Monday, March 7 |
07:00 - 08:45 |
Breakfast ↓ Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building. (Kinnear Center 105) |
08:45 - 09:00 |
Introduction and Welcome by BIRS Staff ↓ A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions. (TCPL 201) |
09:00 - 09:50 |
Matthew Hedden: On Murasugi sum and knot Floer homology ↓ The Murasugi sum operation in knot theory provides an interesting generalization of the better-known connected sum operation. The special case of plumbing is central to the Giroux correspondence, and therefore figures prominently in the study of contact structures on 3-manifolds. Gabai's work on taut foliations and sutured manifolds showed that the Murasugi sum interacts predictably with regard to geometric features of the knot pertaining to Seifert surfaces e.g. whether they are fibered, or minimal genus. Floer homology has provided algebraic invariants that can serve as receptors for some of the information provided by Gabai's techniques. In the context of Murasugi sums, Ni proved that the rank of a particular (extremal) knot Floer homology group is multiplicative under these operations. We refine Ni's result to show that Murasugi sums induce a graded tensor product of the extremal knot Floer homology groups and, moreover, that in certain cases one can obtain information about other invariants derived from knot Floer homology (so-called "tau" invariants). I'll give an overview of the Murasugi sum and some of its roles in low-dimensional topology, discuss our results, and their corresponding applications. This is joint work with Zhechi Cheng and Sucharit Sarkar. (Online) |
09:50 - 10:20 |
Coffee Break (TCPL Foyer) |
10:20 - 11:10 |
Roger Casals: Legendrian knots & Cluster algebras ↓ The talk will focus on studying Legendrian knots in the standard 3-dimensional contact Darboux ball, with an emphasis on their Lagrangian fillings. First, I will discuss some of the geometric techniques that we currently use to understand Legendrian knots and their Lagrangian fillings, including Legendrian weaves. Then, we will motivate the notion of a cluster algebra through the lens of contact and symplectic topology and present one of the new results in this area: the existence of cluster algebras associated to a large class of Legendrian knots, including all positive braids. Even if we discuss pieces of algebra, symplectic geometry, and in particular the study of Lagrangian skeleta in 4-dimensions, will be our guiding light. (Online) |
11:30 - 13:30 |
Lunch ↓ Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Kinnear Center 105) |
14:00 - 14:20 |
Group Photo ↓ Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo! (TCPL Foyer) |
14:30 - 15:20 |
Ian Zemke: Bordered perspectives on the Manolescu-Ozsvath link surgery formula ↓ The Manolescu-Ozsvath link surgery formula is a powerful tool for computing Heegaard Floer homology. In this talk, we will describe how to interpret their link surgery formula in terms of A_infty modules over a new algebra K. We will describe how to naturally interpret this theory as an theory for bordered manifolds with torus boundary (with some aspects of the theory still in progress). A pairing theorem for gluing torus boundary components takes the form of a connected sum formula for the Manolescu-Ozsvath link surgery formula. This new bordered theory has as an antecedent and inspiration the dual-knot surgery formula of Eftekhary, Hedden and Levine. We will describe how to recover their dual-knot surgery formula as a bimodule for changing the boundary parametrization of a bordered manifold. We will also describe works in progress related to this theory. (TCPL 201) |
15:20 - 15:50 |
Coffee Break (TCPL Foyer) |
15:50 - 16:40 |
Sherry Gong: An A-infinity category from instantons ↓ Given n points on a disk, we will describe how to build an A-infinity category based on the instanton Floer complex of links, and explain why it is finitely generated. This is based on work in progress with Ko Honda. (TCPL 201) |
17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Kinnear Center 105) |