Title: â€‹Multiplicative Diophantine Approximation and Homogeneous Dynamics

Abstract: 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 lebesgue measure) of the corresponding Diophantine sets.

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