Research Interests

In my group, we use mathematical modeling to gain insight to the workings of the brain. Our goal is to help reveal and understand the physiological mechanisms generating experimentally observed brain and neural activity. Our approach is guided by two primary motivations : 1) to provide the neuroscience community with quantitative support of experimental hypotheses and rigorous theoretical frameworks for exploring and developing experimentally-testable predictions; and 2)  provide the mathematical community with  rigorous analyses of the solution structure of our models to identify nonlinear dynamics in neural processing.

Current research projects address:

  • Neuronal control of sleep-wake regulation
  • Acetylcholine modulation of network dynamics and rhythms
  • Influence of neuron and network properties on neural activity
  • Circadian rhythms in pain processing

MATH 568: Computational and Mathematical Neuroscience course

In the field of neuroscience, the brain is investigated at many different levels, from the activity of single neurons, to computations in small local networks, to the dynamics of large neuronal populations. This course introduces students to modeling and quantitative techniques used to investigate, analyze and understand the brain at these different levels.