Max Lipton

MAX LIPTON

I am a PhD candidate in mathematics at Cornell University, working under Steve Strogatz. My research interests include geometric analysis, physical knot theory, and dynamical systems. I am working on three projects: electrostatic knot theory, the hyperbolic geometry of higher-dimensional Kuramoto oscillators, and Plateau problems with Möbius energy on the boundary. In the Spring 2023 semester, I will be a visiting student at the MIT mathematics department to study minimal surfaces with Bill Minicozzi.

I am graduating in 2023 and I am currently seeking postdoctoral opportunities.

You may reach me at ml2437@cornell.edu.

CURRICULUM VITAE

View my CV here.
Current as of January 2023.

TEACHING

Math 4200/5200: Dynamical Systems and Differential Equations (Fall 2022)

Math 1120: Calculus II (Fall 2020)

RESEARCH

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 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.