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Dynamics seminar: Erez Nesharim (HUJI) Approximation by algebraic numbers and homogeneous dynamics | Einstein Institute of Mathematics

Dynamics seminar: Erez Nesharim (HUJI) Approximation by algebraic numbers and homogeneous dynamics

Date: 
Tue, 08/12/202014:00-15:00
Abstract: Diophantine approximation quantifies the density of the rational numbers in the real line. The extension of this theory to algebraic numbers raises many natural questions. I will focus on a dynamical resolution to Davenport's problem and show that there are uncountably many badly approximable pairs on the parabola. The proof uses the Kleinbock--Margulis uniform estimate for nondivergence of nondegenerate curves in the space of lattices and a variant of Schmidt's game. The same ideas applied to Ahlfors-regular measures show the existence of real numbers which are badly approximable by algebraic numbers. This talk is based on joint works with Victor Beresnevich and Lei Yang.

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