Mathematical Biology

The biological world stands as the next great frontier for mathematical modeling and analysis. This group studies complex systems and dynamics arising in various biological phenomena. Areas of interest include neuroscience, movement disorders, immunology, cellular function, and genetic regulation. The groups uses a wide array of approaches, from applied mathematics and nonlinear analysis, including computer simulations, bifurcation theory, perturbation methods, and mathematical model building, to rigorous analysis.

Constantine's Research (Professor)

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.

Ermentrout's Research (Distinguished University Professor)

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.

Rubin's Research (Professor, Department Chair)

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 transitions in activity patterns in respiratory pacemaker networks, tremor and deep brain stimulation for movement disorders such as Parkinson's disease, spike-timing dependent synaptic plasticity, and traveling waves in neuronal media. Many of his projects fall into the general theme of spatio-temporal pattern formation in coupled cell networks.

Swigon's Research (Assoc. Professor, Graduate Director)

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.