James Bagrow, Associate Professor, is interested in understanding the underlying rules and organizing principles of complex physical and social systems. His work combines mathematical models with large-scale data analysis to better understand these systems, with a particular emphasis on network science, computational social science, and human dynamics. Other interests include data science, dynamical systems, and novel optimization and machine learning methods. He is a member of the Vermont Complex System Center and co-director of the UVM-Google OCEAN project. |
Daniel Bentil, Associate Professor, does research at the interface of Applied Mathematics and Mathematical Biology. His work, which focuses on mathematical modeling in biology and medicine, is highly interdisciplinary. In physiology, for example, he is currently working on model mechanisms for muscle contraction, aerosol deposition in the lungs, and the dynamics of hemodialysis administered to end-stage renal disease patients. Some ecological studies have involved modeling invasive species spread and host-parasite interactions. Together with his collaborators and graduate students, Daniel Bentil has been developing and analyzing mathematical models, and interpreting and comparing modeling results to real experimental data. He is very well funded and his graduate students have always had no difficulty obtaining jobs right after graduation.
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Chris Danforth, Professor, is the director of the Vermont Advanced Computing Core. Along with Peter Dodds, he co-directs the Computational Story Lab, a group of applied mathematicians at the undergraduate, masters, phd, and postdoctoral level working on large-scale, system problems in many fields including sociology, nonlinear dynamics, networks, ecology, and physics. His research has been covered by the New York Times, Science Magazine, and the BBC among others. Recent projects include quantifying levels of happiness using Tweets & depression using Instagram photos.
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Taras Lakoba, Professor, applies his expertise in perturbation methods to a variety of topics in applied mathematics. Most recently, he has been interested in proving convergence of certain numerical iterative schemes for finding stationary solutions of nonlinear wave equations. In the past, he developed perturbation theories for a number of nonlinear wave equations integrable by the inverse scattering transform. Taras also worked, and still maintains interest, in fiber optics, where his expertise lies in nonlinear signal transmission, polarization effects, and noise accumulation. He was part of the team at Lucent Technologies that developed an ultra-long haul, dense wavelength-division multiplexed transmission (WDM) system in 2002.
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Jianke (Jackie) Yang, Williams Professor of Mathematics, University Distiguished Professor, and University Scholar. His research interests are nonlinear waves and their physical applications --- an important branch of applied mathematics. Nonlinear waves are prevalent in science and engineering, with examples such as water waves in the ocean and light waves in optical fibers. Mathematically, nonlinear waves are described by nonlinear partial differential equations (PDEs). He develops advanced analytical and numerical methods to solve important nonlinear PDEs, and explores applications of such theoretical results to physical problems. His current research interests are on nonlinear optics, rogue waves, parity-time symmetry and numerical methods. |
Jun Yu, Professor, works in the area of applied mathematics with applications in biomedicine, geophysics, fluid mechanics and combustion. A major focus of his research has been on the dynamics of the intracranial system in the human brain. This problem involves a blending of fluid mechanics, elasticity, and theoretical and computational methods with both clinical and experimental aspects of human physiology. Recently, he has become involved in the study of the dynamics and thermodynamics of oceans and ice mass of the Earth, using satellite data from NASA as well as mathematical modeling techniques. At the same time he continues to do research in the area of classical fluid mechanics. There, his research focus is on nonlinearity and stability of water waves. He has examined the evolution of the weakly nonlinear solution for the case in which a parameter (Froude number) goes through its critical value and the linear solution fails. More recently, a solid combustion model was studied, and the onset of linear instability as well as the weakly nonlinear solution behavior in the presence of the linear instability was also analyzed. |