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Moduli Spaces of Pseudo-holomorphic curves and their applications to Symplectic Topology

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Organized by Kenji Fukaya, Dusa McDuff, and John Morgan
January 2 – June 30, 2014

Gromov-Witten theory, Lagrangian-Floer homology and symplectic field theory arise from the notion of pseudo-holomorphic curves, possibly with boundary conditions, in symplectic manifolds. All these theories rely in a fundamental way on Gromov’s compactness result for moduli spaces of pseudo-holomorphic curves, as well as on results about gluing and transversality. A central issue is how to use these analytic results in various contexts to produce appropriate structures on the moduli spaces, structures that allow one to define a virtual fundamental cycle that can then be used to produce algebraic invariants.

The program will focus on two basic approaches to understanding the structure of these moduli spaces:
(1) local finite-dimensional models derived from the local Kuranishi obstruction picture, and
(2) infinite dimensional analysis — the polyfold approach.

The purpose of this program is to examine foundational analytic and topological questions associated with these approaches, especially in key examples such as the closed case (Gromov-Witten theory), Hamiltonian- and Lagrangian-Floer theory and contact homology. The aim is to compare and contrast the approaches with each other and with alternative methods, such as those in algebraic geometry or those provided by Joyce’s derived smooth manifold theory.

Speaker and Seminar Schedule:

The weekly talks take place on Tuesdays at 11:15am and 2:30pm (beginning January 21) in room 313.

-Dusa McDuff will host a minicourse on Kuranishi Atlases, Thursdays at 11:45am in the Simons Center for Geometry and Physics Seminar Room, 313.  More details about these lectures can be found here:  http://scgp.stonybrook.edu/scientific/mini-courses/mini-course-by-dusa-mcduff-kuranishi-atlases

-Kenji Fukaya will host a minicourse on Kuranishi Structures, Fridays at 12:00pm in the Simons Center for Geometry and Physics Seminar Room, 313.  More details about these lectures can be found here:  http://mysbfiles.stonybrook.edu/~mfarajzadeht/Fukaya.html

-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:  http://scgp.stonybrook.edu/scientific/mini-courses/regularization-of-moduli-spaces-of-pseudholomorphic-curves-katrin-wehrheim

 

Date and Time Title Presenters
1/21 at 11:15am – Room 313 Lifted Floer homology and topology of monotone Lagrangian submanifolds Mihai Damian Video
1/21 at 2:30pm – Room 313 Some remarks on hydrodynamic stability Kai Cieliebak Video NA due to inclement weather
1/28 at 11:15am – Room 313 Minimal Discrepancy of Isolated Singularities and Reeb Orbits Mark McLean Video
1/28 at 2:30pm – Room 313 Cylindrical contact homology as a well-defined homology? Joanna Nelson Video
1/31 at 12:00pm – Room 313 Virtual fundamental chain, pseudo-holomorphic curve and Kuranishi structure Kenji Fukaya More Details / Video
2/4 at 11:15am – Room 313 Minimal Discrepancy of Isolated Singularities and Reeb Orbits Continued Mark McLean Video
2/4 at 2:15pm – Room 313 Cylindrical contact homology as a sometimes well-defined homology Joanna Nelson Video 
2/6 at 11:45am – Room 313 Kuranishi Atlases Dusa McDuff More Details / Video
2/7 at 12:00pm – Room 313 Virtual fundamental chain, pseudo-holomorphic curve and Kuranishi structure Kenji Fukaya More Details / Video 
2/11 at 2:30pm – Room 313 Length and volume in Seiberg-Witten theory Daniel Cristofaro-Gardiner Video
2/14 at 12:00pm – Room 313  Cancelled Kenji Fukaya More Details
2/18 at 11:15am – Room 313 Minimal Discrepancy of Isolated Singularities and Reeb Orbits Continued Mark McLean Video 
2/18 at 2:30pm – Room 313  On Floer cohomology and non-archimedian geometry Mohammed Abouzaid Video 
2/20 at 11:45am – Room 313  Kuranishi Atlases Dusa McDuff More Details / Video
2/21 at 12:00pm – Room 313 Virtual fundamental chain, pseudo-holomorphic curve and Kuranishi structure Kenji Fukaya More Details / Video
2/25 at 11:15am – Room 313 Transversality via the Donaldson hypersurface technique – Part 1 Klaus Mohnke Video / Notes
2/25 at 2:30pm – Room 313 Kuranishi Atlases Dusa McDuff More Details
2/28 at 12:00pm – Room 313  Virtual fundamental chain, pseudo-holomorphic curve and Kuranishi structure Kenji Fukaya More Details / Video

MARCH

3/4 at 11:15am – Room 313 Transversality via the Donaldson hypersurface technique – Part 2 Klaus Mohnke Video / Notes
3/4 at 2:30pm – Room 313 Analysis of contact Cauchy-Riemann maps and canonical connection on contact manifolds, I Rui Wang Video
3/6 at 11:45am – Room 102 Introduction to virtual neighborhood technique Bohui Chen Video
3/7 at 12:00pm – Room 313 Virtual fundamental chain, pseudo-holomorphic curve and Kuranishi structure Kenji Fukaya Video 
3/11 at 11:15am – Room 313 Transversality via the Donaldson hypersurface technique – Part 3 Klaus Mohnke Video 
3/11 at 2:30pm – Room 313 Analysis of contact Cauchy-Riemann maps and canonical connection on contact manifolds, II Yong-Geun Oh Video 
3/13 at 11:45am – Room 102 Seminar Series on Kuranishi Atlases Dusa McDuff More Details / Video
3/14 at 12:00pm – Room 313 Seminar Series on Kuranishi Structures Kenji Fukaya Video
3/25 at 11:15am – Room 313 GW invariants relative normal crossing divisors Eleny Ionel Video 
3/25 at 2:30pm – Room 313 GW invariants relative normal crossing divisors Eleny Ionel Video 
3/28 at 12:00pm – Room 313 Seminar Series on Kuranishi Structures Kenji Fukaya Video
4/1 at 11:15am – Room 313 Towards Viterbo functoriality for nonexact Liouville embeddings Janko Latschev Video
4/3 at 11:45am – Room 313 Seminar Series on Kuranishi Atlases:  The role of additivity Dusa McDuff More Details / Video
4/4 at 12:00pm – Room 313 Seminar Series on Kuranishi Structures Kenji Fukaya Video
4/8 at 11:15am – Room 313 Looking for flexibility in higher-dimensional contact manifolds Olga Plamenevskaya Video
4/10 at 11:45am – Room 313 Seminar Series on Kuranishi Atlases Dusa McDuff More Details / Video
4/11 at 12:00pm – Room 313 Seminar Series on Kuranishi Structures Kenji Fukaya Video
4/15 at 2:30pm – Room 313 Cyclic homology in Toric A Landau-Gizburg B Mirror symmetry Kenji Fukaya Video
4/17 at 11:45am – Room 313 Seminar Series on Kuranishi Atlases Dusa McDuff More Details / Video
4/18 at 12:00pm – Room 313 Seminar Series on Kuranishi Structures Kenji Fukaya Video
4/22 at 2:30pm – Room 313  Periodic Symplectic Cohomologies Jingyu Zhao Video
4/24 at 11:45am – Room 313 Seminar Series on Kuranishi Atlases Dusa McDuff More Details / Video
4/25 at 12:00pm – Room 313 Seminar Series on Kuranishi Structures Kenji Fukaya Video
4/29 at 11:00am – Room 313 Absolute vs Relative Gromov-Witten Invariants Aleksey Zinger Video
4/29 at 2:30pm – Room 313 Absolute vs Relative Gromov-Witten Invariants Aleksey Zinger Video
5/20 at 11:15am – Room 313 The Lagrangian Cubic Equation Paul Biran Video
5/27 at 2:30pm – Room 313 Category of Kuranishi structure germs and a forgetful functor from polyfold Fredholm sections Dingyu Yang Video 
6/10 at 2:30pm – Room 313 Cyclic homology and S^1-equivariant symplectic cohomology Sheel Ganatra Video 
6/16 at 11:15am – Room 313 Applications and computations of contact homology revisited Frederic Bourgeois
6/16 at 2:00pm – Room 313 Obstruction bundle gluing in cylindrical contact homology Michael Hutchings
6/17 at 11:15am – Room 313 Symplectic and contact differential graded algebras Alex Oancea
6/17 at 2:00pm – Room 313 TBA Mohammed Abouzaid
6/18 at 11:15am – Room 313 Two approaches to S^1-equivariant symplectic homology Frederic Bourgeois
6/18 at 2:00pm – Room 313 Transversality for multiple covers Chris Wendl
6/19 at 11:15am – Room 313 Transversality for S^1-equivariant symplectic homology Alex Oancea
6/19 at 2:00pm – Room 313 Daniel Christofaro-Gardiner

 

Additional information:

– Workshop on Moduli Spaces of Pseudo-holomorphic Curves I occurs from March 17 – 21, 2014. Please see the workshop webpage here: http://scgp.stonybrook.edu/archives/7149

– There will be joint seminar series by Helmut Hofer and Dominic Joyce May 5 – 9, 2014.  More details can be found HERE

– A workshop on Equivariant Gromov-Witten Theory and Applications occurs from May 12 – 16, 2014. Please see the workshop webpage here: http://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: http://scgp.stonybrook.edu/archives/7151

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


Moduli Spaces Program Seminar:  Sheel Ganatra, Stanford

Moduli Spaces Program Seminar: Sheel Ganatra, Stanford

Title: Cyclic homology and S^1-equivariant symplectic cohomology Speaker:  Sheel Ganatra, Stanford Date: Tuesday, June 10, 2014 Time: 2:30pm-3:30pm Place: Seminar Room 313, Simons Center     [box, type=”download”]Watch the video.[/box] Abstract: In this talk, we study two natural circle actions in Floer theory, one on […]

Moduli Spaces Program Seminar:  Dingyu Yang, Jussieu Institute, UPMC

Moduli Spaces Program Seminar: Dingyu Yang, Jussieu Institute, UPMC

Title: Category of Kuranishi structure germs and a forgetful functor from polyfold Fredholm sections Speaker:  Dingyu Yang, Jussieu Institute, UPMC Date: Tuesday, May 27, 2014 Time: 2:30pm-3:30pm Place: Seminar Room 313, Simons Center   [box, type=”download”]Watch the video.[/box]