CRG Novel Techniques in Low Dimension- 1 Day Virtual Conference (Online)

This event is being held virtually, below is the schedule:

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)

Obstructions to immersed lagrangian fillings with double points of vanishing index and action.

Abstract: For immersed, exact Lagrangian fillings of a Legendrian knot where all double points have vanishing action and index, the genus, g, and the number of double points, p, satisfies a linear relationship determined by the Thurston-Bennequin invariant of the Legendrian boundary. It is always possible to decrease p at the cost of increasing g; we show that it is not always possible to decrease g at the cost of increasing p. To show this, we extend a result Pan and show that an embedded, exact Lagrangian cobordism between Legendrian links Λ± induces an injective map on associated augmentation categories. This is joint work with Noemi Legout, Maylis Limouzineau, Emmy Murphy, Yu Pan and Lisa Traynor.

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.

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..