Hi, I'm Jaiden.
Currently, I'm a 1st-year engineering graduate student at Waterloo with a mathematics+physics undergrad. I'm interested in applying methods from mathematics and theoretical physics to problems in engineering, partly inspired by the work of Robert Hermann.
The majority of my mathematical activity occurs independently; I have studied differential geometry, algebraic topology, classical mechanics/field theory, representation theory, quantum mechanics, etc.
Research
My current research is broadly in applying geometric methods to control. A project I'm close to publishing is using Riemannian geometry to design
path following algorithms. A larger project which I'm very excited about bridges control and PDE symmetries (my undergraduate research topic). In short, in a mechanical system when you impose holonimic constraints
via control actuation, the resulting dynamics may no longer be lagrangian. But we still wish to find symmetries and have an analog of noethers theorem! This can in fact be done with modern
symmetry toold, but the metods are quite unknown to the broader community.