Meet Dr. Jose Vélez-Marulanda, 2023 VSU Presidential Excellence Award for Research Honoree

Dr. Richard A. Carvajal, president of Valdosta State University, recently honored Dr. José A. Vélez-Marulanda with the 2023 Presidential Excellence Award for Research.

VALDOSTA — Dr. Richard A. Carvajal, president of Valdosta State University, recently honored Dr. José A. Vélez-Marulanda with the 2023 Presidential Excellence Award for Research.

The Presidential Excellence Award for Research recognizes a faculty member with a strong record of creative scholarship.

Vélez-Marulanda joined the faculty of VSU’s College of Science and Mathematics in 2010 as an assistant professor in the Department of Applied Mathematics and Physics. He was promoted to full professor in 2020.

VSU: What are your favorite classes to teach and your favorite topics to research?

Vélez-Marulanda: There are three classes that I consider my favorite ones. The first is MATH1112: Trigonometry. I consider this class fundamental for the understanding of many advanced topics in mathematics, and it is fun to teach for you have to use geometry, arithmetic calculations, and technology to understand the topics under discussion. The second one is MATH2262: Calculus II. This class is essential to understand many topics in applied sciences, such as probability distributions, financial mathematics, and actuarial mathematics. Finally, my third favorite class to teach is MATH4110: Number Theory. In this class you get to learn many fascinating things about numbers that you have known since you were in elementary school, but in a deeper way. Furthermore, you also get to realize that there are many things about numbers that are still unknown, and which need to be explored.

My research interests are in the field of representation theory of associative algebras. During many years my research was based on a deformation theory of modules developed by my dissertation adviser, Dr. Frauke M. Bleher at University of Iowa, and by me in my doctoral thesis. I am currently interested in applications of representation theory to topological data analysis, which is fun and useful in many other areas in applied sciences, such as neuroscience, financial mathematics, and silica glasses. You also get to implement your results in programs like Python and R.  I am also interested in methods from machine learning in statistical risk modeling.

VSU: Why do you believe it is important for faculty to conduct research and contribute new knowledge to their fields?

Vélez-Marulanda: I feel I need to do research in order to learn new ways of looking at a specific situation. For example, people in topological data analysis realized not a long time ago that many results from representation theory of algebras were extremely useful to them in order to obtain new results. People in my area of research found through this connection that our results were actually useful for real-life applications, which is great. I also feel that by doing research you will have a better understanding of what is of interest and what needs to be done in the academic world. I think that when you create new results, you also enhance the prestige of your institution, as well as the networking of collaborators, which in turn increases the chances for your students to be admitted in graduate programs, or in other ones like Research Experiences for Undergraduates or internships.   

VSU: How many publications, presentations, and other scholarship have you completed? What drives you to find time outside of teaching, mentoring, and serving the university to conduct this research? 

Vélez-Marulanda: I have so far 15 articles that are published in academic journals, such as Journal of Algebra, Journal of Pure and Applied Algebra, and Proceedings of the American Mathematical Society. I had the opportunity of giving research talks all over the United States, Canada, Colombia, Mexico, and Ecuador. I had the opportunity of successfully co-advising the Doctor of Philosophy thesis of three graduate students at the Universidad de Antioquia in Colombia. I have co-organized four research conferences, one sponsored by the Centre International de Mathématiques Pures et Appliquées (CIMPA) organization in France, and another one by the National Science Foundation. I try to be very organized with my time, and being a workaholic helps a lot to find spaces to get things done. However, there are two main factors that motivate me to do research. One is mathematical curiosity, and the other is an enjoyment for learning new things.  

VSU: What advice do you have for other faculty who wish to get more involved in research?

Vélez-Marulanda: It is important to have conversations with your peers about what you have in mind to get explored. Organizing departmental seminars or colloquia can provide a perfect place for such conversations. Sponsoring undergraduate research projects can also bring new ideas and motivation for getting bigger results. One major factor that can discourage research is when you get your article rejected or when you get highly critical reviews by the referees, which has happened to me many times in the past and can still happen to me in the future. If you have to deal with this type of situation, you can try what I usually do — take some days off from doing research to “lick your wounds,” do what you like the most to clear your mind (e.g. yoga, walking, or in my case, playing your favorite video game), spend a lot of time with your loved ones, and then, when you feel ready, go again over your article by implementing the constructive criticism provided by the referees, fix the typos, etc.,  and submit your article again to a suitable journal.