Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	关力凡,西湖大学
Inviter:	何伟锟
Title:	Dirichlet is not just singular and bad
Language:	Chinese
Time & Venue:	2022.12.15 16:00-17:00 腾讯会议：782 2460 5514
Abstract:	The subject of Diophantine approximation studies how a real vector is approximated by rational vectors. Diophantine sets are subsets of real vectors defined by certain approximate functions. Among the most studied Diophantine sets are the set of badly approximable, singular and Dirichlet approximable vectors. It is well-known that, if a vector is badly approximable or singular, then it is also Dirichlet improvable. In case of dimension 1, the converse also holds true. Then it is natural to ask if Dirichlet improvable is still just singular or bad in higher dimensions. In this talk, we give a negative answer by showing uncountableness of certain intersection of Diophantine sets involving also very-well approximable vectors. This is based on joint work with Beresnevich, Marnat, Ramirez and Velani.