-canonical divisor in a toric Calabi Yau manifold.

Speaker: Yoel Groman, Columbia University
Location:
IAS Room S-101
October 16, 2017
4:00pm - 5:00pm
Compactification of moduli spaces of J-holomorphic maps relative to snc divisors

In this talk, I will describe an efficient way of compactifying moduli spaces of J-holomorphic maps relative to simple normal crossings (snc) symplectic divisors, including the holomorphic case.  The primary goal of this construction is to define Gromov-Witten invariants relative to snc divisors, and to establish a GW-degeneration formula for any semistable degeneration with an snc central fiber. It is also possible to extend the construction to the case of J-holomorphic maps with boundary on a Lagrangian, even if the Lagrangian intersects the divisor non-trivially (intersecting each stratum in a Lagrangian again); especially, if the Lagrangian is a real locus.

Speaker: Mohammad Farajzadeh Tehrani, Stony Brook University
Location:
Fine Hall 224
October 23, 2017
4:00pm - 5:00pm
Wrapped Fukaya categories and Functors

Inspired by homological mirror symmetry for non-compact manifolds, one wonders what functorial properties wrapped Fukaya categories have as mirror to those for the derived categories of the mirror varieties, and also whether homological mirror symmetry is functorial. Comparing to the theory of Lagrangian correspondences for compact manifolds, some subtleties are seen in view of the fact that modules over non-proper categories are complicated. In this talk, the story concerning the fundamental construction of Fourier-Mukai type functors of wrapped Fukaya categories is discussed, under slightly modified framework of wrapped Floer theory. Applications of the relevant techniques to be presented include the Kunneth formula and restriction maps.

Speaker: Yuan Gao, Stony Brook University
Location:
IAS Room S-101
October 30, 2017
4:00pm - 5:00pm
TBA-Laura Starkston
Speaker: Laura Starkston, Stanford University
Location:
IAS Room S-101
November 13, 2017
4:00pm - 5:00pm
TBA-Li-Sheng Tseng
Speaker: Li-Sheng Tseng, University of California at Irvine
Location:
Fine Hall 224
November 27, 2017
4:00pm - 5:00pm
TBA-Yu-Shen Lin
Speaker: Yu-Shen Lin, CMSA, Harvard University
Location:
IAS Room S-101
December 11, 2017
4:00pm - 5:00pm
TBA-Lenny Ng
Speaker: Lenny Ng, Duke University
Location:
IAS Room S-101