Research

Loosely speaking, I am interested in algebra, combinatorics, discrete dynamical systems, and mathematical biology. I have a special affinity for problems in the intersection of these topics.

• Algebraic systems biology. This includes modeling biological systems with Boolean functions, developing and using computational algebraic techniques to analyze models. It also involves exploring new (non-applied) mathematics that arises along the way.
• Finite dynamical systems. Objects of study include Boolean networks, cellular automata, and sequential dynamical systems. This work ranges from computer science and physics, to computational algebra in nature.
• Mathematical crystallography. Group theory that arises in chemistry and material science.
• Dynamical algebraic combinatorics. Topics include actions of groups on finite sets, toggle groups, and homomesy.
• Toric partial orders. Cyclic analogous of ordinary posets, which involves geometric and algebraic combinatorics, and cyclic reducibility and conjugacy in Coexter groups.

Like many people, I am constantly grappling with finding the ideal balance of research breadth vs. depth. One of the downsides of having a wide breadth of interests is the inordinate amount of cumulative peer review requests I get, from journals in pure math (combinatorics, algebra), applied math, mathematical biology, bioinformatics, computer science, physics, and engineering.

I sometimes wait until an interesting date to post a paper. Thus far, I have papers time-stamped with the following dates, in spirit with the Stone Vertical Epic Ales, 8/8/08, 9/9/09, 10/10/10, and 11/11/11, several leap days: 2/29/08, 2/29/12, and 2/29/20, and birthdays and anniversaries. I also like to hide "secret messages" in arXiv papers, sometimes related to the posting date. Three such examples includes ones from 10/21/15, 11/8/16, and this one. Can you find them?

Frequently asked questions

• Q: What the heck is "Algebraic Biology"?
  A: Read my gentle survey article!

• Q: What do you mean "new mathematics arising from biology"?
  A: Start with essays from Joel Cohen (2004), and Bernd Sturmfels (2005), and then read my survey article (see above), and my paper on pseudomonomials.

• Q: How can I learn more about discrete and algebraic biology?
  A: A good place to start are edited volumes by Robeva/Hodge (2013), and Robeva (2015), and Robeva/myself (2018). The chapters are freely available with a ScienceDirect subscription.

• Q: What is "Dynamical Algebraic Combinatorics"?
  A: Read these two fantastic survey articles: by Striker (2017), and by Propp/Roby (2015).

• Q: Is there any overlap between your interests in dynamics algebraic combinatorics (math), and the more traditional CS/physics field of cellular automata?
  A: I wrote a paper on this, in the 2021 AUTOMATA proceedings.

• Q: What do you work on in mathematical crystallography? There's nothing in it in your CV.
  A: It's a new interest, and a collaboration with a crystallographer. We're finishing up a paper, and I'll share it when it's done.

• Q: Do you go by Matt or Matthew?
  A: Either. No preference.

• Q: Do all of your co-authors know about the hidden message in your joint arXiv papers?
  A: No.