Featured Grantee

Quick Facts

  • Name: Luis A. Medina
  • Comes from: Yabucoa, Puerto Rico
  • Lives in: San Juan, Puerto Rico
  • In three words: perseverance, family, and math
  • Leisure time activities: playing video games with my kid, watching movies with my family, learning about new Linux distributions
  • Likes: riding bike with my family, visiting friends, eating out
  • Unsuspected talent: I play Puerto Rican cuatro
  • Currently reading: several research articles

 In a nutshell

  • My research matters because in the current age of technology scientific fields like information theory and cryptography are important for internet communication security.
  • One of the inspirations for my research has been the enlightenment and happiness I get when a new idea comes to mind and when connections to previously unconnected areas or ideas appears in front of my eyes.
  • The best thing about my job is working on research problems with real world applications and mentoring students in the process.
  • My career highlights so far have been being selected as an Associate Editor of the peer-reviewed Journal of Algebraic Combinatorics (Springer) and being showcased as one of the hispanic mathematicians in the USA during the Hispanic Heritage Month (2017; Lathisms).
  • My advice to aspiring researchers is to never give up, to be perseverant, to pay attention to mentors, to buid a network of scientists, to share your knowledge and to enjoy the ride.

Interview:

When I was an undergraduate student, I was exposed to research by my then mentor Dr. Ivelisse Rubio.  All of the sudden, I was not just learning new mathematics, but producing it.  That was a big paradigm shift for me, as I thought at the time that all that it needed to be known in mathematics was already established.

Research became my favorite part of being an university student.  I was discovering new things, writing about it and presenting my results to other mathematicians in the island.  I was also able to get funding to travel to scientific conferences outside Puerto Rico to present my results to international audiences. At the time, that was just a dream for me since it was something that my family couldn’t afford.  After all these experiences (and more), I decided to pursue a Ph.D in Mathematics in order to become an established researcher.  Today, I am a Professor and a researcher at the Department of Mathematics of the University of Puerto Rico, Río Piedras Campus and I mentor several students at the undergraduate and graduate levels.

I am work on the field of Booleans functions.  Specifically, I work on the recursive nature of exponential sums and Walsh transformations of some families of Boolean functions fixed under the action of finite groups.  This sounds technical, but the important thing is that this area has applications to cryptography and information theory.  Cryptography is the scientific field that studies techniques for secure communication in the presence of third parties.  For instance, it is because of cryptography that you feel secure when shopping online.

The subject is expanding quite fast, and many applications found in the binary field (0’s and 1’s) have been extended to other finite fields.  Also, many scientists are working on applications with good cryptographic properties and fast implementations.  Part of the work that out team does is to find families of Boolean functions with good properties and fast implementations and to extend these results to finite fields beyond the binary one.

The most enjoyable aspect of my job is, without a doubt, mentorship.  I enjoy, very much, sharing my knowledge with my students, seeing them engage in research and expand their potential.  I am happy that some of them go on to graduate school to purse graduate degrees.

The current age of computers has brought important challenges to society.  Security on internet communication is today one of the most important issues in society.  My research has applications to this important scientific field.

My research work also gives me the opportunity to share my knowledge with my students.  It has been instrumental in bringing a new generation of mathematicians into mathematical research and to the benefits this human activity brings.

In terms of the academia, when I am not doing research, I enjoy teaching (every aspect of it).  I also enjoy computer programming (as it aids my research), learning about new computer algebra systems and learning about computer languages that I don’t currently know about.

Outside the academia, when I am not doing research, I enjoy spending time with my family and friends.