My group constructs mathematical models of the dynamics of neural networks, with emphasis on the synaptic basis of learning and memory. Neurons do not stand alone; they communicate with each other via an intricate web of synaptic connections. Neural networks behave in complex ways because they are nonlinear, in both the topological and algebraic senses of the word. Their synaptic connectivity cannot be decomposed into simple linear pathways, because of the existence of many feedback loops. Furthermore, signal transmission in neural networks is mediated by nonlinear processes.
These nonlinearities make it difficult to understand neural networks using purely intuitive means, which is why we construct mathematical theories. To achieve the goal of reducing behavior to biophysics, our theories should succeed in two aspects. First, they should explain how mental functions arise from the dynamics of neural networks. Second, they should elucidate how the dynamics of neural networks is rooted in the biophysical properties of single neurons.
Affiliate Member, Picower
Center for Learning and Memory Robert A. Swanson Career Development Chair
Assistant Professor, Department of Brain and Cognitive Sciences
Assistant Investigator, Howard Hughes Medical Institute
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