PIMS-UWashington Mathematics Colloquium: Alex Kontorovich

Recent decades have seen a lot of progress in the "orbital circle method" attacking classical problems from dynamics, geometry, and number theory under the umbrella of "thin groups". There was always a danger that the circle method was too crude a tool for the job, and indeed that danger has recently been realized. We will discuss these various problems, the progress towards them, and where things currently stand.