Mark Hughes                                                                       


Assistant Professor
Department of Mathematics
Brigham Young University


Contact:

Office: 324 TMCB
E-mail: hughes at mathematics dot byu dot edu
Phone: (801) 422-7416



Fall 2019 Teaching:      

Math 313 - Linear Algebra, Sections 02 and 15

 

Fall 2019 Office Hours:      

Monday 1:00pm-2:00pm
Wednesday 11:00am-12:00pm
Friday 10:00am-11:00am

(or by appointment).
    

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