Mathematics / Research
Research in Mathematics
The Department of Mathematics at Tulane University is home to a vibrant community of researchers pushing the boundaries of mathematical science. Our faculty engage in dynamic, interdisciplinary work that spans fundamental theoretical advancements and high-impact applications, with world-class strengths in areas like Mathematical and Computational Biology, modern Algebra, Geometry & Number Theory, Analysis, and Probability & Statistics.
Our Research Clusters
To better reflect the diverse and interconnected research activities of our faculty, we have organized our strengths into four dynamic research clusters. Explore each cluster to learn more about the specific areas of focus and the faculty driving innovation. You can dive deeper into the specific research interests and publications of our dedicated faculty members by checking out the Faculty Directory.
Mathematical & Computational Biology
Developing and applying mathematical models, computational simulations, and statistical methods to understand complex biological systems.
Algebra, Geometry & Number Theory
Studying fundamental algebraic, geometric, and arithmetic structures, including their interactions and applications.
Analysis & Differential Equations
Rigorous study of differential equations and dynamical systems, including nonlinear and stochastic PDEs, and integrable systems.
Probability and Statistics
Theory and application of probability, stochastic processes, and advanced statistical methods, including high-dimensional data analysis.
Interdisciplinary Work
Our faculty's expertise often bridges multiple mathematical disciplines and extends into critical applied fields. These cross-cutting themes demonstrate the broad impact of our research across Tulane University and beyond:
Mathematics in Health & Biological Sciences
From modeling cancer progression and tumor-immune interactions to simulating complex biological fluid dynamics—such as the locomotion of microorganisms and blood flow in flexible vessels—our mathematicians are at the forefront of biological and medical research. Faculty in our Mathematical & Computational Biology and Probability and Statistics clusters collaborate extensively to tackle pressing health challenges. Key partnerships include work with the Tulane Cancer Center, the Center for Computational Science, and the application of statistical genetics and phylogenetics to bioinformatics and evolutionary biology.
Data Science & Information Theory
In an increasingly data-driven world, our researchers are developing the mathematical foundations for statistical learning, high-dimensional data analysis, and predictive modeling. Contributions from across our clusters provide both the theoretical rigor and practical tools for understanding complex data. This includes pioneering work in topological data analysis, statistical phylogenetics, and the application of algebraic geometry to error-correcting codes and cryptography, directly informing critical decisions across various societal and technological domains.
Fluid Dynamics & Mathematical Physics
Our department boasts a strong tradition of bridging pure analysis with the physical sciences. Faculty apply rigorous mathematical frameworks to understand the fundamental laws of nature, exploring topics in global general relativity, quantum field theory, and quantum cosmology. Additionally, deep research into stochastic partial differential equations (SPDEs), nonlinear wave equations, and integrable systems fuels advancements in fluid mechanics, helping us to unravel complex physical phenomena like chaos, turbulence, and biological locomotion.
Computational Science & Engineering
Complementing our theoretical work is a robust focus on scientific computing and numerical analysis. Mathematicians at Tulane develop and analyze novel numerical methods to solve challenging differential equations that arise in multiscale dynamical systems. This computational expertise extends to creating high-performance computing libraries and advancing scientific machine learning, serving as a crucial link between fundamental mathematics and the Center for Computational Science (CCS), delivering applied solutions in engineering, biomedical science, and physical modeling.
