# SL2-actions, modular hyperbolas and Kloosterman sums

Ilya D. Shkredov

## Affiliation:

Moscow State University

## Date:

Wed, 13/11/2019 - 3:00pm

## Venue:

RC-4082, The Red Centre, UNSW

## Abstract:

We are going to talk about the connection between growth in $SL2(F)$ for various fields $F$ and a series of problems of Number Theory and Additive Combinatorics such as Zaremba's conjecture (original and modular) from the theory of continued fractions, distribution of points onto modular hyperbolas and estimates of bilinear forms of Kloosterman sums.