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APRG Seminar

Title: Counting rational points near flat hypersurfaces
Speaker: Rajula Srivastava (Hausdorff Center / Universitaet Bonn / Max Planck Institute, Germany)
Date: 21 February 2024
Time: 4 pm
Venue: Microsoft Teams (online)

How many rational points with denominator of a given size lie within a given distance from a compact hypersurface? In this talk, we shall describe how the geometry of the surface plays a key role in determining this count, and present a heuristic for the same. In a recent breakthrough, J.J. Huang proved that this guess is indeed true for hypersurfaces with non-vanishing Gaussian curvature. What about hypersurfaces with curvature only vanishing up to a finite order, at a single point? We shall offer a new heuristic in this regime which also incorporates the contribution arising from “local flatness”. Further, we will describe how several ideas from Harmonic Analysis can be used to establish the indicated estimates for hypersurfaces of this type immersed by homogeneous functions. Based on joint work with N. Technau.

The video of this talk is available on the IISc Math Department channel.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 29 Feb 2024