Ian McPherson

I am a Ph.D. student studying Applied Mathematics and Statistics at Johns Hopkins University, primarily advised by Professor Mauro Maggioni. I am also currently collaborating with Mateo Díaz and Ben Grimmer. I obtained a Masters in Mathematics from Tufts University in 2022, and a B.A. in Biochemisty and Economics from Occidental College in 2019. For more details, see my CV.

My research is in Optimal Transportation and Riemannian Optimization, with a focus on asking how we can lift algorithms from the Euclidean setting to more exotic metric spaces. In particular, my current projects center on:

• Computing Barycenters on Unknown Wasserstein Submanifolds;
• Convergence Rate Analysis of Riemannian Bundle Methods.

Outside of my current projects, I am also interested in:

• Statistical Optimal Transportation, and Different Regularization Schemes (Entropic Optimal Transport and Quadratically Regularized Optimal Transport;
• Analysis of Wasserstein Gradient Flows, and Different Algorithmic Approximations and Applications thereof;
• Different Approximations for Riemannian Geoemtric Tools (Retractions and Vector Transports) and How to Obtain Quantitive Bounds on Approximation;
• High Dimensional Probability and Geometry, and Statistical Learning Theory.

I am greatful to have been recognized among my many talented peers in recent years. Notably, I have been given the Rufus P. Isaacs Graduate Fellowship, which distinguishes promising early graduate students for research within my department, as well being the Sole Recipient across the Whiting School of Engineering of the 2024 Whiting School of Engineering Teaching Assistant Award, an award given in recognition of excellence and talent as a graduate TA. I am incredibly humbled by these acolades, and I hope I can rise to these titles through more hardwork and unbridled curiosity.