Taft Lectures

The Charles P. Taft Memorial Fund sponsors a program of public lectures each year, including one or more in mathematics. These lectures feature prominent mathematicians speaking on recent important developments in their field. Taft Lectures are aimed at a fairly general audience. Taft Lecturers sometimes also give a seminar talk which includes more specialized material. The name of each lecture under "Topic of Talk" below is a link to detailed information, including the date of each talk, the location, and the abstract. The Taft Lectures are free and open to the public.

The Department of Mathematical Sciences and the Taft Research Center welcome: 

Dr. Anton Lukyanenko

Assistant Professor of Mathematics

George Mason University

Friday, March 24th, 2023

Swift Hall Room 800


Fractal Geometry of Numbers

Dr. Anton Lukyanenko

Pick a random real number and write it in base-2, so that all of its digits are 0s and 1s. How many 0s do you see in the first 1000 digits, and how many 1s? The counts should be roughly equal, displaying a dynamical property called ergodicity. In fact, regardless of the number you chose, any finite string of 0s and 1s (say, encoding your name) will almost surely appear infinitely many times in the infinite string of digits, with a certain guaranteed frequency.

In this talk, I will show how the study of ergodicity for base-b and continued-fraction expansions reveals a fractal structure in the real numbers, which gets all the more intricate when we work over complex numbers, quaternions, and octonions. As a bonus, we will talk about number theory in the non-Euclidean Heisenberg group, which comes up in a variety of fields ranging from quantum physics to models of the human visual cortex.

Refreshments will be served 2:45-3:20 pm in the Math Faculty  & Graduate Student Lounge
Room 4118 French Hall West



Fractal Demonstrations