Yuktibhasa seminar series: Rational Points Near Planar Curves

Abstract: Fix your favorite smooth, compact curve C in the plane. How many rational points of a prescribed denominator size are in a given neighborhood of C? In the first part of the talk, we motivate this question and discuss a simple random model predicting the answer. 

In the second part, we use (purely) analytic and geometric tools to approach the question. Special emphasis will be placed on explaining the role of the Fourier transform of the surface measure.

All are cordially invited to the seminar.