July, 2024
Juan Miranda is a Ph.D. student in the Department of Mathematics and Statistics, housed in the Charles E. Schmidt College of Science at Florida Atlantic University (FAU). Juan Miranda joined the department as a graduate student in the Fall of 2019. He attended FAU High School in 2014 and completed the Bachelor of Science degree in Mathematical Sciences at FAU in 2019. Starting in the Summer of 2024, he will hold a graduate research assistantship supported by the National Science Foundation Grant DMS - 2307987: "Fine Structure in Hamiltonian Systems."
What are your research interests?
Functional analysis and Dynamical Systems. The study of dynamical systems uses differential equations to describe time dependent dynamics, such as water flow, movement of particles through space, celestial mechanics, just to name a few.
What are your past/current research projects?
Currently, I’m studying dynamical systems under Dr. Jason Mireles-James, professor of Mathematics at Florida Atlantic University. We are currently working on Resurgence Theory using the Borel Transform along with divergent series. Divergent series can be important in dynamics for so-called “edge cases” where stable/unstable manifolds are associated with a zero eigenvalue.
Tell us about your research experiences, i.e., conference presentations, publications, research ventures with faculty, other students?
In my undergraduate studies, I was able to participate on a research team with fellow colleagues, who collaborated with the Moffit Cancer Center, to build a mathematical model in order to find parameters to aid in the research of melanoma treatments. My colleagues and I presented results in the poster presentations during the Fifth Conference on Computational and Mathematical Population Dynamics held in Fort Lauderdale, Florida (CMPD5).
In June, 2024, I presented my current preliminary research results to a large group of mathematicians attending the PiotrFest conference “From Topology to Computations” held in Jagiellonian University in Krakow, Poland.
What’s life like at FAU?
Life at FAU is quite nice. FAU has quite a diverse population, so it’s not hard to find a group of people to get along with, even in other departments like Engineering or Chemistry. The campus is also very beautiful and greatly located with plenty to do. There are lots of wonderful restaurants to try, bowling alleys, movie theaters, the beach, etc.
What attracted you to FAU?
As a former FAU high school student, I was able to become part of the FAU math community early on. When I graduated from FAU high school and finished my Bachelor of Science degree in Mathematical Sciences, I decided to stay at FAU and pursue a graduate degree to be close to the community I became so fond of, to continue my research with wonderful professor and to be close to my family as well.
What has been the most beneficial aspect of your time here at FAU?
My peers and professors. It was not hard for me to find people in my cohort with whom I quickly developed, and continue to nurture, life-long friendships with, and who will one day become strong research collaborators. We all learn and work together and can rely on one another for help of any kind. Also, it is not hard to find a mentor/advisor as the professors are very encouraging and supportive.
What are your plans for after graduation?
I don’t have a concrete plan just yet as graduation is still a bit away. But I am hoping to stay in academia, and to be able to continue teaching and doing research.
