※ 시간: 10:30-12:00, 13:30-15:00

제목: Twisted Diophantine approximation via parametric geometry of numbers

초록: Kurzweil's theorem (1955) gives a Khintchine type zero-one law in twisted Diophantine approximation when the fixed matrix is badly approximable. A natural question is to understand what happens beyond the badly approximable setting. In dimension one, this question was completely resolved by Fuchs and Kim (2016), showing that the answer depends in a precise way on the Diophantine properties of the fixed irrational number. In higher dimensions, however, the general zero-one law remains much less understood. In this talk, I will present a new higher-dimensional zero-one law for twisted Diophantine approximation, described in terms of the parametric geometry of numbers associated with the fixed matrix. This is joint work in progress with Vasiliy Neckrasov.