Seminar in Algebraic Geometry and Number Theory

Abstract: The set of badly approximable vectors in Diophantine approximation plays a significant role. In a recent work with Victor Beresnevich, Anish Ghosh, and Ben Ward, we developed a general framework to show that the set of badly approximable points has measure zero in a metric space equipped with certain natural measures. I will explain a few applications of our method in various number theoretic questions.