Welcome to Ian McPherson’s Personal Site

I am currently a second-year Ph. D. student in the Applied Math and Statistics Department at Johns Hopkins University. I have the privilege of currently being primarily advised by Mauro Maggioni. I am fortunate to have been distinguished amongst talented peers by my dpeartment through the Rufus P. Isaacs Graduate Fellowship. Previously, I obtained my M. Sc. in Mathematics with a concentration in Probability from Tufts University where much of early perspectives on mathematics have been shaped by James Murphy and Kasso Okoudjou. Even before then, I received my B.A. in Biochemistry and B.A. in Economics at the Occidental College.

I am most interested in what kind of algorithms can be developed with robust guarantees when losing Euclidean structure. Currently, I am interested in graph-based manifold learning in more general spaces such as $(P_{2,ac}(\mathbb{R}^d), W_2)$, and Riemannian Optimization methods. For such problems, I have grown an affinity for using tools that draw inspiration from High Dimensional Probability and Statistics, Convex Analysis, Riemannian Geometry, and Nonlinear Optimization. Beyond these core domains, I am becoming interested in Particle-Based Methods for working within Wasserstein Space, with a hope of learning more about Interacting Particle Systems and Mean Field Games in the near-future.

Concretely, I am currently working on two research projects: one collaborating with Mauro Maggioni and the other collaborating with Ben Grimmer and Mateo Diaz Diaz. More to come soon.

I am fortunate enough to be funded to travel and learn from future collaborators and mentors in the near future. I will be visiting ICERMs Interacting Particle Systems: Analysis, Control, Learning and Computation Workshop in May, Berkeley’s SL Math Graduate Summer School Particle interactive systems: Analysis and computational methods in June, and Princeton’s ML Theory Graduate Summer School in August. Please feel free to reach out if you happen to be attending any of these!

Outside of research, I am fortunate to be able to partake in teaching at a capacity beyond providing support as a Teaching Assistant, although as a TA I have recieved a department wide award - the Whiting School of Engineering Teaching Assistant Award - for contributions as a TA. I have also been priviledges to geek with incoming Masters students as the Masters Probability Bootcamp instructor. Moreover, I will have the opportunity to try and persuade incoming undergraduate first-years to learn more about the intersection of mathematics and application in a self-contained and personally constructed survey course this upcoming fall titled Geometric Toolbox for High Dimensional Statistics and Optimization. I am beyond excited by all of the opportunities I have to not only pursue my research interests, but to share my wonder at differing levels of abstraction!

Beyond my duties as a fledgling academic, I find joy in challenging myself in long distance sports - via Marathon training and long-distance cycling. If you’ve gotten this far in this long rambling webpage, thank you for visiting my corner of the internet!