William Mahaney

Why did you choose the Mathematics Department at Virginia Tech?

My grandfather, father, and brothers came to VT for undergrad; so I did as well. While I was here in undergrad I met some interesting people including Dr. Peter Haskell who helped me understand mathematics at a much deeper level and in new ways I never considered. While looking for graduate schools, among other professors at VT I also appreciate, I met Dr. Travis Morrison, my current advisor, and I recognized his ability to enable another evolution for me in the spirit of my role model Dr. Haskell. In short, I stayed at VT after my undergrad because of the mathemeticians and people I met here and my belief that mixing multiple diverse perspectives in my own thought and work can enable me to become the best mathemetician I can possibly be.

Tell us about your research.

My advisor is Dr. Travis Morrison. Travis and I study Computational Number Theory and Post-Quantum Cryptography. In particular we focus on designing and analyzing algorithms for working with Elliptic Curves and Quaternion Algebras.
My dissertation is untitled presently as I spend most of my time writing individual papers currently. A hypothetical title might be: "Estimating Security of Isogeny Cryptography via Arithmetic Statistics".

You've been accepted to an SLMath Summer Graduate School! Where are you heading this summer?

This summer, I will be participating in the SLMath Summer Program at the University of Paris-Saclay Mathematics Institute in France on "Local Limits of Random Graphs". A graph can be represented pictorially as a collection of dots called 'vertices' with lines connecting them called 'edges'. Graphs have important application in Computer Science, Mathematics, Biology, and beyond. Random Graphs, as the name suggests, are essentially graphs that are produced via random processes. It turns out in certain respects sufficiently random graphs have amazing properties. I'm hoping to take what I learn in this summer school and use it to help other people with research as well as further my own with new ideas and insights I couldn't have found myself.

Congratulations on your Julian Chin Ph.D. Fellowship! What are some of the ways that you've become involved as a graduate student?

Thanks! I am honored to be one of two Julian Chin Fellows in Cybersecurity, a fellowship offered by the Hume Center at Virginia Tech. I also serve as one of three members of the Directed Reading Program committee.  

What advice do you have for math grad students?

Do something! The VT motto is "Ut Prosim", Latin for "That I may serve". Mathematics is a communal activity, by building a strong web of peers and embedding yourself into the mathematical community you can learn and achieve much faster than alone. Your community is a reflection of you, and so by committing yourself to strengthening your surroundings and helping others become the best they can be you will in turn become a better mathematician and person.

What is your favorite memory as a graduate student?

I mentored a student in Fall of 2024 as part of participation in the Directed Reading Program. I put a lot of value into increasing mathematical participation and engagement. At the end of the semester my mentee told me they would like to continue studying Number Theory and felt they had fun studying it more deeply, and now they are considering doing research in a similar area to me. I felt a great sense of accomplishment in that moment. 

What is a fun fact that most might not know about you?

Growing up my parents had lots of cats and dogs, and to this day I love animals. One of my favorite things to do is walk with dogs and play ball, or cuddle up with a fluffy cat. I grew up in Appalachia, and this gave me a deep appreciation for nature, I feel most at home surrounded by trees and mountains.

Do you have a favorite quote?

My [algebraic] methods are really methods of working and thinking; this is why they have crept in everywhere anonymously. - Emmy Noether