My research interests include Iwasawa theory, Galois representations, and -adic -functions. For my senior thesis, I studied growth patterns of Selmer groups and fine Selmer groups in infinite towers of number fields. I enjoy problems that have a computational aspect, or where patterns can be discovered through examples.
Vanishing of Iwasawa Invariants of weight- newforms. Submitted for publication. This paper proves that if is a prime number satisfying mild conditions, there exists a weight newform of level whose Iwasawa - and -invariants vanish for some branch of the -adic -series of .
Non-vanishing of central -values of weight- cuspforms. Submitted for publication. This paper proves the following result: if is a prime number and modulo , then there exists a weight newform of level whose -series is non-vanishing at .
The non--part of the Fine Selmer group in a -extension. Accepted for publication at Acta Arithmetica. This paper studies how the -part of the Fine Selmer group of an elliptic curve grows in a -extension when . It proves that there exist -extensions where the -part of the Fine Selmer group can grow arbitrarily quickly. This generalizes a theorem of Washington which proves an analogous statement for -parts of class groups.
Crank equidistribution and -overlined partitions (with Joshua Males and Shuyang Shen). Submitted for publication. This paper studies a variant of Ramanujan's partition function called the -overlined partition function. We give an asymptotic for how this function grows, analogous to Ramanujan's celebrated asymptotic for the classical partition function.