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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 |
