Exposition

A short report I wrote that introduces characteristic classes from the perspective of (Serre and Bockstein) spectral sequences. This method very cleanly avoids the complications of working out the cell structures on Grassmannians.

A proof of elliptic regularity using the formalism of pseudodifferential operators, mostly following Lawson-Michelsohn.

An expository summary of results relating representations of Lie groups and their Lie algebras, plus why this is important in physics.

A short but careful introduction to geometric gauge theory, from an appendix to my undergraduate thesis.

Heavily explicated notes from a series of lectures by Burt Totaro on Algebraic Cycles and Birational Geometry from the workshop Geometry at the ANU in 2016.

Notes I took at the 2018 British Isles Graduate Workshop: Singularities in Symplectic Topology, can be found here.

My Master's thesis on Global Monodromy for Fukaya-Seidel Categories can be found here; this was intended to give an exposition of ideas of Seidel on categorical structures associated to Lefschetz fibrations, not a rigorous development of the subject, and should not be cited as such. In particular, the argument of Proposition 4.3 is not complete as written.

My Minor Thesis I wrote at Harvard giving an expository introduction to Perverse Sheaves and D-modules, aimed at symplectic geometers.

LiveTeXed notes from a class on Riemann surfaces taught by Peter Kronheimer at Harvard in Fall 2019. To complement this, a short set of notes on elliptic curves and their moduli.

I created a final project for Harvard's Math Mb where students would apply integration, differentiation, and ODE to make decisions about resource management based on real-world data. It didn't end up being used but here's part 1 and part 2 in case you'd like to use them for your students.

Reference

Some worksheets I wrote for a series of introductory LaTeX workshops with the ANUMS can be found here.

Some notes I wrote on probability theory and algebraic geometry for the Harvard qualifying exam.

A summary of results for Sobolev spaces on manifolds (also from my undergraduate thesis).

A useful table of adjoint functors.

Some diagrams I drew illustrating: relations between modes of convergence (here); duality in toric geometry (here); models of homotopy-enriched categories (here); and string topology (here).

Another diagram illustrating the Sobolev embedding theorems in dimension 3, based on a similar diagram by Terence Tao.

Research

A new proof that the plane is connected