Research

My research interests are in number theory. My dissertation work, under the guidance of Francesc Castella, focuses on Iwasawa Theory.

Current Research

I am working on a project (collaborating with Elvira Lupoian and Leo Mayer) started under the guidance of Valentijn Karemaker at the Arizona Winter School 2024 where we are looking at the intersections of various stratifications of the moduli space of principally polarized Abelian varieties of rank 5.

PhD Research

In 2000, The Clay Mathematics Institute selected seven Millennium Prize Problems. One of these problems is the Birch and Swinnerton-Dyer Conjecture. The rank part of this conjecture states that the rank of an elliptic curve is equal to the vanishing order of the corresponding L-function. Work by Gross-Zagier and Kolyvagin proves that a modular elliptic curve E for which L_s=1(E, 1) = 0 will have rank 1. A p-coverse theorem is one in which information about the rank of the curve is used to determine information about the vanishing order of the L-function. For my current research, I am generalizing a result of Burungale, Castella, Skinner, and Tian in which they prove a p-converse to a theorem for Hecke characters of infinity type (-1, 0), to one for Hecke characters of infinity type (1-k, 0) with k any positive integer.

MS Research

The subalgebra classification problem is to create a list of all subalgebras of a given Lie algebra up to equivalence. For this project I contribute to the software toolkit within the Differential Geometry package of Maple for classifying subalgebras. My thesis can be found here .

Past Presentations/Talks

● Intersections of Stratifications , Arizona Winter School, University of Arizona, March 2024, (joint presentation with Elvira Lupoian and Leo Mayer)

● A p-converse Theorem in Weight Greater Than 2 , WiMSoCal, Pomona College, February 2024

● The Million Dollar Problem: Number Theory and Elliptic Curves , Math Matters Series, Bakersfield College, February 2024

● A Brief Introduction to Topology , DRP Universal Cover Workshops, UCSB, January 2024

● Research in Number Theory: Elliptic Curves and Related Groups , Association for Women in Mathematics (UCSB Chapter), UCSB, November 2022

● Rubin's Thoerem , Preprint Seminar, UCSB, March 2022

● Katz and Rankin p-adic L-functions , Preprint Seminar, UCSB, March 2022

● Kobayashi's "Control Theorem" for Signed Selmer Groups , Student Learning Seminar on Iwasawa Theory for Elliptic Curves, UCSB, November 2021

● Everything I Should Have Learned About CW Complexes, but Never Did , Graduate Topology Seminar, University of California - Santa Barbara, April 2021

● Maximal Regular Semisimple Subalgebras of Simple Lie Algberas , Summer Research Poster Session, Utah State University, August 2018

● Regular Subalgebras of Semisimple Lie Algebras , DGCAMP Student Daze, Utah State University, April 2018

● Three Dimensional Subalgebras of Simple Lie Algebras , DG Rendezvous, Utah State University, November 2016

Conferences Attended

● Arisona Winter School (AWS) 2024, March 2nd - 6th
 - At the conference I was in Valentijn Karemaker's project group

● Symposium for Women and Gender Minorities in Mathematics in Southern California (WiMSoCal) 2024, February 24th

● Nebraska Conference for Undergraduate Women in Mathematics (NCUWM) 2024, January 26th - 28th

● Joint Math Meeting (JMM) 2024, January 2nd - 6th

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