Next week's seminar and schedule change starting in Spring.

[Bianca Viray]

Hello everyone,

Our first external NT seminar speaker of the quarter, Alexander Smith, will be speaking next week, Tuesday, November 4, at 11am in PDL C-401. He will be speaking on Diophantine approximation for hypersurfaces (abstract below). As usual, we will go to lunch with the speaker after the talk.

Starting in Spring 2026, the NT seminar will move to Thursdays, still at 11am.

Abstract: 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.

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Bianca Viray (she/her)

Craig McKibben and Sarah Merner Professor of Mathematics

University of Washington

Seattle, WA 98195

https://sites.math.washington.edu/~bviray/