Alladi Ramakrishnan Hall

Multiplicative Diophantine approximation and Homogeneous dynamics

Prasuna Bandi

University of Michigan

I will discuss a problem in uniform multiplicative diophantine approximation, motivated by the celebrated Littlewood Conjecture on the simultaneous rational approximation of two real numbers. I will explain how this uniform-multiplicative problem connects to homogeneous dynamics and ergodic theory, and then present some recent results that estimate the size (in terms of the Lebesgue measure) of the corresponding Diophantine sets.