Videos

Full Course Lecture Series

Partial Differential Equations
Example-driven introduction to partial differential equations. Features derivations and solutions to the heat, wave, Helmholtz, and transport equations.
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Dynamical Systems Extra Credit
A collection of some of my favourite topics in dynamical systems that I couldn't fit into the regular curriculum.
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Dynamical Systems
An introduction to dynamical systems with many applications. Features steady-state analysis, bifurcations, conservative systems, limit cycles, and chaos theory.
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Mathematical Modelling
Example-driven exposition on both constructing and analyzing mathematical models for physical, biological, and social phenomena, divided into three modelling techniques: optimization, dynamic, and stochastic models.
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Ordinary Differential Equations
An introduction to the theory and solutions of ordinary differential equations. Topics include integrating factors, numerical approximation, power series, and the Laplace transform.
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Analytic Geometry and Calculus II
Integral calculus from the ground up for undergraduates who have completed differential calculus. Topics include computing volumes, integration techniques, sequences, and series.
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Single Variable Real Analysis
Starts from the definition of the real numbers and moves through integral and differential calculus, vector spaces, and Taylor series in a completely rigorous way.
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Deep learning of conjugate mappings
Video abstract for the paper “Deep learning of conjugate mappings” with Kutz and Brunton.
Paper
Sparse identification of slow timescale dynamics
Video abstract for the paper “Sparse identification of slow timescale dynamics” with Dylewsky and Kutz.
Paper
Bounding minimum wave speeds
Video abstract for the paper “Minimum wave speeds in monostable reaction-diffusion equations” with Goluskin.
Paper
Discovering Poincaré mappings
Video abstract for the paper “Poincare maps for multiscale physics discovery and nonlinear Floquet theory” with Kutz.
Paper
Data-driven stabilization of periodic orbits
Video abstract for the paper “Data-driven stabilization of periodic orbits” with Brunton and Kutz.
Paper

Data-driven system analysis using the Koopman operator and polynomial optimization
Talk for the McGill QLS-CAMBAM Seminar
Localized patterns on graphs
Talk from the workshop on Dynamics of Waves and Patterns held at the Mathematisches Forschungsinstitut Oberwolfach
Deep learning of conjugate mappings
Talk for the CRM Applied Mathematics Seminar at McGill University
Sparse identification of slow timescale dynamics
Talk at Dynamics Days Europe 2020
Snaking bifurcations in higher space dimensions
Talk for University of Washington's applied PDE seminar in spring 2019