Teaching
Current Courses
In Spring 2024, I am teaching Math 30: Calculus I and Math 111: Differential Equations.
The easiest way to reach me is to send me email. But it's usually easier to discuss math in real time. So feel free to drop by or call my office anytime. If I'm free, I'd be happy to talk; else, we can easily arrange to talk another time. I will announce my semi-regular office hours soon.
Projects with Students
Feel free to send me an email if you are interested in working on a project together. In the past, I've supervised student research, where we work on a current unsolved problem. Sometimes we solve the problem, and sometimes we don't; but it's always a learning experience for everyone (especially me!). I've also supervised projects where students develop new curricular materials.
Current and past research projects
(with Robert Bowden and Claire Chang) Jones-Wenzl idempotents and central elements in the Roger-Yang Skein Algebra. Robert and Claire are investigating properties of arcs threaded by Jones-Wenzl idempotents and Chebyshev polynomials.
(with Sike Wang) Multiplicative Relations in Skein Algebra of a One-puncture Torus. Siki started the project while a CMC student, continued while she earned a Master's at CGU, and is now preparing a draft for publication while in graduate school for Theoretical CS at CalTch. She received academic year and summer funding through my NSF. She presented her work at the Binghamton University Graduate Combinatorics, Algebra, and Topology (BUGCAT) Conference in Nov 20222.
(with Aryamun Gulati) Extension of a Double-Loop-Flipping Model. Research as a part of senior thesis.
(with Madeline Brown, Miriam Caron) Extending the Aharonov-Jones-Landau Quantum Algorithm for computing the Jones polynomial. Madeline and Miriam received a mix of academic credit and NSF funding throughout the project.
(with Noah Haig, Matthew Hines, Fred Qin, Hannah Zhang) Knotting in Proteins. We analyzed "topological fingerprints" of different families of proteins, in order to find likely folding pathways for them.
(with Nathan Bern, Nate Osher, Thomas Redding and co-advised with Prof. Joshua Davis) Persistence Homology Applied to Structural Geology. We studied a data set (obtained by Sarah Titus et al.) consisting of orientations of spinel crystals from a fault site in New Caledonia. Nathan and Nate received summer funding from my NSF grant.
(with Crystal Lai, Julian Skotheim, Matt Sikkink Johnson) Finite Generators for the Muller Arc Algebra. Julian and Matt received summer funding from my NSF grant, and they each gave a 10-minute presentation at the Joint Mathematics Meetings in Seattle about their results. I'd love to find a current student to help me to extend this project.
(with Ross Jennings, Bibek Pokharel, Ken Schiller) Approximating the Jones polynomial using a Topological Quantum Computer.
(with Sarah Milstein, Rachel Schuh, Nora White) Product-to-Sum Formula for the Roger-Yang Arc Algebra.
(with Martin Bobb, Dylan Peifer and co-advised with Prof. Stephen Kennedy) Finite Generators for the Roger- Yang Arc Algebra. Martin and Dylan received summer funding from my NSF grant, and they each gave a 10-minute presentation at the Joint Mathematics Meetings in San Antonio. Dylan also presented our results at Binghamton University Graduate Conference in Algebra and Topology. Our work led to two articles, one in Involve and one in J. of Knot Theory and its Ramifications.
(with Jonathan Hahn, Collin Hazlett) Product-to-Sum Formula for a Punctured Torus. Jon and Collin presented their results at the Unknot Conference at Denison University.
(with Jeremy Grevet, Qi Li, Daisy Sun) Products of Site-specific Recombination on Torus Knot Substrates. Our work led to an article co-written with Erica Flapan that appeared in J. of the Korean Mathematics Society.
(with Alex Fisher, Rosemary Phelps, Danny Wells) On Torus Knots. This was my first student project that I supervised. Although we didn't solve any significant research problems, I (and hopefully the rest of the them too) learned A LOT from the experience.
Current and past curricular projects
(with Ruth Efe) Economic applications of Differential Equations. We researched topics suitable for independent final projects for Math 111.
(with Ryan Burton and Ruth Efe) Economic applications of Calculus. We developed worksheets to use in my calculus classes.
(with Samuel Harrison and Annika Ozizmir and co-advised with Mike Malced) 3D-printing. We're learning how to use a 3D-printer. Eventually, we will develop projects to use in my classes.
(with Jackson van Fleet Brown) Geology applications in Multivariable Calculus.
(with Krissy Lunz and Jacque Oman) Art in Topology and Geometry. Through funding from Carleton's Visuality Initiative, I hired two students to create mathematical model. Their work was exhibited in the college library.
Mathematical Art Exhibits
If It’s Knot Theory, What Is It, 2015, Gould Library, Carleton College. This exhibit was designed collaboratively with my students from Senior Seminar: Knot Theory and with library curator Margaret Pezalla- Granlund.
Quilting, Copper, and Yarn: Math with Models, 2011, Gould Library, Carleton College. This exhibit featured models created by two studio art students, and the accompanying wall-cards were written by students, as a part of the course Senior Seminar: Surfaces.
Curating Across Disciplines: Intersections between Mathematics and Art, 2008, Museum of Art, Bowdoin College.