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), weak Maass 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 modular and mock modular forms, weak Maass forms, q-series, and related functions, with particular emphasis on their applications to the fields of Combinatorics and Lie Theory.
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 the research and professional mentoring of undergraduate (and graduate) students, as well as public school outreach within the community.
K. Bringmann, A. Folsom, and K. Ono, Harmonic Maass Forms and Mock Modular Forms: Theory and Applications, American Mathematical Society Colloquium Publications, 66. American Mathematical Society, Providence, RI, to appear (2017).
K. Bringmann and A. Folsom, "Almost harmonic Maass forms and Kac-Wakimoto characters," J. Reine Angew. Math. (Crelle's J.), to appear (2014).
A. Folsom, K. Ono, and R.C. Rhoades, "Mock theta functions and quantum modular forms," Forum of Mathematics Pi, 1 (2013), 1-27.
A. Folsom and R. Masri, "Equidistribution of Heegner points and the partition function," Mathematische Annalen 348 no. 2 (2010), 289-317.
A. Folsom, "WHAT IS...a mock modular form?," Notices of the American Mathematical Society 57 issue 11 (2010), 1441-1443.
A full publication list is available here.
Recent Awards and Honors
National Science Foundation CAREER Grant, DMS-1252815 (2013-2018)
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 (publications, teaching, CV, and math outreach) is available here.