I am a number theorist specializing in combinatorial number theory and modular forms. My research is currently focused on the following areas and the interplay between them:
I study various partition functions, including multipartition functions. I am interested in combinatorial properties, congruences, asymptotics, and connections with modular forms.
I study both classical and generalized modular forms, including zeros of modular forms, and connections with partition theory.
Mock Modular Forms
I am interested in the recently developing theory of mock modular forms, arising from the study of Ramanujan's mock theta functions. In particular, I am interested in the connections with partition rank functions, and arithmetic connections between mock modular forms and their modular form ''shadows.''
I am interested in Ramanujan type supercongruences, hypergeometric series, and their connections to the geometry of elliptic curved and K3 surfaces.