Mark Hughes
Assistant
Professor
Office: 324 TMCB
E-mail: hughes at mathematics dot byu dot edu
Phone:
(801) 422-7416
Fall
2020
Office Hours:
Mondays 10:00am-11:00am
Wednesdays 9:00am-10:00am
Fridays 1:00pm-2:00pm
Research
Interests:
My research interests lie mainly in
low-dimensional topology, and in particular knot theory
and the topology of 4-dimensional smooth
manifolds.
Recently I've been using techniques from machine learning and neural
networks to try to predict and compute difficult knot
invariants, like the slice genus
of a knot. I am especially interested in using techniques
from reinforcement learning to solve difficult topological
problems.
Another problem I've been interested in involves understanding
how various surfaces can be knotted and "braided" in a given
4-dimensional manifold, and what these surfaces can tell us
about the topology of the overall space. The boundaries of
these surfaces are knots (closed braids actually) in 3-space,
and I've been trying to find ways to use the algebraic
information from the boundary link to provide geometric
information about the surface itself. Some of the tools
I've been using to do this include Khovanov and
Khovanov-Rozansky homology, Dehornoy orderings of the braid
group, Garside normal forms, etc.
Links:
Papers and Preprints
Education
CV
Linear
Algebra Links:
Implementing
Technology in the Linear Algebra Classroom
A Primer on Proof Writing
