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Graduate Workshop on 4-Manifolds: August 18 – 22, 2014

Application for workshop is now closed.

Organized by Selman Akbulut (Michigan State), Anar Akhmedov (University of Minnesota, Twin Cities), Mehmet Firat Arikan (METU), Weimin Chen (University of Massachusetts, Amherst), Yasha Eliashberg (Stanford University), Cagri Karakurt (University of Texas, Austin), Tian-Jun Li (University of Minnesota, Twin Cities), Danny Ruberman (Brandeis University), and Nikolai Saveliev (University of Miami).

Dates: August 18 – 22, 2014

Attendee ListDownload Talk ScheduleView Videos

With the advent of gauge theories and the developments of symplectic topology and the 4-dimensional handlebody techniques, the field of 4-manifolds has experienced a period of phenomenal growth and development. By using gauge theory, Donaldson showed that smooth 4-manifolds are very different from their higher dimensional counterparts. For example, four is the only dimension in which a fixed homeomorphism type of closed 4-manifolds can be represented by infinitely many diffeomorphism types, and in which there exist exotic R^4, that is, manifolds homeomorphic but not diffeomorphic to R^4. Further results followed with the development of Seiberg-Witten gauge theory, which significantly simplified and extended use of gauge theory in the topology of 4-manifolds. Taubes related the Seiberg-Witten and Gromov-Witten invariants of symplectic 4-manifolds, thereby establishing a very important link between smooth and symplectic topology. Ever since, techniques from symplectic and contact topology have provided some of the most important tools in low-dimensional topology, making available a number of new invariants for the study of a large class of smooth 4-manifolds.

Our  workshop will bring together leading researchers and graduate students working in the fields of three- and four-dimensional topology, gauge theory, contact and symplectic topology. It will expose graduate students to current topics in the above mentioned fields.  The workshop will also provide an opportunity to initiate and enhance the interaction, exchange of ideas, and possible collaboration between the participants.  There will be a six minicourses  given by the experts in their fields.

All workshop talks will be held in the Simons Center Lecture Hall (Room 102).

Tea time will either be in the Simons Center Lobby or on the patio outside of the Art Gallery (weather permitting) at 3:30pm.

Graduate Workshop on 4-Manifolds Schedule

Time Title Presenters  Video
 8:30am Breakfast and registration begins (8:30am – 9:30am) SCGP Lobby and Cafe
 9:30am The minimal genus problem for smooth surfaces Tian-Jun Li video
slides
10:30am Coffee Break SCGP Cafe
11:00am Stein fillings of contact 3-manifolds I Burak Ozbagci video
Lecture Notes
12:00pm Lunch SCGP Cafe
 2:15pm Corks, Plugs and exotic structures Selman Akbulut video
 3:30pm Tea Time SCGP Patio/Lobby
 5:00pm Introduction: connections and characteristic classes Daniel Ruberman video
Lecture Notes


Time Title Presenters  Video
 8:30am Breakfast (8:30am – 9:30am) SCGP Lobby and Cafe
 9:30am Symplectic and Lagrangian surfaces—existence and uniqueness Tian-Jun Li video
slides
10:30am Coffee Break SCGP Cafe
11:00am Khovanov homology and homotopy I Robert Lipshitz video
12:00pm Lunch SCGP Cafe
 2:15pm Stein fillings of contact 3-manifolds II Burak Ozbagci video
Lecture Notes
 3:30pm Tea Time SCGP Patio/Lobby
 5:00pm Chern–Simons; construction of Floer homology as a Morse theory. Daniel Ruberman video

Lecture Notes

Time Title Presenters  Video
 8:30am Breakfast (8:30am – 9:30am) SCGP Lobby and Cafe
 9:30am Loose Legendrian knots and flexible Weinstein structures Yasha Eliashberg video
10:30am Coffee Break SCGP Cafe
11:00am Khovanov homology and homotopy II Robert Lipshitz video
12:00pm Lunch SCGP Cafe
 2:15pm Configurations of surfaces and applications Tian-Jun Li video
slides
 3:30pm Tea Time SCGP Patio/Lobby
 4:00pm Floer homology of admissible bundles and examples Nikolai Saveliev video
Lecture Notes

Time Title Presenters  Video
 8:30am Breakfast (8:30am – 9:30am) SCGP Lobby and Cafe
 9:30am Lagrangian caps and their applications Yasha Eliashberg video
10:30am Coffee Break SCGP Cafe
11:00am Floer exact triangle, and various Floer homology theories of knots and links Nikolai Saveliev video
Lecture Notes
12:00pm Lunch SCGP Cafe
 2:15pm Handlebodies of exotic 4-manifolds Selman Akbulut video
slides
 3:30pm Tea Time SCGP Patio/Lobby
 4:00pm Stein fillings of contact 3-manifolds III Burak Ozbagci video
Lecture Notes
 5:00pm TBA Tom Mrowka video
 6:00pm Workshop banquet: Covered for all funded participants. SCGP Cafe

 

Time Title Presenters  Video
 8:30am Breakfast (8:30am – 9:30am) SCGP Lobby and Cafe
 9:30am Construction of  contact structures Yasha Eliashberg video
10:30am Coffee Break SCGP Cafe
11:00am TBA Tom Mrowka video
12:00pm Lunch SCGP Cafe
 2:15pm Handlebodies of exotic 4-manifolds (Akbulut); On Stein rational balls (Williams) Selman Akbulut; Luke Williams video
slides
 3:30pm Tea Time SCGP Patio/Lobby
 4:00pm Khovanov homology and homotopy III Robert Lipshitz video

2013 FRG Workshop and Conference: Topology and Invariants of Smooth 4-Manifolds
http://www.math.umn.edu/~akhmedov/UMN2013

2012 FRG Workshop and Conference: Topology and Invariants of Smooth 4-Manifolds
http://www.math.umn.edu/~akhmedov/Stanford2012

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