Some NFL players spend their offseason working out. Others travel around the world. Baltimore Ravens offensive lineman John Urschel has done both while also getting an article published in a math journal.
Urschel, the Ravens' 2014 fifth-round pick who graduated from Penn State with 4.0 GPA, also happens to be a brilliant mathematician. This week he and several co-authors published a piece titled "A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians" in the Journal of Computational Mathematics. You can read the full piece here.
If that title left you wanting more, here's the summary of the paper:
"In this paper, we develop a cascadic multigrid algorithm for fast computation of the Fiedler vector of a graph Laplacian, namely, the eigenvector corresponding to the second smallest eigenvalue. This vector has been found to have applications in fields such as graph partitioning and graph drawing. The algorithm is a purely algebraic approach based on a heavy edge coarsening scheme and pointwise smoothing for refinement. To gain theoretical insight, we also consider the related cascadic multigrid method in the geometric setting for elliptic eigenvalue problems and show its uniform convergence under certain assumptions. Numerical tests are presented for computing the Fiedler vector of several practical graphs, and numerical results show the efficiency and optimality of our proposed cascadic multigrid algorithm."
Memorizing a playbook must have been a piece of cake a this guy whose Twitter handle is @mathmeetsfball.
When he's not protecting Joe Flacco, the 23-year-old Urschel enjoys digging into extremely complicated mathematical models. In a recent article for The Players' Tribune, Urschel discussed his varied interests.
"I am a mathematical researcher in my spare time, continuing to do research in the areas of numerical linear algebra, multigrid methods, spectral graph theory and machine learning. I’m also an avid chess player, and I have aspirations of eventually being a titled player one day."
Urschel somehow found the time to compete in a chess tournament earlier this month:
Just finished my first chess tournament ever. Scored 3 points in five rounds in the U1700 of the Pittsburgh Open!!!
— John Urschel (@MathMeetsFball) March 8, 2015
While at Penn State, Urschel helped teach a math class:
There must be something about brilliant offensive linemen and the Baltimore Ravens. Before Urschel arrived, Harvard graduate Matt Birk manned the line for Baltimore.