My research investigates mathematical structures, models, and methods that connect theoretical mathematics with interdisciplinary applications. Within mathematics, we can categorize research into two main areas: theoretical and applied. I have experience in both areas and continue to expand my abilities to be able to explore and examine new ideas and approaches. Theoretical research involves proving conjectures, developing new mathematical theories, and establishing results that can help provide new perspectives for addressing challenging mathematical questions. Applied research uses these theories and methods to help answer questions from other disciplines. I have focused many years of my training on learning about both sides of mathematical research, but have always found the love of applied research. My work over the years has allowed me to apply mathematics to other disciplines and identify meaningful connections between seemingly distinct areas of study. When I explore the possibilities of a new project, I am guided by three questions:
Can I use my existing mathematical tools to meaningfully address the questions being asked?
Can I learn and incorporate new mathematical tools to better understand the problem?
Will someone outside of mathematics be able to understand the purpose, significance, and potential impact of this project?
The third question is particularly important to me because I genuinely enjoy discussing and demonstrating the applications of mathematics across different fields. Mathematics is often perceived as a complex and abstract discipline, but I believe that it can also be accessible, tangible, and meaningful when presented in the appropriate context. One of the aspects of research that I find most rewarding is identifying these connections and communicating them in ways that allow individuals outside of mathematics to recognize the value of mathematical thinking. Whether mathematics is being used to model a real-world phenomenon, understand growth and change, optimize a process, analyze data, or provide insight into a problem from another discipline, I am interested in showing how mathematical ideas can extend beyond the classroom and contribute to broader questions.
Over the years, I have been fueled by Xavier's mission to promote a more just and humane society. Our mission has further strengthened my commitment to addressing issues of representation, access, and participation in mathematics and education. Through my research and mentorship, I seek to:
engage with students in meaningful mathematics research and help them see themselves as capable contributors to the broader scientific community
develop projects that are both mathematically substantive, attainable, and accessible for students based on their coursework, interests, and developing skills
demonstrate that mathematics is not simply theoretical or abstract; it is also a powerful and tangible tool for understanding and engaging the world around us.
Most importantly, I seek to advance Xavier University's commitment to excellence, equity, and service by preparing students to use their mathematical knowledge not only to pursue successful careers but also to become thoughtful leaders and advocates for positive change.
Upon arriving at Xavier, Dr. Gurdial Arora became my first mentor. With more than 30 years of research experience spanning recurrence relations, pattern recognition, Euler-Lagrange systems, and other areas of mathematics, Dr. Arora inspired me to deepen my focus on theoretical research. His mentorship helped shape my interests in analysis, Fibonacci sequences, and differential equations while encouraging me to pursue questions that can help students engage meaningfully in mathematical inquiry by observing the areas of mathematics outside the classroom.
In collaboration with Dr. Arora and Dr. Richard Vernon, we investigated generalizations of the four different 2-Fibonacci sequences defined by Atanassov. Dr. Vernon and I continued our exploration with the conditions for the initial values in which a generalized 2-Fibonacci sequence is eventually strictly monotonic. This research has allowed me to study how relatively simple recurrence relations can produce complex long-term behavior. More importantly, it has strengthened my appreciation for the role of theoretical mathematics in developing foundational knowledge that can serve as a starting point for future mathematical and interdisciplinary investigation.
Guided by the university's mission, I view that my work contributes to building a more just and humane society by advancing knowledge, cultivating critical and analytical thinking, and creating opportunities for students to develop as researchers in STEM. Although theoretical mathematics may not always have an immediate or visible application, it provides the foundational structures, reasoning, and problem-solving skills upon which applications can be built. By involving undergraduate students in this type of research, I hope to broaden their understanding of what mathematics can accomplish and develop their confidence as emerging scholars capable of sharing their knowledge and contributing to society.
Current and past work:
Ma, T., Vernon, R. (2026). “Stable Solutions of Fibonacci Relations of Higher Order.” Pre-print of paper on arxiv. Submitted to Notes in Number Theory and Discrete Mathematics Journal.
Ma, T., Vernon, R., & Arora, G. (2024), “Generalization of the 2-Fibonacci Sequences and their Binet formula.” Notes on Number Theory and Discrete Mathematics, 30(1), 67-80, DOI: 10.7546/nntdm.2024.30.1.67-80.
My applied research journey began in graduate school. It was then that I learned about mathematical modeling of complex social phenomena. This experience broadened my understanding of mathematics as more than a theoretical discipline; it showed me how mathematical frameworks can be used to translate real-world questions into problems that can be analyzed, interpreted, and explored quantitatively. Applied research has allowed me to draw upon my training in differential equations and analysis while engaging with questions from other disciplines. Over the years, I have explored topics in economics, international relations, and mathematical biology.
My research has expanded through collaborations with colleagues on projects supported by NSF funding. With this funding, we have investigated the production and evolution of mutant cells in mice. As an organism ages, mistakes are made during cell production, generating mutant cells. These mutations can contribute to chronic health conditions and possibly initiate cancer. It is not well understood why these mutant cells persist and expand. Mathematics combined with epidemiological data offers a solution to explore this behavior by developing mathematical models to describe the evolution of mutant cells in blood over time. This work can suggest ways to reduce the mutant cells in patients, which can alleviate chronic health conditions and reduce cancer risk, thus having an impact on public health.
In keeping with the university's mission, I view my work as contributing to the building of a more just and humane society by using mathematics to address questions that have meaningful implications for human health and well-being. In particular, my work in mathematical biology demonstrates how theoretical and modeling methods can contribute to a deeper understanding of diseases and health disparities. I also have work in economics and education that uses mathematics to help provide new perspectives on the factors that influence human behavior and shape social outcomes. I believe that mathematicians have a responsibility not only to advance knowledge but also to serve society by helping us better understand the challenges that affect individuals and communities.
Current and Past work:
Ma, T., Fleischman, A., Wodarz, D., Komarova, N., (2026). "Hierarchical tissue structure creates history-dependent barriers to clonal invasion." bioRxiv, https://www.biorxiv.org/content/10.64898/2026.08.04.742588v1. Submitted to the Journal of Royal Society.
Wodarz, M., Ma, T., Komarova, N. (2025). "The dependence of K-12 student performance on the household income in U.S. school districts." PLoS one, 20(9), e0329296.
Ma, T., Fernando, A., & Gurski, K. (2024). “A Research Introduction for Early College Students: Based on the OSU-HBCU Pilot Project.” PRIMUS, 34(9), 969-987. https://www.tandfonline.com/doi/full/10.1080/10511970.2024.2396497
Dong, T., Zheng, R., Ma, T. (2019), "Diplomatic Dynamics of International Treaty Negotiations.” The PUMP Journal of Undergraduate Research, 2, 199-224.
Ma, T., & Komarova, N. L. (2019), “Object-Label-Order Effect When Learning From an Inconsistent Source.” Cogn Sci, 43: e12737.
Ma, T., Wood, K., Xu, D., Guidotti, P., Pantano, A., & Komarova, N.L., (2017). “Diversity and Admission Predictors for Mathematics PhD Success.” Notices of the AMS, vol 65, No 6, p 676.
Ma, T., & Komarova, N.L., (2017). “Mathematical Modeling of Learning from an Inconsistent Source: A Nonlinear Approach.” Bulletin of mathematical biology, 79(3), pp.635-661.
My future research will continue exploring the applications of mathematics to interdisciplinary fields, examining why certain patterns and behaviors emerge within society.
As I continue to expand my collaborations across disciplines, colleagues have encouraged me to pursue the Stanford Medicine-HBCU Faculty Fellows Research Program as an opportunity to strengthen my professional network and broaden my research. I believe that this program is the natural next step in the development of my research. Through the fellowship, I will find collaborators at Stanford University and bring my experience in mathematical modeling to new scientific questions.
As a mentor to young mathematicians and researchers, I want to continue demonstrating how mathematical reasoning can offer valuable insight into complex questions that extend beyond the traditional boundaries of mathematics. In line with Xavier's mission, I will create a safe place for my students to learn about how diverse mathematics can be as we discover its reaches across disciplines. In doing so, I will contribute to the preparation of students to assume roles of leadership and service to promote a more just and humane society.