Geometry MMA Seminar: Convergence of higher-dimensional continued fractions
Mar 7, 2022, 10:30 - 11:45 AM
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