I am an NSF Mathematical Sciences Postdoctoral Research Fellow at MIT, sponsored by Tobias Colding. My research interests are at the intersection of geometric analysis, physical knot theory, and dynamical systems. I also employ computer visualization to search for mathematical results. Specifically, I am working on electrostatic knot theory, the hyperbolic geometry of higher-dimensional Kuramoto oscillators, and Plateau problems with Möbius energy on the boundary.

I recieved my mathematics PhD at Cornell University, where I was advised by Steve Strogatz. Before that, I was an undergraduate at Willamette University, where I double majored in mathematics and computer science.

You may reach me at liptonm@mit.edu.

*View my CV here.*

Current as of May 2023.

I am not teaching during the 2023-24 academic year.

*Here are some selected preprints and publications.*

Stationary curves under the Möbius-Plateau energy (with G. Nair). Preprint.

Exploring the electric field around a loop of static charge: Rectangles, stadiums, ellipses, and knots. (with S. Strogatz and A. Townsend). Phys. Rev. Research, Vol. 4.

A lower bound on critical points of the electric potential of a knot. J. Knot Theor. Ramif., Vol. 30, Iss. 4.

Kuramoto models on spheres: Using hyperbolic geometry to explain their low-dimensional dynamics (with R. Mirollo and S. Strogatz). Chaos, Vol. 31.

Part of my research involves the level surfaces of the electric potentials of charged knots. I have written code in Python to visualize these surfaces, and you can view an interactive 3D rendering of them here. (NOTE: It may take a few minutes for the webpage to load). You can view interactive plots of the critical sets here. The code can be found here.