Workshop on Moduli Spaces of Pseudo-holomorphic Curves I: March 17 – 21, 2014

by

Application for workshop is now closed.

Organized by Kenji Fukaya, Dusa McDuff, and John Morgan

Dates: March 17 – 21, 2014

Attendee List Download Detailed Schedule DocumentView Videos

This workshop will study various constructions of the virtual moduli cycle with the aim of clarifying exactly how to count pseudoholomorphic curves. Mostly it will look at the simplest case: that of closed curves. Various methods have now been proposed.  The workshop will be centered around four mini courses, each devoted to one approach, that explain how the analytic and topological problems are solved within the given framework. There will be an introductory lecture, a few other lectures on related topics, plus discussion sections led by designated commentators. The workshop will be technical, and is intended for advanced graduate students, postdocs and other workers in symplectic topology who have a basic acquaintance with the theory of J-holomorphic curves.This workshop is associated with the Spring 2014 program:  Moduli Spaces of Pseudo-holomorphic curves and their applications to Symplectic Topology 

The four mini courses:

I. Kuranishi structures – led by Fukaya, a discussion of the construction by Fukaya-Oh-Ohta-Ono.  (MORE DETAILS CAN BE FOUND HERE)

II. Kuranishi atlases – led by McDuff, based on work by McDuff-Wehrheim.  (MORE DETAILS CAN BE FOUND HERE)

III. Virtual manifolds – led by Bohui Chen, An-Min Li and Bai-Ling Wang, a reworking of the Chen-Tian approach.

IV. Construction of the VMC – led by Ionel and Parker; this uses Donaldson divisors and the sum construction, extending an initial approach by Cieliebak and Mohnke.

Also, Katrin Wehrheim is hosting an online course on Regularization of Moduli Spaces of Pseudholomorphic Curves.  All videos, notes and live stream can be accessed here:  https://scgp.stonybrook.edu/scientific/mini-courses/regularization-of-moduli-spaces-of-pseudholomorphic-curves-katrin-wehrheim

Please contact Kenji Fukaya or Dusa McDuff for more information.

This workshop is a part of the Spring 2014 program, Moduli Spaces of Pseudo-holomorphic curves and their applications to Symplectic Topology, which is organized by Kenji Fukaya, Dusa McDuff, and John Morgan. This program takes place from January 2 – June 30, 2014. More information on the program can be seen here: https://scgp.stonybrook.edu/scientific/programs

 

*All workshop talks and discussion periods will be held in the Simons Center Lecture Hall (Room 102)
*The schedule for Wednesday, March 19th, has the afternoon free (ending after the 12:00pm talk). Lunch and tea time will still be served on Wednesday.

Workshop on Moduli Spaces of Pseudo-holomorphic Curves I Schedule

Time Title Presenters  Video
 9:00am Breakfast/registration begins (9:00am – 10:00am) SCGP Lobby and Cafe
10:00am The Geometry, Analysis, and Topology of Moduli Spaces in Symplectic Geometry Helmut Hofer video
11:00am Coffee Break SCGP Cafe
11:30am Kuranishi structures – Virtual fundamental class – Pseudo holomorphic curve (more info) Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, and Kaoru Ono I video
12:30pm Lunch SCGP Cafe
 2:15pm Kuranishi atlases (more info) Dusa McDuff I video
 3:15pm Tea time SCGP Lobby
 3:45pm Symplectic sum formulas: an overview Mohammad Tehrani video
 4:45pm Break
 5:15pm Some applications of pseudo-holomorphic curves Paul Seidel No Video


Time Title Presenters  Video
 9:00am Breakfast begins (9:00am – 10:00am) SCGP Cafe
10:00am Virtual neighbourhood techniques for Gromov-Witten invariants Bohui Chen, An-Min Li, and Bai-Ling Wang I video
11:00am Coffee Break SCGP Cafe
11:30am Construction of the VFC Eleny Ionel and Thomas Parker I video
12:30pm Lunch SCGP Cafe
 2:15pm A construction of the Deligne-Mumford orbifold Dietmar Salamon video
 3:15pm Tea time SCGP Lobby
 3:45pm Kuranishi structures – Virtual fundamental class – Pseudo holomorphic curve (more info) Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, and Kaoru Ono II video
 4:45pm Break
 5:15pm Kuranishi atlases (more info) Dusa McDuff II video

Time Title Presenters  Video
 8:00am Breakfast begins (8:00am – 9:00am) SCGP Cafe
 9:00am Virtual neighbourhood techniques for Gromov-Witten invariants Bohui Chen, An-Min Li, and Bai-Ling Wang II video
10:00am Coffee Break SCGP Cafe
10:30am Construction of the VFC Eleny Ionel and Thomas Parker II video
11:30am Break
12:00pm The moduli problems in the approach to transversality via Donaldson hypersurfaces (notes) Andreas Gerstenberger video
 1:00pm Lunch SCGP Cafe
 3:15pm Tea time SCGP Lobby

 

Time Title Presenters  Video
 9:00am Breakfast begins (9:00am – 10:00am) SCGP Cafe
10:00am Kuranishi structures – Virtual fundamental class – Pseudo holomorphic curve (more info) Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, and Kaoru Ono – Discussion video
11:00am Coffee Break SCGP Cafe
11:30am Kuranishi atlases (more info) Dusa McDuff – Discussion video
12:30pm Lunch SCGP Cafe
 1:45pm Virtual neighbourhood techniques for Gromov-Witten invariants Bohui Chen, An-Min Li, and Bai-Ling Wang – Discussion video
 2:45pm Tea time SCGP Lobby
 3:15pm Construction of the VFC Eleny Ionel and Thomas Parker – Discussion
 4:15pm Break
 4:45pm Implicit atlases and virtual fundamental cycles John Pardon video
 6:00pm Workshop banquet: Available to all funded participants and invited locals/program visitors. SCGP Cafe

Time Title Presenters  Video
 8:00am Breakfast begins (8:00am – 9:00am) SCGP Cafe
 9:00am Kuranishi structures – Virtual fundamental class – Pseudo holomorphic curve (more info) Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, and Kaoru Ono IV video
10:00am Coffee Break SCGP Cafe
10:20am Kuranishi atlases (more info) Dusa McDuff IV video
11:20am Break
11:40am Virtual neighbourhood techniques for Gromov-Witten invariants Bohui Chen, An-Min Li, and Bai-Ling Wang IV video
12:40pm Lunch SCGP Cafe
 1:30pm Construction of the VFC Eleny Ionel and Thomas Parker IV video
 3:15pm Tea time SCGP Lobby

Additional information:

-Katrin Wehrheim is hosting an online course on Regularization of Moduli Spaces of Pseudholomorphic Curves.  All videos, notes and live stream can be accessed here:  https://scgp.stonybrook.edu/scientific/mini-courses/regularization-of-moduli-spaces-of-pseudholomorphic-curves-katrin-wehrheim

– There will be an informal workshop on polyfolds May 5 – 9, 2014.

– A workshop on Equivariant Gromov-Witten Theory and Applications occurs from May 12 – 16, 2014. Please see the workshop webpage here: https://scgp.stonybrook.edu/archives/7153

– Workshop on Moduli Spaces of Pseudo-holomorphic Curves II occurs from June 2 – 6, 2014. Please see the workshop webpage here: https://scgp.stonybrook.edu/archives/7151

– There will be an informal workshop on the foundations of contact homology from June 16 – 20, 2014.