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 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. Key to this work is the close interaction with experimental collaborators whose labs: (a) record and image propagating activity in cortical tissue; (b) administer decision-making tasks to humans and non-human primates while simultaneously imaging neural activity as well as taking pupillometric readings; and (c) identify mechanisms underlying swarm intelligence in house-hunting honeybees.
stochastic processes in spatiotemporal systems, large-scale neuronal network dynamics, probabilistic inference models of decision making, analyzing recurrent neural networks, dynamics of swarm/collective decisions, nonlinear analysis of waves and patterns in partial differential equations, data-driven modeling of neuronal networks underlying sensory processing, motor output, working memory
APPM 2360 - Introduction to Differential Equations with Linear Algebra
Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Credit not granted for this course and both MATH 2130 and MATH 3430.
APPM 3570 - Applied Probability
Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, joint distributions, moment generating functions, law of large numbers and the central limit theorem. Degree credit not granted for this course and ECEN 3810 or MATH 4510. Same as STAT 3100.
APPM 8400 - Mathematical Biology Seminar
Spring 2018 / Spring 2019 / Fall 2019 / Spring 2020
Introduces advanced topics and research in mathematical and computational biology. Instructor consent required.