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Ian is a Lecturer and Associate Research Scientist in the Mathematics Department at Yale University. He is also part of the Applied Mathematics program at Yale where he serves as Associate Director of Undergraduate Studies. He directs the Summer Undergraduate Mathematics Research at Yale (SUMRY) REU program. In addition to his research, Ian is an effective communicator of mathematics and enjoys teaching across the undergraduate curriculum.

What do you do with Data Science?

Ian is classically trained in Riemannian geometry where he uses variational methods to study closed geodesics. More recently, he has lent this geometric perspective to manifold learning, where he studies the geometry and topology of the data manifold. Together with the Krishnaswamy Lab he has pioneered non-linear dimension reduction and embedding techniques that leverage and preserve the intrinsic geometry of the data manifold. Current work continues to probe the mathematical foundations of data science, through projects on shortest path (geodesic) discovery, data manifold curvature, and metric learning. Recent publications include Diffusion Curvature (NeurIPS 2022), Neural Fisher Information (ICML 2023), and Heat Diffusion for Dimension Reduction (NeurIPS 2023).

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