Faculty Research

Department Faculty Research

The faculty members in the Department of Mathematics and Statistics carry out research in applied mathematics and statistics, bifurcation theory, bioinformatics, biostatistics, combinatorics and graph theory, commutative algebra and algebraic geometry, computational statistics, computer graphics, ordinary differential equations, dynamical systems, functional analysis, harmonic analysis, linear algebra and matrix theory, mathematics education, multivariate analysis, numerical analysis, operator theory, inverse and ill posed problems theory, qualitative theory of differential equations, and probability theory, where faculty members have the national and international reputations in these and related areas. It is this combination of the strengths and the flexibility of curriculum offerings that sets the department apart from mathematics and statistics programs elsewhere in the state and the region.

For more information about the research of faculty members, please see their profiles.

Faculty Research Spotlight

Dr. Igor Belykh‘s research fields are Mathematical Biology and Neuroscience, Applied Dynamical Systems, and Applied Mathematics. Dr. Belykh’s research spans several interdisciplinary research areas, such as the origin of motor diseases, reconstruction of functional connectivity in neuronal and social networks, dynamical instabilities in mechanical systems, data-driven models of human gait, computational methods in robotics, energy harvesting, and understanding causal relationships among firearm prevalence, state legislation, and people’s opinion of firearm safety.

Dr. Vladimir Bondarenko‘s research areas include mathematical modeling cardiac ion channels, cardiac cells, cardiac tissues, pro-arrhythmic events, and arrhythmias. He is also working on the models of neural cells and neural networks, as well as artificial neural network models producing mammalian electroencephalograms.

Dr. Guantao Chen‘s research interests are mainly in graph theory and its applications. He works on graph structural problems in several areas, such as cycles and paths in graphs, graph coloring, and graph Ramsey theory. In recent years, most of his efforts have been in developing and understanding graph edge recoloring techniques and using them to solve some classic problems in the area.

Dr. Florian Enescu works in the area of commutative algebra with applications to problems with geometrical or number theoretical flavor, generally involving multiplicities, local cohomology, special classes of rings, Frobenius complexity, and intersection algebras among other topics. He is also interested in algebraic problems with applications to electrical engineering and computer science.

Dr. Yi Jiang’s research lies in the interface between mathematics, physics and biology by developing mathematical tools for complex biological and biomedical systems. Research in her lab combines two approaches: 1) Mechanistic: develop multiscale mathematical models based on experimental data, and 2) Data-driven: image analysis and statistical analysis tools and apply them on biomedical data. We have developed models and tools and applied them to problems range from single cell migration to cancer development (tumor growth, angiogenesis, invasion), epithelium morphogenesis, eye diseases, and collective cell patterning. In the last 10 years, one focus of my lab has been on studying cell-ECM interactions during cell migration, particularly in the context of cancer invasion. Her lab is also current involved in COVID-19 related projects.

Dr. Jun Kong‘s research interests focus on big imaging data analytics for characterizing cancer diseases, multi-modal biomedical image analysis, computer-aided diagnosis, machine learning, computational biology, and large-scale translational bioinformatics with heterogeneous data integration and mining. His long-term research goal is to establish an interdisciplinary research program engaged with mathematicians, biostatisticians, computer scientists, biologists, pathologists, and oncologists, among other domains of experts, for computational disease characterization, accurate modeling analysis, and granular-resolution understanding of diseases with large-scale, multi-modal, and multi-scale biomedical data.

Dr. Mariana Montiel‘s research revolves around Mathematical Music Theory. This research topic involves several mathematical areas used in scientific musicology, such as Category Theory, Abstract Algebra, Algebraic Combinatorics on Words. It is cross disciplinary not only with Music, but with areas such as Computer Science and Cognitive Science. Simultaneously she does research about pedagogical aspects, in particular, the use of abstract and symbolic representations, common to both disciplines, mathematics and music.

Dr. Gengsheng (Jeff) Qin‘s research interests are in statistics and biostatistics, specifically statistical methods and applications dealing with diagnostic medicine and biological research, survival analysis, bootstrap and empirical likelihood methods, nonparametric and semi-parametric regression.

Dr. Alexandra Smirnova‘s research interests lie in regularized numerical algorithms for inverse and ill-posed problems and their applications in epidemiology and other fields.

Dr. Michael Stewart’s research is in numerical linear algebra, matrix theory, and numerical analysis. His specific areas of focus are on fast algorithms for densely structured linear algebra problems and issues of numerical stability and accuracy.

Dr. Yongwei Yao‘s research interests lie in Commutative Algebra, with particular interests in rings of prime characteristics.

Dr. Xiaojing Ye‘s research focuses on applied and computational mathematics. His main research includes analysis and numerical methods for stochastic point processes on networks, modeling and computations of optimal transport and applications, and theory and computations in machine learning with applications in deep learning and image processing.

Dr. Yichuan Zhao‘s current research interests focus on survival analysis, nonparametric statistics, statistical analysis of ROC curves, Monte Carlo methods, high-dimensional data analysis.