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MSCS Seminars Today

Calendar for Friday October 24, 2025

Friday October 24, 2025

Number Theory Seminar
Diophantine approximation for hypersurfaces
Alex Smith (Northwestern University)
view abstract 12:00 PM in 636 SEO

Among the nondegenerate C^4 hypersurfaces, we characterize the rational quadrics as the hypersurfaces that are the least well approximated by rational points. For all other hypersurfaces, we give a heuristically sharp lower bound for the number of rational points near them, improving the sensitivity of prior results of Beresnevich and Huang. Our methods are dynamical, involving the application of Ratner's theorems for unipotent orbits, and we will show how our work relates to the dynamical resolution of the Oppenheim conjecture by Margulis.