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Gauge Theory and Low Dimensional Topology: April 24-28, 2017

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Organized by: Simon Donaldson, Kenji Fukaya, and John Morgan

Gauge Theory and Low Dimensional Topology: With the introduction of Seiberg-Witten theory in the mid 1990s the study of the instanton moduli spaces in dimensions 3 and 4 took a secondary role. Nevertheless, these moduli spaces have a rich geometric structure that has not been fully explored. One focus of the workshop will be the Witten Conjecture relating Instanton theory and Seiberg-Witten theory in dimension 4, where there are fundamental gaps in the mathematical understanding.

Another focus will be the relation between Instanton-Floer and Seiberg-Witten Floer theories dimension 3, and their connections with symplectic Floer theories [for example the Atiyah-Floer Conjecture] and Khovanov homology. Also, recent new applications and possible future applications of these theories to topological and geometric problems will be discussed.

Talk Schedule


Time Title Presenter Location
10:30am Coffee Break N/A SCGP Cafe
11:00am Heegaard Floer invariants in codimension one Daniel Ruberman SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:00pm Pin(2)-equivariant Floer homology and the homology cobordism group Matt Stoffregen SCGP 102
3:15pm Tea N/A SCGP Lobby
3:45pm SO(3) monopoles and relations between Donaldson and Seiberg-Witten invariants Paul Feehan SCGP 102

Time Title Presenter Location
9:30am Heegaard Floer homology of manifolds with torus boundary Jake Rasmussen SCGP 102
10:30am Coffee Break N/A SCGP Cafe
11:00am A Symplectic Instanton Homology via Traceless Character Varieties Henry Horton SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:00pm Coulomb branches of 4d N=2 SUSY gauge theories for $\mathbb R^3\times S^1$ SCGP Weekly Talk Hiraku Nakajima (Colloquim) SCGP 102
3:15pm Tea N/A SCGP Lobby
3:45pm N/A Problem session (Chaired by Donaldson) SCGP 102

Time Title Presenter Location
10:00am What categorification of knot and 3-manifold invariants can tell us about 4-manifolds Sergei Gukov SCGP 102
11:00am Coffee Break N/A SCGP Cafe
11:30am Teichmuller TQFT and a Conjecture for Kapustin-Witten Equations Mikhaylov Victor SCGP 102
12:30pm Lunch N/A SCGP Cafe
2:30pm The $u$-Plane Integral As A Tool In The Theory Of Four-Manifolds Gregory Moore SCGP 102
3:30pm Tea N/A SCGP Lobby
5:30pm N/A WS Banquet SCGP Cafe

Time Title Presenter Location
10:00am A candidate for symplectic side of Atiyah-Floer Conjecture Kenji Fukaya SCGP 102
11:00am Coffee Break N/A SCGP Cafe
11:30am Admissible Bundles and Atiyah-Floer Conjecture Daemi Aliakbar SCGP 102
12:30pm Lunch N/A SCGP Cafe
2:15pm From instantons to holomorphic curves David Duncan SCGP 102
3:15pm Tea N/A SCGP Lobby
3:45pm Towards extended Floer Field theories Guillem Cazassus SCGP 102

Time Title Presenter Location
9:00am Bar Natan’s deformation of Khovanov homology and involutive monopole Floer homology Francesco Lin SCGP 102
10:00am Coffee Break N/A SCGP Cafe
10:30am Traceless SU(2) character varieties of tangles in 3-manifolds Paul Kirk SCGP 102
11:30am The mod 2 cohomology of some SU(2) representation spaces for a surface Christopher Scaduto SCGP 102
12:30pm Lunch N/A SCGP Cafe
3:15pm Tea N/A SCGP Lobby


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