# Manchester Number Theory Seminar - Chris Lutsko

Dates: | 16 April 2024 |
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Times: | 15:00 - 16:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Current University students |

Speaker: Chris Lutsko (University of Zurich)

Title: Average variance bounds for points on the sphere.

Abstract: Consider the integer points lying on the sphere of fixed radius projected onto the unit sphere. There is a well known problem to characterize the distribution of these points. Duke showed that, on congruence conditions for the radius squared, these points equidistribute. To further this study of equidistribution, we consider the variance of the number of points in a spherical cap. An asymptotic for this variance was conjectured by Bourgain-Rudnick-Sarnak. We prove an upper bound of the correct size on the average (over radii) of these variances. In this talk I will sketch the proof of this bound which relies on a careful analysis of the Fourier coefficients of modular forms of half-integer weight.

Room: Frank Adams 1

This seminar talk is sponsored by the Heilbronn Institute for Mathematical Research.