Institute Colloquium
Title: Counting, Curvature and Convex Duality
Abstract: How many rational points with denominator of a given size lie within a specified distance from a compact, “non-degenerate” manifold? This question, deceptively simple in form, has significant implications for a host of problems including Diophantine approximation on manifolds. In this talk, we will explore how the analytic and geometric properties of the manifold govern this count and provide a heuristic for it. We will then discuss recent work that leverages Fourier analytic methods to establish the desired asymptotic for manifolds satisfying a “strong curvature condition”. Finally, we’ll sketch how this model setting sheds light on the more intricate problem of counting rational points near space curves.
About the speaker: Dr. Rajula Srivastava is an Assistant Professor at the University of Wisconsin-Madison, USA. From 2022 to 2025, she was a Hirzebruch Research Instructor with joint appointments at the University of Bonn and the Max Planck Institute for Mathematics. In addition, from 2024–2025, she was a research visitor at the University of Edinburgh with an Argelander Mobility Grant. Dr. Rajula obtained a Ph.D. from UW-Madison in 2022. Prior to this, she graduated with an Integrated Master of Science degree from the National Institute of Science Education and Research, Bhubaneswar.
Dr. Rajula's research interest lies broadly in Harmonic Analysis, both Euclidean and on the Heisenberg group. Of late, she has also become interested in applications of oscillatory integral techniques to number theory; in particular, to count rational points near submanifolds. Recently, Dr. Rajula was awarded the 2025 Maryam Mirzakhani New Frontiers Prize by the Breakthrough Prize Foundation.
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