• Speaker: Chris Gerig, Harvard University
• Title: Probing 4-manifolds with near-symplectic forms
• Date: 08/29/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

Most closed 4-manifolds do not admit symplectic forms, but most admit "near-symplectic forms", certain closed 2-forms which are symplectic outside of a collection of circles. This provides a gateway from the symplectic world to the non-symplectic world. I will first briefly sketch a geometric interpretation of the Seiberg-Witten invariants in terms of J-holomorphic curves that are compatible with the near-symplectic form. Although the Seiberg-Witten invariants don't apply to (potentially exotic) 4-spheres, nor do these spheres admit near-symplectic forms, there is still a way to bring in near-symplectic techniques.

• Speaker: Honghao Gao, MSU
• Title: Augmentations and sheaves for links
• Date: 09/12/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

We study two different invariants of framed oriented links. Augmentations are rank one representations of a non-commutative algebra, whose definition is motivated by Floer homology. Sheaves in microlocal theory can be thought of as generalizations of link group representations. We will demonstrate two constructions going back and forth between these invariants. We will also tell a motivating story behind the scene, using SFT and microlocalization correspondence in symplectic topology.

• Speaker: David Boozer, UCLA
• Title: Holonomy perturbations of the Chern-Simons functional for lens spaces
• Date: 09/26/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

We describe a scheme for constructing generating sets for Kronheimer and Mrowka's singular instanton knot homology for the case of knots in lens spaces. The scheme involves Heegaard-splitting a lens space containing a knot into two solid tori. One solid torus contains a portion of the knot consisting of an unknotted arc, as well as holonomy perturbations of the Chern-Simons functional used to define the homology theory. The other solid torus contains the remainder of the knot. The Heegaard splitting yields a pair of Lagrangians in the traceless $SU(2)$-character variety of the twice-punctured torus, and the intersection points of these Lagrangians comprise the generating set that we seek. We illustrate the scheme by constructing generating sets for several example knots. Our scheme is a direct generalization of a scheme introduced by Hedden, Herald, and Kirk for describing generating sets for knots in $S^3$ in terms of Lagrangian intersections in the traceless $SU(2)$-character variety for the 2-sphere with four punctures.

• Speaker: Jesse Madnick , McMaster University
• Title: TBD
• Date: 10/17/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Boyu Zhang, Princeton University
• Title: TBD
• Date: 10/31/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Akram Alishahi, University of Georgia
• Title: TBA
• Date: 11/21/2019
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

TBA