(From left: Maria Dascalu '18, Ilias Stitou '19, Jonah Kudler-Flam '17, and me. Photo credit: Noam Elkies.)

**Graduated Colgate student trainee:** Jonah Kudler-Flam '17 (*Next job:* PhD Student in Theoretical Physics at University of Chicago).

**Colgate student trainees (as of Fall '17):** Ilias Stitou '19, Quan Vu '18, and Ruoyu (Tony) Guo '19.

**NEW!** Ongoing & nearly completed projects from **Spring 2017**:

- Jonah worked on automata models on the Sierpinski gasket (SG), and numerically obtained several (asymptotically) sharp shape results, some of which have been turned into theorems.

We are writing a paper, entitled*Strong shape theorems in cellular automata models on the Sierpinski gasket*, to be made available later in Summer 2017.

In conjunction with the recent preprints arXiv:1702.04017 and arXiv:1702.08370, our paper proves a "limit shape universality" result for cellular automata models on SG. - Ilias is working on automata models on the Vicsek tree, and has begun to observe corresponding patterns analogous to (but not identical to) those on SG.

(Summer 2017) I have presented joint work with Jonah at the Institut Henri Poincare (May, poster) and at the Cornell Fractals 6 conference (June).

Later in the summer, I will present the limit shape universality result in my scientific block course at Universität Bielefeld, Germany (July), and at the international conference "Analysis & Geometry on Graphs & Manifolds" in Potsdam, Germany (August).

Jonah is expected to present at the AMS Fall Western Sectional Meeting in Riverside, CA (November).

(May 2017) Jonah Kudler-Flam won the **2017 Phi Beta Kappa Daniel H. Saracino Prize for Scholarship of Exceptional Merit**, for his work on numerical cosmology (honors thesis, advised by Cosmin Ilie) and on sandpile/aggregation models (advised by me).
Only two graduating seniors are awarded this prestigious prize. (See Colgate academic awards convocation.) Congratulations Jonah!

(April 22, 2017) I gave a follow-up presentation on my ongoing work with Jonah at the 2017 Finger Lakes Probability Seminar, held at Syracuse University. [Program pdf]

(April 8, 2017) Jonah presented sharp (limit) shape results in several sandpile/aggregation models on the Sierpinski gasket at the Hudson River Undergraduate Mathematics Conference. [Full program pdf]

I'm always looking for bright, self-motivated, and mathematically inclined students to do research with me. Contrary to what you might have heard, it does not take a genius to do math research. With the right skill sets and persistence, anyone can contribute to the solution of an open mathematical problem.

For the past few years I have led projects that address open math questions via *numerical experiments*:
By writing and running programs that numerically simulate the given problem, one produces results or pictures that suggest the existence of certain patterns, and then aims to
justify their existence through rigorous proofs.
Depending on your background and training, you may choose to focus on the theory, the numerics, or both.

My research problems are drawn from the intersection of probability, statistical physics, and theoretical computer science. In particular I like studying random (drunkard's) walks and the associated (discrete) calculus on various graphs, and then discover the appropriate limit theorems under a suitable space-time scaling. (Why take limits? Read about the infinite monkey theorem, and maybe you'll be convinced why taking limits is a good idea.)

**My philosophy:**
I take a hands-on approach to supervising research. Roughly speaking, I meet with research students once a week, to discuss any issues they have come across and to debrief them on the necessary theory.
Beyond the weekly meetings, it is up to the students to organize their own schedules to make progress.
Usually I have some intuition about what the expected results may be, but I am also ready to be proven wrong if you can demonstrate accurate numerics (or even better, supported by proofs)!
If you produce good results, I will encourage you to give conference presentations, and then (possibly) write a research paper (with me or on your own).
(That way you'll have something to put on your resumé when applying for grad schools or jobs!)

*Doing research is a highly NONLINEAR process: * expect bruises and bumps (not literally, but figuratively) along the way. But don't easily give up: work hard, be persistently creative, and chances are that you will experience that
moment of eureka!

**Suggested preparation:**
I expect some level of mathematical maturity developed through coursework in math. Thus a (concurrent) background in linear algebra (MATH 214) is a bare minimum.
Ideally I would look for someone who has further taken a course on mathematical proofs (MATH 250) and/or mathematical computations (MATH 260),
plus a 300-level course that uses calculus actively, such as differential equations (MATH 308) and probability (MATH 316).
A solid background in physics or CS is also desirable. (Extensive programming experience is a real plus!)

**How to get involved?**
I anticipate hiring 2 students in each of Fall 2017 and Spring 2018 to work on projects TBA.
(Unfortunately I'm not hiring in Summer 2017 due to my own travel schedule.)
Look for the job posting in the Student Employment section of the Colgate portal approximately 4 weeks prior to the start of the semester.
Apply through the portal; be sure to describe your previous course and research experience.
Successful candidates will be notified shortly before the start of the semester.
(You can choose to work with me for either $$$ or credit through independent study, but not both.)

Back to JPC's research page

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