# GAN

## Seminar

### Effective Ratner Theorem for ASL(2, R) and the gaps of the sequence \sqrt n modulo 1

Seminar Room 1, Newton Institute

#### Abstract

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.#### Video

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