Mathematical Biology
The Mathematical Biology research group uses mathematical modeling, analysis, and data-driven discovery to understand biological processes. Its members investigate complex biological systems spanning neuroscience, ecology, disease dynamics, molecular and cellular biology, and immunology using tools from nonlinear dynamics, applied mathematics, computation, and network science. Research topics include neuronal sensory encoding and information processing, rhythmic and pathological brain dynamics, discrete models of ecological and epidemic systems, DNA and protein mechanics, parameter estimation and uncertainty quantification, and experimental design and statistical learning. Across these areas, the group combines mathematical model development, simulations, and rigorous analytical techniques—such as bifurcation theory, perturbation methods, evolutionary game theory and dynamics, applied graph theory, and data-informed inference—to uncover the mechanisms driving biological structure, function, and behavior.
Bard Ermentrout (Distinguished University Professor, PhD)
Dr. Ermentrout is interested in the applications of nonlinear dynamics to biological problems. His main focus is in the area of mathematical neuroscience, where he tries to understand the patterns of activity in networks of neurons. Dr. Ermentrout models recurrent activity, waves, and oscillations in a variety of neural systems, including olfaction (sense of smell), rat whisker barrels, cortical slices, and working memory. He is also interested in problems from physiology, immunology, and cell biology, all of which he has modeled with students and postdocs.
Chengcheng Huang (Assistant Professor, PhD
Dr. Huang is interested in computational modeling and mathematical analysis of neural networks. She develops theoretical approaches to understanding circuit dynamics and information processing in sensory systems. Her work focuses on how different task and stimulus contexts change neuronal responses and the implications on neural coding, with an emphasis on neural variability.
David Swigon (Professor, PhD)
Dr. Swigon works in molecular biology, with a focus on quantification of the relation between the sequence, mechanical properties, and biological function of intracellular components. He has developed micromechanical models of DNA and protein elasticity that combine atomic-scale and continuum mechanics approaches with recent advances in computational chemistry and employ information obtained by x-ray crystallography, single-molecule manipulation, and other experimental techniques.
Gregory Constantine (Professor, PhD)
Gregory Constantine contributes to the planning of scientific experiments, and is using data to build a wide range of data-driven statistical models. Such models may include nonparametric as well as parametric mechanistic ones, probabilistic Bayesian and neuro-network models, predictive parametric models, and models driven by discrete mathematics techniques. His activities involve also the fit of dynamical discrete system models, such as systems of ordinary difference or differential equations, to experimental data for parameter estimation, validation and calibration.
Jonathan Rubin (Professor, PhD)
Dr. Rubin works on both theoretical and applied problems coming from neuroscience, as well as on inflammation and related medical issues, in collaboration with students, postdocs, and medical school faculty. In the neuroscience area, Dr. Rubin's research focuses on rhythmic activity patterns and control in respiratory and locomotor networks, pathological dynamics and therapeutic interventions for movement disorders such as Parkinson's disease, neuronal dynamics associated with decision-making, propagation of activity on graphs, and bursting and other multiple timescale activity patterns. Many of his projects fall into the general theme of spatio-temporal pattern formation in coupled cell networks.
Sabrina Streipert (Assistant Professor, PhD)
Dr. Streipert is interested in applying discrete mathematical models to biology with a specific focus on ecology and disease modeling. Dr. Streipert is interested in formulating and applying biologically relevant discrete models and developing analytical techniques to analyze these systems. Questions of particular interest to her are the effects of intrinsic factors (such as evolution of traits, delay, and underlying time structure) and extrinsic factors (such as environmental fluctuations, harvest, and habitat loss) on a species' survival, coexistence, and movement. In an epidemic setting, the corresponding interests relate to the effects of intrinsic and extrinsic factors on the development of a pandemic and recovery of such.