The research activity in differential equations at CSU includes both ordinary and partial differential equations and embraces numerical/computational as well as theoretical investigations. There is considerable activity in the area of dynamical systems, particularly in the study of instabilities and pattern formation with applications to pattern analysis and neural networks. This activity is leading to increasing collaboration (in the form of joint seminars and cooperative degree programs etc.) with various departments of biological sciences on campus.
Research activity in partial differential equations includes such topics as: new techniques for a posteriori error analysis for finite element solutions of elliptic boundary value problems, computational fluid dynamics, vector algorithms and numerical methods for conservation laws, reconstruction algorithms for electrical impedance tomography (EIT), as well as direct and inverse problems associated with flow in porous media, including modelling of contaminant transport in groundwater. These efforts have led to cooperative links with various engineering departments and with soil physicists in the agronomy department.
The following faculty members have research interests in Differential Equations.
My research focuses on how the interplay between ecological and evolutionary mechanisms affects the dynamics and persistence of ecological systems. We particularly focus on disease ecology and trait-based approaches in ecology and use quantitative techniques to address questions in these areas.