Research

My research interests include Iwasawa theory, Galois representations, and pp-adic LL-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.

Publications and Preprints

  1. Vanishing of Iwasawa Invariants of weight-22 newforms. Submitted for publication. This paper proves that if pp is a prime number satisfying mild conditions, there exists a weight 22 newform ff of level pp whose Iwasawa λ\lambda- and μ\mu-invariants vanish for some branch of the pp-adic LL-series of ff.

  2. Non-vanishing of central LL-values of weight-22 cuspforms. Submitted for publication. This paper proves the following result: if N11N \geq 11 is a prime number and N3N \equiv 3 modulo 44, then there exists a weight 22 newform ff of level NN whose LL-series is non-vanishing at s=1s=1.

  3. The non-pp-part of the Fine Selmer group in a Zp\mathbf{Z}_p-extension. Accepted for publication at Acta Arithmetica. This paper studies how the \ell-part of the Fine Selmer group of an elliptic curve grows in a Zp\mathbf{Z}_p-extension when p\ell \neq p. It proves that there exist Zp\mathbf{Z}_p-extensions where the \ell-part of the Fine Selmer group can grow arbitrarily quickly. This generalizes a theorem of Washington which proves an analogous statement for \ell-parts of class groups.

  4. Crank equidistribution and (k,j)(k,j)-overlined partitions (with Joshua Males and Shuyang Shen). Submitted for publication. This paper studies a variant of Ramanujan's partition function called the (k,j)(k,j)-overlined partition function. We give an asymptotic for how this function grows, analogous to Ramanujan's celebrated asymptotic for the classical partition function.