Ian Adelstein

Ian Adelstein is a Lecturer and Associate Research Scientist in the Department of Mathematics at Yale University, where he also serves as Associate Director of Undergraduate Studies for the Applied Mathematics program. He directs the SUMRY REU program and is affiliated with the Yale Institute for Foundations of Data Science. His research focuses on geometric manifold learning and geometric analysis, combining techniques from differential geometry with machine learning and data science. He has organized workshops on topics such as geometric data science and Ricci curvature, and has presented at international conferences like NeurIPS and ICML.

Education: Ph.D., Dartmouth College.

Research Interests:

• Geometric manifold learning, including diffusion curvature and neural network-based metrics
• Geometric analysis of closed geodesics and variational methods
• Applications of geometry to high-dimensional data analysis

Recent work highlights include contributions to graph signal processing (BLIS-Net) and the development of diffusion-based methods for curvature estimation. His geometric analysis work explores properties of geodesics on spheres and projective spaces, with implications for spectral geometry and singularity theory.

Advising & Grants: Advises undergraduate research through SUMRY, organizes academic workshops, and collaborates with the Krishnaswamy Lab. No explicit grants mentioned in provided texts.

Labs/Teams: Member of the Krishnaswamy Lab and part of the Yale Institute for Foundations of Data Science. Active in organizing interdisciplinary research events.