Disproof of the uniform Littlewood Conjecture (ULC)

Bandi, Fregoli, Kleinbock recently introduced a uniform version of the famous Littlewood problem (ULC). The talk presents a sketch of the disproof of ULC, for the case of two-dimensional vectors, as in the classical Littlewood problem. Indeed, the set satisfying ULC is meager (however of full Lebesgue measure by B.F.K.). The method is semi-constructive, it uses a deep result on Zaremba's Conjecture by Bourgain, Kontorovich. Some variants of ULC and open problems are discussed as well.