NTAG Seminar: Luroth expansions in Diophantine approximation - metric properties and conjectures

In this talk, we study Diophantine approximation in the setting of Luroth expansions, an alternative representation of real numbers to continued fractions. We discuss Lüroth analogues of several classical results on well-approximable numbers, including those of Khintchine, Jarnik, Besicovitch, and Dodson. In particular, we strengthen a dimensional theorem of Cao-Wu-Zhang and construct a counterexample that necessitates a revision of a conjecture by Tan-Zhou, for which we also obtain a partial result.