Notes + Expos

These are notes transcribed from classes previously I have taken.

Credit for the material goes to those who taught the courses; errors in the notes are entirely my own (I would be grateful to be notified of any errata.)

[pdf] “Representation Theory of Lie Groups and Lie Algebras.”
From MAT 449 (Topics in Algebra), taught by Sophie Morel at Princeton in Fall 2013.
[pdf] “Topology of Algebraic Links.”
From MAT 469 (Advanced Topology), taught by András Némethi at Princeton in Spring 2014.
[in preparation] “Train Tracks: Automorphisms of Free Groups and Surfaces.”
From a NSF-RTG course taught by Mladen Bestvina at the University of Utah, July 7-18 2014.
[pdf] “An Introduction to Geometric Group Theory.”
From MATH 697, taught by Richard Canary at Michigan in Fall 2014.
[pdf] “An Introduction to Teichmüller Theory.”
From MATH 697, taught by Richard Canary at Michigan in Fall 2015.

For the interested layperson

I am more generally interested in trying to communicate to non-specialists / non-mathematicians ~~my research~~ ~~the mathematics I encounter~~ some of the beautiful and sometimes surprisingly applicable mathematics developed over this past century or two, which usually gets thrown into the "too obscure for non-experts" bin.

Here are some attempts at this:

I wrote an expository article for the MiSciWriters blog about chaos (published in two parts, here and here.)
I participated in the RELATE summer workshop in 2020; as my final project for this workshop I made a video about negatively-curved geometries and the intuition behind their possible use in machine learning.