Speaker: Nikolay Moshchevitin
8 July, 2020 13:30 UTC
Abstract: Many concepts in Diophantine Approximation have their origin in the famous paper “Über eine Klasse linearer diophantischer Approximationen” by A. Khintchine (1926). The results of this paper were rediscovered many times by different mathematicians. In particular, Khintchine was the first who observed the phenomenon of singularity in higher-dimensional Diophantine Approximation. In our lecture we discuss several problems related to singular vectors and best approximation (minimal points) as well as some related topics dealing with Diophantine exponents and approximation on algebraic and analytic surfaces which were considered recently in author’s joint papers with D. Kleinbock and B. Weiss. Also we suppose to discuss some related open problems.