NT Seminar Tomorrow: Katy Woo (Stanford)

[Bianca Viray]

Hi everyone,

Our first number theory seminar of the quarter is tomorrow at 11am in PDL C-401. Our speaker is Katy Woo from Stanford University and she will be speaking on: Counting points on a family of degree one del Pezzo surfaces (abstract below). As usual, we will go to lunch with the speaker after the talk.

Best,

Bianca

PS - Yes, I am on jury duty, but court is not in session tomorrow so there will still be seminar. The seminar that was scheduled for Feb. 10 has been postponed to Mar. 10.

Abstract: We study the rational points on the elliptic surface given by the equation: y^2 = x^3 + AxQ(u,v)^2 + BQ(u,v)^3, where 4A^3-27B^2 is nonzero and Q(u,v) is a positive-definite quadratic form. We prove asymptotics for a special subset of the rational points of increasing height, specifically those that are integral with respect to the singularity. This method utilizes Mordell's parameterization of integral points on quadratic twists on elliptic curves, which is based on a syzygy for invariants of binary quartic forms. We reduce the point-counting problem to the question of determining an asymptotic formula for the correlation sums of representation numbers of binary quadratic and binary quartic forms, where the quartic forms have certain invariants. These sums are then treated using a connection to modular forms.

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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/