Geometry of Multidimensional Diophantine approximation and Diophantine exponents

主讲人 Speaker:Nikolay Moshchevitin (Israel Institute of Technology)
时间 Time:Fri., 16:00-17:00, Nov. 10, 2023
地点 Venue:Lecture Hall C548, Tsinghua University Shuangqing Complex Building A(清华大学双清综合楼A座C548报告厅); Tecent Meeting ID: 908-3255-9891


It is a well known fact  that most of the Diophantine properties of a real number $\alpha$ are determined by its regular continued fraction expansion.In particular, from continued fraction we obtain all the best approximations to $\alpha$.In my talk, I will discuss  the behaviour of  best approximations in higher dimensional problems related to approximation of irrational linear subspaces in  $\mathbb{R}^d$  by integer vectors. It happened, that rational subspaces generated by the best approximations may have rather unusual properties.We will consider some  geometric observations including the phenomenon of degenerate dimension, behaviour of irrationality measure functions, definitions and properties of Diophantine exponents.