For a General Mathematical Audience

Talks I've given ranging from public, to undergraduate level.

Ray Optics and Differential Geometry

This talk describes a beautiful connection between the geometry of curved spaces (differential geometry) and the physics of light in complicated media (with varying indices of refraction). Starting from the physics, we get pulled into questions of pure mathematics, and then emerge ready to take a first look at General Relativity.

Visualizing Low Dimensional Geometry

This talk was given as part of the Celebration of Mind series by the Gathering For Gardner. I talk a bit about the different approaches mathematicians use to visualize their work in dimensions 2, 3 and 4, and how this necessairly depends on the dimension. For most of the talk, I describe the intrinsic visualization for 3-dimensions, from the project at 3-dimensional.space.

From Courses

Lectures from some recent courses that may be of interest to a wider audience.

Linear Algebra and the Periodic Table

This was made to be the final lecture of a linear algebra course, but when classes abruptly moved online, I put together this video instead.

Ptolemy, Ibn al Shatir and Fourier, I

The first of a two-part lecture from the end of a real analysis course, attempting to answer the question "where would one go from here" starting with some historical questions that set the scene for functional analysis.

Ptolemy, Ibn al Shatir and Fourier, II

Second part of the lecture series from above, introducing the ideas of functional analysis.