Speaker: Baowei Wang
22 July, 2020 13:30 UTC
Note: This talk will only take one hour.
Abstract: As is well known, Dirichlet’s theorem and Minkowski’s theorem are two fundamental results in Diophantine approximation. One says that all points in $\mathbb{R}^d$ will fall into infinitely many balls centered at rationals with specific radius; while the other says that all points will fall into infinitely many rectangles centered at rationals with specific sidelengths. This motives a further study on the metric theory of limsup sets defined by a sequence of balls or rectangles. Since the landmark works of Beresnevich & Velani (2006) and Beresnevich, Dickinson & Velani (2006) where the mass transference principle was found, the metric theory for limsup sets defined by a sequence balls or istropic thicken of general sets has been sufficiently well established. While, the metric theory for limsup sets defined by a sequence of rectangles are not as rich as the ball case. In this talk, I will talk about some progess on the metric theory of the latter case by modifying the settings in the above mentioned impressing works.