In this talk, we will discuss multiplicative Diophantine approximation on submanifolds. Using techniques from homogeneous dynamics, we are able to prove the following statement: Given a planar straight line with a natural Diophantine condition, a strengthening of Littlewood conjecture holds for almost every point on the line. This talk is based on an ongoing joint work with Allen, Beresnevich, Chow and Velani.

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