Dror Bar-Natan, University of Toronto

Patrick Orson, California Polytechnic State University, San Luis Obispo

Rhea Palak Bakshi, University of California, Santa Barbara

Sucharit Sarkar, University of California, Los Angeles

10:00-10:30: Registration & Breakfast and Coffee 

10:30-11:30:  Sucharit Sarkar

11:30-11:45: Coffee Break 

11:45-12:45: Patrick Orson 

12:45-2:15: (Catered) Lunch

2:15-3:15: Rhea Palak Bakshi 

3:15-3:45: Coffee Break

3:45-4:45: Dror Bar-Natan 

4:45-5:00: Closing and Dinner Coordination

5:00: Dinner (Location: TBA)

Speaker: Dror Bar-Natan, University of Toronto

Title: A Seifert Dream

Abstract: Given a knot 𝐾 with a Seifert surface Σ, I dream that the well-known Seifert linking form 𝑄, a quadratic form on 𝐻_1(Σ), has a docile local perturbation 𝑃_𝜖 such that the formal Gaussian integral of exp(𝑄+𝑃_𝜖) is an invariant of 𝐾. In my talk I will explain what the above means, why this dream is oh so sweet, and why it is in fact closer to a plan than to a delusion. Joint with Roland van der Veen. 

Speaker: Patrick Orson, California Polytechnic State University, San Luis Obispo

Title:  Do exotic symmetries of 4-manifolds survive stabilisation?

Abstract: In 4-manifold topology, differences between the smooth and topological categories often "dissolve" after stabilisation by connected sum with enough copies of S^2xS^2. I will discuss recent joint work exploring whether this holds for the mapping class group of a 4-manifold: if two self-diffeomorphisms are topologically isotopic, are they always smoothly isotopic, after stabilisation? We produce general conditions on the fundamental group that guarantee the answer is indeed "yes". On the other hand, by weakening the initial hypothesis to topologically pseudo-isotopic, we produce examples where the answer is “no”. This is joint with Mark Powell and Oscar Randal-Williams.

Speaker: Rhea Palak Bakshi, University of California, Santa Barbara

Title:  Skein Modules and Their Structure

Abstract: Skein modules were introduced by Przytycki and independently by Turaev as generalizations of the polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. Among these, the Kauffman bracket skein module (KBSM) has been studied most extensively. Recently, Gunningham, Jordan, and Safronov demonstrated that for any closed 3-manifold, the KBSM is finite-dimensional over ℚ(A); however, this finiteness does not extend to the KBSM over ℤ[A^±1]. Moreover, computing the KBSM of a 3-manifold remains a notoriously challenging problem, especially over this ring. In this talk, we will survey these developments and explore several open questions concerning the structure of the KBSM over ℤ[A^±1].

Speaker: Sucharit Sarkar, University of California, Los Angeles

Title:  Legendrian knot contact homotopy type 

Abstract: I will briefly review the Chekanov-Eliashberg dga (viewed as a curved A-infty category by dualizing) associated to the xy-projection of a Legendrian knot in R^3, and Fukaya category of its (co-)augmentations. I will then describe a framework to lift this construction to spectra via flow multi-categories. This is joint work with Robert Lipshitz and Lenny Ng.