Title: Mahler’s question in Diophantine approximation: a summary of recent developments

Abstract: In 1984, at the age of 81, the number theorist Kurt Mahler published a paper called “Some suggestions for future research.” In this paper he outlined some of his favorite open problems. One of these came to be called “Mahler’s conjecture” and concerns the Diophantine properties of typical points in Cantor’s middle thirds set. After several “near-solutions” by Khalil-Luethi and by Datta-Jana, a solution was announced recently by Benard, He and Zhang. The new results build on earlier works of Kleinbock, Lindenstrauss, Simmons and myself. Much of the progress in these papers involves ideas from homogeneous dynamics and probability. I will describe the history of the problem and some of the ingredients in recent works. I will also discuss some new related work with Khalil and Luethi.

Livestream/Recording Link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=f9997c72-fc96-4448-bdc2-b21900f12bd8