Ian McPherson

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I exploit mathematical structures to design and analyze optimization algorithms, and construct statistical estimators from high-dimensional data.

Welcome to my website! I am currently pursuing a PhD in Applied Mathematics and Statistics under the joint supervision of Mauro Maggioni and Mateo Díaz at Johns Hopkins University.

Research Interests

I am interested in the theoretical and algorithmic foundations of Data Science, motivated by the impact of exploiting data for advancing scientific discovery. To exploit data, one must use fast/scalable algorithms while side-stepping the curse of dimensionality which negatively effects convergence and statistical rates.

To this end, I explore the interplay of optimization, geometry, and statistics through a variety of different mathematical lenses including Riemannian geometry, optimal transport, and high-dimensional probability.

Research Areas »

Research Pipeline

Below are some of my ongoing and recent research projects.

  • Neural Dynamic Portfolio Control with Provable Learning Guarantees (Revise and Resubmit at Management Science)
    with Yizhe Huang, Rui Gao, Shuang Li, Luhao Zhang

    Are there neural approaches to portfolio control that incorporate historical returns with provable end-to-end global guarantees? See more… »

  • Nonsmooth Riemannian Optimization with Inexact Information (Submitted)
    with Mateo Díaz and Benjamin Grimmer

    Can nonsmooth convex Riemannian optimization admit nonasymptotic convergence rates using only subgradients, first-order retractions, and vector transports? See more… »

  • Constrained Fréchet Means of Unknown Submanifolds of Non-Euclidean Spaces (In-Preparation)
    with Mauro Maggioni

    Given only a local sampler of a non-convex submanifold of some non-Euclidean space, i.e., Riemannian or Wasserstein, is there an algorithm to compute the empirical intrinsic mean up to arbitrary accuracy with provable guarantees?

For a full list of publications, see Publications.

Upcoming Talks

Below are some upcoming talks. If you will be at any of these, please say hi! I promise I’ll say hi back!

  • MOPTA 2026 — August 18, 2026 · Lehigh University

    Talk: Nonsmooth Riemannian Optimization with Inexact Manifold Primitives via Bundle Methods

  • INFORMS Annual Meeting — November 1–4, 2026 · San Francisco

    Talk: Constrained Fréchet Means of Unknown Submanifolds of Non-Euclidean Spaces
    Co-organizing session Optimization in Data Science with Mateo Díaz

  • SIAM Conference on Mathematics of Data Science (MDS26) — November 16–20, 2026

    Talk: Constrained Fréchet Means of Unknown Submanifolds of Non-Euclidean Spaces
    Co-organizing session Geometry, Dynamics, and Inference with Mauro Maggioni and George Kevrekidis

For a full list of talks and poster presentations, see Presentations.

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