Mathematics Colloquium: Lagrange spectra for spheres

Speaker:  Byungchul Cha, Muhlenberg College

Title:  Lagrange spectra for spheres

Abstract :  Near the end of the 19th century, Markoff published two papers containing a fundamental theorem in the area of Diophantine approximation. His theorem characterizes the irrational numbers that are the most badly approximated by rationals. The approximabilities of these irrational numbers are encapsulated in, so called, the Lagrange spectrum. The goal of the talk is to discuss some generalizations of the Lagrange spectrum, especially in the context of intrinsic Diophantine approximation of spheres. The talk will assume no background in Diophantine approximation. Most new results in the talk are based on joint projects with Dong Han Kim.

Time:  Friday, October 18, 3:30pm – 4:20pm

Place:  Exploratory Hall, room 4106

Zoom and In-person