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Workshop on Topology and Invariants of 4-Manifolds: August 23 – 27, 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 23 – 27, 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 working in the fields of three- and four-dimensional topology, gauge theory, contact and symplectic topology as well as some researchers in the topology of higher dimensional geometric structures. The workshop will provide an opportunity to initiate and enhance the interaction, exchange of ideas, and possible collaboration between the participants. We expect that the workshop will also present an opportunity for the participants to learn the recent advances as well as to reflect upon on previous known techniques for studying the smooth and symplectic 4-manifolds, and contact 3-manifolds. Specifically, we plan to focus on the following research topics: Invariants of Smooth 4-Manifolds, Symplectic Topology, Exotic Group Actions on 4-Manifolds, Exotic 4-Manifolds, Handlebodies of Exotic 4-Manifolds, Stein Fillings and Contact 3-Manifolds, and the Topology of higher dimensional geometric structures.

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

***Please note: Both Saturday 8/23 and Sunday 8/24 will be informal days of the workshop. We will not have our full staff around on these two days (talks will still be recorded and there will be one other staff member present).

Workshop on Topology and Invariants of 4-Manifolds Schedule

Time Title Presenters  Video
 9:00am Breakfast and registration begins (9:00am – 10:00am) SCGP Lobby and Cafe
10:00am Arbitrarily Long Factorizations in Mapping Class Groups Mustafa Korkmaz (1 hour) video
11:00am Coffee Break SCGP Cafe
11:30am Existence of overtwisted contact structures on high dimensional manifolds Emmy Murphy (1 hour) video
12:30pm Lunch SCGP Cafe
 1:30pm A Morse-Bott approach to the Triangulation conjecture Francesco Lin (1 hour) video
 2:30pm Coffee Break (no regular tea time this day) SCGP Cafe
 3:00pm Star surgery operations on symplectic 4-manifolds Laura Starkston (1 hour) video
 4:00pm The minimum $b_2$ problem for right-angled Artin groups Alyson Hildum (30 min) video
slides


Time Title Presenters  Video
 9:00am Breakfast begins (9:00am – 10:00am) SCGP Cafe
10:00am Yamabe invariant of a class of symplectic 4-manifolds Ioana Suvaina (1 hour) video
11:00am Coffee Break SCGP Cafe
11:30am Abelian Gauge Theory, Knots and Odd Khovanov Homology Aliakbar Daemi (1 hour) video
12:30pm Lunch SCGP Cafe
 2:15pm Exotic spheres and the topology of symplectomorphism groups Jonny Evans (1 hour) video
slides
 3:30pm Tea Time SCGP Lobby/Patio
 4:00pm The perturbation of the Seiberg-Witten equations revisited Mikio Furuta (30 min) video
 6:00pm Workshop banquet: Covered for all funded participants. SCGP Cafe

Time Title Presenters  Video
 9:00am Breakfast begins (9:00am – 10:00am) SCGP Cafe
10:00am Classification of fake projective planes and related geometric problems Sai-Kee Yeung (1 hour) Video
slides
11:00am Coffee Break SCGP Cafe
11:30am Multisections of Lefschetz fibrations and topology of symplectic 4-manifolds Inanc Baykur (1 hour) No Video
12:30pm Lunch SCGP Cafe
 2:15pm Stein domains inside complex surfaces Robert Gompf (1 hour) video
 3:30pm Tea Time SCGP Lobby/Patio
 4:00pm Geometric structures, Gromov norm and Kodaira dimensions Weiyi Zhang (1 hour) video
 5:00pm Shake concordance of knots (joint work with Tim Cochran) Arunima Ray (30 min) video

Time Title Presenters  Video
 9:00am Breakfast begins (9:00am – 10:00am) SCGP Cafe
10:00am Concordance homomorphisms from knot Floer homology Peter Ozsvath (1 hour) video
11:00am Coffee Break SCGP Cafe
11:30am Twisted substitutions and fundamental groups of Lefschetz fibraitons Naoyuki Monden (1 hour) video
12:30pm Lunch SCGP Cafe
 2:15pm Partial twists and exotic Stein fillings Kouichi Yasui (1 hour) video
 3:30pm Tea Time SCGP Lobby/Patio
 4:00pm Einstein metrics, 4-manifolds, and differential topology Claude LeBrun (1 hour) video

 

Time Title Presenters  Video
 9:00am Breakfast begins (9:00am – 10:00am) SCGP Cafe
10:00am How we shortcut Lagrangian Floer theory in 4 dimensional case Kenji Fukaya (1 hour) video
11:00am Coffee Break SCGP Cafe
11:30am Tightness and Legendrian surgery Andy Wand (1 hour) video
12:30pm Lunch SCGP Cafe
 2:15pm Cobordisms between tangles Akram Sheikh Alishahi (1 hour) video
slides
 3:30pm Tea Time SCGP Lobby/Patio
 4:00pm Symplectic Divisorial Capping in Dimension 4 Cheuk Yu Mak (30 min) 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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