Mark Hughes                                                                       

Assistant Professor
Department of Mathematics
Brigham Young University


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.


Papers and Preprints

Linear Algebra Links:

Implementing Technology in the Linear Algebra Classroom
A Primer on Proof Writing