Topology, coast to coast

A virtual conference
Wednesday May 13, 2020

This one-day conference was originally envisioned as a test; but in the intervening months instances of virtual seminars, conferences, and working groups have exploded. Our original aim was to join two seminars–one at PIMS/UBC and the other at NC State–for a one-day conference, experimenting with virtual platforms. In doing so, we hoped to provide another venue for early-career researchers and create new connections for them. Rather than connect two seminar spaces virtually as originally planned, which is not possible in the current climate, this conference will be carried out using Zoom.

This is organized by Tye Lidman (NC State) and Liam Watson (UBC), and is supported by PIMS through the Collaborative Research Grant Novel Techniques in low dimension.

Zoom meeting ID: 948-9281-1254
Password hint: four-letter word for an embedding of the circle into the three-sphere (no caps)

In the schedule below, all times are Pacific Standard Time.

• 9:30 to 10:30, Niny Arcila Maya (UBC)
  
  Decomposition of Azumaya Algebras
  
  Abstract: An Azumaya algebra of degree n over X is a bundle of algebras over X that is locally isomorphic to the matrix algebra. The tensor product of algebras can be extended to Azumaya algebras by performing the operation fiberwise. In topology, we can give conditions for positive integers m and n and the space X such that a topological Azumaya algebra of degree mn can be decomposed as the tensor product of Azumaya algebras of degrees m and n, but no such conditions are known in algebra. We will explain the topological proof and indicate the difficulties in extending these to the algebraic context.
• 10:30 to 11:00, break
  
• 11:00 to 12:00, Onkar Gujral (Duke)
  
  Khovanov homology and the linking of component-preserving cobordisms
  
  Abstract: In this paper we show that up to homotopy up to unit, the Khovanov functor is indifferent to the linking of component-preserving cobordisms between split links. As an application, this allows Levin-Zemke's result on Khovanov homology inducing injective maps on ribbon concordances to be extended to strongly homotopy ribbon concordances. This is joint work with Adam Levine.
• 12:00 to 13:45, break
  
• 13:45 to 14:45, Orsola Capovilla-Searle (Duke)
  
  Weinstein handle decompositions of complements of toric divisors in toric 4-manifolds.
  
  Abstract: We consider toric 4-manifolds with certain toric divisors that have normal crossing singularities. The normal crossing singularities can be smoothed, changing the topology of the complement. We develop an algorithm to draw the Stein handlebody decomposition for the complement of such toric divisors. Joint work with Bahar Acu, Agnes Gadbled, Aleksandra Marinkovic, Emmy Murphy, Laura Starkston and Angela Wu.
• 14:45 to 15:15, break
  
• 15:15 to 16:15, Keegan Boyle (UBC)
  
  Periodic Knots and Alexander Polynomials
  
  It was proved by Murasugi that the Alexander polynomial of a periodic knot is a multiple of the Alexander polynomial of its quotient knot. This is already an extremely strong restriction on the relationship between these polynomials. However using knot Floer homology, specifically a spectral sequence due to Hendricks, Lipshitz and Sarkar, we can prove (in certain cases) and conjecture (more generally) new relationships between these polynomials.