I'm a number theorist specializing in [[Modular Forms|modular forms]] and a Ph.D. candidate (ABD) at the [University of Illinois](https://math.illinois.edu/research/faculty-research/number-theory), currently on the job market for the 2027-2028 academic year. My Ph.D. 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 and am webmaster for the [Graduate Number Theory Seminar at UIUC](https://gradnumbertheory.web.illinois.edu/). I'm also a family man with 3 kids, U.S. Marine (2015-2021), and member of [The Church of Jesus Christ of Latter Day Saints.](https://www.churchofjesuschrist.org/?lang=eng).[^1] [[Clay_Williams_CV_2026_vII.pdf|Curriculum Vitae]] >[!tldr]- Research Interests >My research interests are in the theory of modular forms and related functions.[^2] In particular, I'm interested in the arithmetic and combinatorial information encoded by the Fourier coefficients of this class of functions. I'm currently working on developing the theory of the recently discovered Shimura Correspondence for the eta multiplier, especially relations between central values of L-functions and Fourier coefficients of modular forms. I also spend a great deal of time thinking about prime-power congruences for the coefficients of modular forms. > ![[pic chalkboard.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)[![[mathscinet.png|48x24]]](https://mathscinet.ams.org/mathscinet/author?authorId=1640066) [![[ORCID-iD_icon_unauth_reversed_16x16.png|20]]](https://orcid.org/0000-0002-3764-6361) [![[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]]. Thank you for visiting my site. [^1]: Also known as "Mormons." [^2]: [[Modular Forms|Modular forms]] are complex-valued functions which respect a particular discrete group action on their domain, up to scaling by a factor of automorphy. The simple definition of modular 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. There are many variations on the core concept of a modular form, coming from either relaxing a smoothness condition, or the transformation condition, or both.