# Student Spotlight June 2014

Allison Perkins - PhD Math

## Allison Perkins

Allison Perkins graduated cum laude from Centre College in Danville, KY in 2009 with a BS in Math and a minor in Computer Science.  She then received her MA in Math from the University of Louisville in December 2011 and will be completing her PhD in August 2014.

Interview

What brought you to the University of Louisville?

I'm from Oldham County so it is close to home and family.

Specific areas of research (how you chose this research, why it interested you):

I've always been interested in Abstract Algebra and Dr. Sahoo was working with functional equations in group settings which stemmed ideas for new research. Our research deals with a couple different functional equations related the sine and cosine functions.

How would you describe your area of study/ specific research to your grandmother?

Instead of solving equations for variables, we solve equations for functions.  So given an equation, we find all of the types of functions that would satisfy that particular equation. The simplest functional equation is known as the Cauchy functional equation and it looks like: f(x+y) = f(x) + f(y). The only types of functions that satisfy this equation are linear functions with no constant term, i.e. f(x) = mx.

What made you go into this field of study?

Ever since I was little I have loved math. Once I graduated from undergrad and still had no idea what I wanted to do, I figured grad school would allow me more time to figure it out.

Awards, honors, publications:

My advisor and I just got a paper accepted to Aequationes Mathematicae:
A. Perkins and P. Sahoo, On Two Functional Equations with Involution Related to Sine and Cosine, Aequationes Mathematicae, Accepted, 2014

Long term goals/ aspirations:

Long term goals? I can't even think that far ahead right now. Short term goals? Finish and defend my dissertation, find an apartment in Cincinnati and find a job!

What accomplishment, academic or otherwise, are you most proud of?

Completing my PhD will make me most proud. When I first started graduate school it was an adjustment, so being able to get through it all and finish feels good. But I am definitely ready to move on from academia; I have been in school for 22 years, and that is absurd.

What has been your favorite part of the graduate school experience at UofL?

Meeting other people who are as into math as I am.

Family life:

My parents, Doug and Susan, live in Ballardsville, KY. My sister, LeeAnn, works for Humana and has a daughter, my super smart, creative niece Lainey. My brother, Brian, and his wife, Trinh, live in Virginia and have a son, my adorable, funny nephew Caden. I live in Louisville with my boyfriend, George, and we are gearing up to move in Cincinnati in August so that he can start school for nurse anesthesia.