Research
Research Interests
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.
I love to collaborate, explore interesting new ideas, expand my
breadth, and learn new things. If you're interested in talking about
my work, your work that I might be interested in, or anything
inbetween, don't hestitate to contact me!
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.
Publications
You can find my complete publication list on
my CV. I post most of my papers to the arXiv. Though
they are scattered across math, q-bio, and cs subject-classes, the
complete list can be found
here.
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.