I'm a number theorist specializing in [[Modular Forms|modular forms]], finishing my Ph.D. at the [University of Illinois](https://math.illinois.edu/research/faculty-research/number-theory). I'm also a family man, U.S. Marine, and member of [The Church of Jesus Christ of Latter Day Saints](https://www.churchofjesuschrist.org/?lang=eng)[^1]. My advisor is [Scott Ahlgren](https://scottahlgren.web.illinois.edu/), and my MS thesis advisor was [Nick Andersen](https://mathdept.byu.edu/~nick/). I co-organize the [Graduate Number Theory Seminar at UIUC](https://gradnumbertheory.web.illinois.edu/). >[!tldr]- Research Statement >My research interests are in the theory of automorphic forms. These are complex-valued functions which respect a discrete group action on their domain, up to scaling by a factor of automorphy. The simple definition of automorphic forms belie their sophisticated structure and fundamental importance not only in number theory, but also in physics, combinatorics, and algebraic geometry, among other mathematical disciplines. > >In particular, I'm interested in explicating the arithmetic and combinatorial information encoded by the Fourier coefficients of modular forms and weak harmonic Maaß forms. I'm currently pursuing advances through the recently discovered [Shimura correspondence](https://www.sciencedirect.com/science/article/abs/pii/S0001870824001701) for half-integer weight modular forms transforming with respect to the eta multiplier. I also spend a great deal of time thinking about prime-power congruences for the coefficients of modular forms. > ![[IMG_2639.jpeg|300]] [![[[email protected]|24x24]]](https://arxiv.org/a/williams_c_4.html)[![[scholar_icon.png|24x24]]](https://scholar.google.com/citations?user=LRWv7xkAAAAJ&hl=en&oi=sra) [![[icons8-email-48.png|24x24]]](mailto:[email protected]?subject=Linked%20from%20your%20personal%20site%3A) You can browse the menu **↖**, or see my papers in [[Selected Work]]. [^1]: Otherwise known as "Mormons."