Ph.D., University of California, Los Angeles (2006)
M.S., University of California, Los Angeles (2002)
B.A., University of Chicago, (2001)
I specialize in Number Theory, one of the oldest branches of mathematics which also continues to be a field of active research today. In particular, I study modular and mock modular forms (certain complex-valued functions), harmonic Maass forms, Jacobi forms, quantum modular forms, q-series, and related objects. Historically, modular forms have played fundamental roles in Number Theory, for example, they are central to the well known Riemann Hypothesis and Fermat's Last Theorem. Modular forms also often yield applications to other areas of mathematics; my research focuses on harmonic Maass forms, q-series, and related functions, with particular emphasis on their applications to the fields of Combinatorics and Representation Theory. On these subjects, I am co-author of the book Harmonic Maass forms and mock modular forms: theory and applications, published by the American Mathematical Society in 2018, and winner of the 2018 AAP Prose Award for best scholarly book in Mathematics.
I enjoy teaching a wide range of students and courses in a variety of settings and levels, including beginning Calculus, Fractal Geometry at the intermediate level, and Number Theory and Abstract Algebra at the more advanced level. I am also actively involved in mentoring and advising student research.
Recent Awards and Honors
AMS Mary P. Dolciani Prize for Excellence in Research (2021)
National Science Foundation Grant, DMS-1901791 (2019-2022)
Simons Foundation Fellowship in Mathematics, ID 561663 (2018-2019)
Prose Award, Association of American Publishers (2018)
National Science Foundation CAREER Grant, DMS-1252815 (2013-2018)
Institute for Advanced Study, Princeton, von Neumann Fellow/Member (Spr. 2019, Spr. 2016)
National Science Foundation Grant, DMS-1049553 (2010-2013)
Yale University Junior Faculty Fellowship (2012-2013)
National Science Foundation Postdoctoral Fellowship, DMS-0701461 (2007-2010)
Honored Instructors Award, University of Wisconsin, Madison (2009)
My personal website (including publications, teaching, CV, math outreach etc.) is available here.