Brandon Williams webpage

I am now a postdoc at TU Darmstadt.


Here are the lecture notes from the course Math 110 (Linear algebra) that I taught in summer 2016. They are intended to accompany the third edition of Axler's Linear Algebra Done Right. Some students found these notes useful.


I am studying modular forms. My thesis adviser was Richard Borcherds.

Computing modular forms for the Weil representation. pdf Includes some minor corrections.

10. The rings of Hilbert modular forms for Q(sqrt29) and Q(sqrt37). pdf Data for Q(sqrt29) and Q(sqrt37)
9. Remarks on the theta decomposition of vector-valued Jacobi forms. pdf link
8. A short proof of Rademacher's formula for k-color partitions. pdf
7. Rankin-Cohen brackets and Serre derivatives as Poincaré series. pdf link
6. A p-adic completion of Zagier's Eisenstein series. pdf
5. Vector-valued Hirzebruch-Zagier series and class number sums. pdf link
4. Overpartition M2-rank differences, class number relations, and vector-valued mock Eisenstein series. pdf
3. Poincaré square series of small weight. pdf link
2. Vector-valued Eisenstein series of small weight. pdf link
1. Poincaré square series for the Weil representation. pdf link

PSS is a program for calculating with vector-valued modular forms for Weil representations. Download the SAGE worksheet here. Most recently updated June 13, 2018. This pdf explains how to use it.
If you find a bug in this program or have other questions or comments please email me at btw at math dot city dot edu.

Here is a worksheet for computing "local L functions" that show up in the vector-valued Eisenstein series.

Here is a worksheet for computing weight 3/2 mock Eisenstein series and their shadows. Here is how to use it.

Here is a short worksheet for working with eta products. It computes the q-series of an eta product and tries to identify an eta product from a q-series.


Undergraduate thesis
Master's thesis
Math 274 final paper - tropical Riemann-Roch theorem