Number Theory Seminar

Thu, 01/05
Ilya Vinogradov (University of Bristol) Number Theory Seminar Add to calendar L5
Let $ G=SL(2,\R)\ltimes R^2 $ and $ \Gamma=SL(2,Z)\ltimes Z^2 $. Building on recent work of Strombergsson we prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of $ \Gamma\G $, which projects to a closed horocycle in the unit tangent bundle to the modular surface. We use this to answer a question of Elkies and McMullen by making effective the convergence of the gap distribution of $ \sqrt n $ mod 1.
Thu, 29/05
Miguel Walsh (University of Oxford) Number Theory Seminar Add to calendar L5
We will discuss some connections between the polynomial method, sieve theory, inverse problems in arithmetic combinatorics and the estimation of rational points on curves. Our motivating questions will be to classify those sets that are irregularly distributed in residue classes and to understand how many rational points of bounded height can a curve of fixed degree have.
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