# Research

My research investigates the structure of certain arithmetic invariants arising in algebraic number theory. Specifically, I seek to develop new algebraic techniques to explore classical questions about the reciprocity between Hecke algebras and Galois deformation rings conjectured in the Langlands program. I also study the behavior of ideal class groups in families of number fields.

From October 2018-July 2020, my work was supported by a Heilbronn Research Fellowship. From July 2017-June 2018, my research was supported by an AAUW American Dissertation Fellowship and the University of Oregon Doctoral Research Fellowship. My research was partially supported by a GAANN Fellowship from Jan 2013 to May 2015.

#### Papers and Preprints

- Small Eisenstein congruences and explicit non-Gorenstein R=T, with P. Wake and C. Wang-Erickson. Preprint (in progress) available upon request.
- Higher congruences between newforms and Eisenstein series of squarefree level. Journal de Théorie des Nombres de Bordeaux, 31.02 (2019): 503-525.
- Two classes of number fields with a non-principal Euclidean ideal. International Journal of Number Theory 12.04 (2016): 1123-1136.
- SET with a twist, with J. Ostroff and L. Van Meter. Math Horizons, 28.4 (2021): 20-23.
- Projectivizing SET, with J. Ostroff and L. Van Meter. Math Horizons, 27.4 (2020): 12-15.

#### Poster

- Higher congruences between modular forms. Poster about my research for a general math audience; presented in the graduate student poster session at the 2017 AWM Joint Mathematics Meetings Workshop in Atlanta, GA.

#### Slides

- Projective and Non-abelian SET. Slides from a talk at ICERM's workshop "Illustrating Number Theory and Algebra." Video of lecture can be found here.
- A Brief Introduction to Modular Forms. Slides from a background talk in the Coding Theory, Cryptography, and Number Theory Seminar at Clemson University.

#### Code

- This MAGMA code implements the algorithm give in Section 4.2 of Higher Congruences Between Newforms and Eisenstein Series of Squarefree Level.
- This Python code uses PARI to calculate the values given in Tables 3.1 and 3.2 of Two Classes of Number Fields with a Non-Principal Euclidean Ideal.

With some fellow number theorists at the WIN4 workshop