Brandon Williams webpage

I am now a postdoc at TU Darmstadt.

Teaching:


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.

Research:

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

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

Preprints:
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.

Other:

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