Author: Salena Fitzgerald
Lecturer Taylor Jones

Taylor Jones is a new lecturer in the Department of Applied Mathematics and Statistics. He joins Johns Hopkins University from the University of North Texas, where he was a teaching fellow. In this Q&A, Jones discusses his interest in fractal geometry, with a particular focus on box-counting dimension: a mathematical concept used to measure the complexity of a shape or a set of points. 


Tell us a little about yourself.  

I am from Dallas, Texas and have lived my whole life in that area. I received both my undergraduate degree and my PhD in mathematics from the University of North Texas. I am very excited to begin a new chapter in my life here in Baltimore! 


Describe your research.  

I am interested in problems relating to fractal geometry. Past publications include work on box-counting dimension and differentiability classification of statistically self-affine functions.  These are (random) continuous functions generated by a process of independent and identically distributed iterated function systems. Their graphs appear like that of 2D Brownian motion, where the particle’s position changes over time due to random fluctuations, although this similarity is simply cosmetic. 

I am currently completing a project with my PhD advisor on random subsets of Cantor sets generated by branching random walks. This is a variation of a once-popular subject from literature in the late 1980s, where statistically self-similar sets were constructed via a Galton-Watson process. The subtle differences between our model and those of the past produce vastly different results, which came as a big surprise to us. 


What drew you to this field and focus area?  

 I developed an interest in fractals towards the end of my undergraduate studies. Initially, I was drawn to them because of the visually appealing patterns they create. However, as I delved deeper into my doctoral studies, my fascination with fractals grew. The research questions in this field are often deceptively simple to ask, but they require a profound understanding to solve. Making progress in this area feels incredibly rewarding due to the level of knowledge and expertise it demands. 


Tell us about the real-world applications of your research.  

Random fractal analysis has been used to study and classify many biological and physical phenomena. One recent example that has caught my interest is the utilization of box-counting dimension and Hurst exponent to characterize features in magnetic resonance imaging (MRI). While my previous research has primarily focused on pure fractal analysis, I am excited to explore the more applied aspects of fractal geometry, particularly in relation to neuroscience, in the coming years. 


What excites you about bringing this work to Johns Hopkins?  

I am most excited to be working with the brilliant students here. My main goal is to be a great lecturer, so I will put most of my focus on my teaching. If I can make research progress as well, then that would be a happy bonus. I am also looking forward to working with the amazing faculty here. There are so many talented people in this department; I am very excited to meet and learn from them all. 


What are some of your goals for your first year here?  

One of the most exciting occurrences when studying math is to come across a problem (be it in real-world applications, academic research, etc.) and realize, “Oh, this is just like ABC concept I learned in XYZ class years ago!” One of the challenges that teachers face is imparting foundational knowledge to students in a way that they will remember for years to come. Therefore, it’s my goal to create engaging lectures and projects for my students. Not just for this first year, but for every year I’m here. 


Anything else we should know? Any fun facts?  

I enjoy long distance and cross country running. I have not run competitively for many years, but I was once not too bad at it. I was not too good at it either, to be clear. A fun fact related to math is my Erdös number is 2.