Geometry MMA Seminar: Convergence of higher-dimensional continued fractions

Speaker: Anton Lukyanenko, George Mason University

Title:   Convergence of higher-dimensional continued fractions

Abstract:  A classical continued fraction (CF) represents a real number

as a descending infinite fraction, e.g. pi=3+1/(7+1/...).

I will discuss a generalization of the CFs to complex, quaternionic,

and octonionic numbers, where the proof of convergence requires

a geometric argument. As a bonus, we will prove the convergence

of a CF representation for all points in R^3 and some points in R^n.

This is joint work with Joseph Vandehey, UT Tyler.

Time: Monday, March 7, 2022 - 10:30am-11:45am

Place: Exploratory Hall, Room 4106