Humans and other animals constantly accumulate sensory evidence, engage short term memory, and navigate their dynamic environment. These neural computations rely on the brain’s ability to robustly integrate information. Our group is extending existing theory and developing new mathematical techniques to understand how the brain’s complex networks and associated cognitive computations robustly integrate spatially structured input. Our work leverages stochastic and spatially-extended models, breaking new ground in the fields of mathematical neuroscience, nonlinear waves, statistical inference, and stochastic processes. A core goal is to develop a theory of the algorithms that underlie organismal behavior using a combination of computational modeling and field and laboratory data analysis. Key to this work is the development of novel methods in applied mathematics emerging from Bayesian sequential analysis in dynamic environments, stochastic analysis of spatiotemporal systems, and nonlinear analysis of coherent structures.
keywords
stochastic dynamics and first passage time problems, probabilistic inference/Bayesian models of decision making, stochastic processes in spatiotemporal systems, large-scale neuronal network dynamics, analyzing recurrent neural networks, dynamics of collective decisions and animal movement, nonlinear analysis of waves and patterns in partial differential equations, data-driven modeling of neuronal networks underlying sensory processing, working memory, stochastic models of foraging
