Activities This Week
Jerusalem - Be'er Sheva Algebraic Geometry Seminar
TBA
Dec 9, 15:00—16:30, 2020,
Speaker
Zev Rosengarten (HUJI)
BGU Probability and Ergodic Theory (PET) seminar
Approximation by algebraic numbers and homogeneous dynamics
Dec 10, 11:10—12:00, 2020, Online
Speaker
Erez Nesharim (The Hebrew University)
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.
Arithmetic applications of o-minimality
Ax–Lindemann with derivatives for Fuchsian groups Online
Dec 15, 10:10—12:00, 2020, online
Speaker
Moshe Kamensky
Abstract
I will review some ALW-type results for the $j$ function and its derivative, following the paper Ax-Lindemann-Weierstrass with derivatives and the genus 0 Fuchsian groups