My Ph.D. thesis was on CM Liftings of Supersingular Elliptic Curves. My thesis may be found here, as well as the two submitted papers from my thesis (the first quadratic.pdf involving representations of integers by quadratic forms, and the second elliptic.pdf involving lifts of supersingular elliptic curves).
I then studied representations of integers by sums of triangular numbers, leading to the paper repset.pdf which gives a certain finiteness theorem similar to the Conway Schneeberger 15 theorem and computes the resulting set under the assumption of GRH. My interests during that period included Partition Theory and other applications of Modular Forms. For interested students, there are a plethora of very accessible and interesting problems coming out of partition theory and modular forms theorm which serve as good Bachelor and Master's thesis problems.
Most of my research in the past few years has centered around mock modular forms and harmonic weak Maass forms. In addition to their applications to Partition theory (see this paper) and Faber polynomials, I have been interested in the theory built around these functions. In recent work with Kathrin Bringmann and Winfried Kohnen, we have constructed interesting examples of what we call Locally harmonic Maass forms. In the coming years, I am interested in further investigating the theory behind these functions, with a first step accomplished in joint work with Kathrin Bringmann and Sander Zwegers in this preprint.
