Research

Research

Current research interests include number theory, arithmetic geometry, elliptic curves, and Galois representations. My thesis, with advisor Álvaro Lozano-Robledo, focuses on classifying torsion subgroups of elliptic curves over function fields of genus zero and one. Recently, I have become interested in torsion subgroups of elliptic curves over function fields of hyperelliptic curves, and with this, bounding the gonality of certain families of modular curves.

Thesis

PhD Thesis: Torsion Subgroups of Ellitpic Curves over Function Fields

Research Articles

  1. Torsion Subgroups of Elliptic Curves over Function Fields of Genus 0 , in JNT

  2. Torsion Subgroups of Elliptic Curves over Function Fields of Genus 1


Talks Given

SEMINAR TALKS

  • Undergraduate Math Club Talk, University of Connecticut, March 11, 2020

  • Number Theory Seminar, Wesleyan University, November 22, 2019

  • Five College Number Theory Seminar, University of Connecticut, March 5, 2019

  • Algebra Seminar, University of Connecticut, November 28, 2018

  • Number Theory Seminar, Boston University, December 11, 2017

  • SIGMA Seminar, University of Connecticut, April 1, 2017

  • Undergraduate Math Club Talk, University of Connecticut

CONFERENCE TALKS

    • AMS Sectional Meeting, April 14, 2019

    • 2019 Joint Math Meetings, January 19, 2019

    • 2018 Automorphic Forms Workshop, Tufts University, March 20, 2018

    • Maine-Québec Number Theory Conference, University of Maine


Conferences Attended

  • Connecticut Summer School in Number Theory - Research Conference

June 2020, online, University of Connecticut, Storrs, CT

  • Cross Atlantic Representation Theory and Other topics ONline (CARTOON)

May 2020, online

  • 1148th AMS Sectional Meeting

April 2019, University of Connecticut Hartford, Hartford, CT

  • Northeast Consortium for Quantitative Literacy XXII Meeting

March 2019, Bay Path University, Longmeadow, MA

  • 2019 Joint Math Meetings

January 2019, Baltimore, MD

  • Connecticut Summer School in Number Theory (CTNT)

May 2018, University of Connecticut, Storrs, CT

  • Automorphic Forms Workshop

March 2018, Tufts University, Boston, MA

  • Arizona Winter School: Iwasawa Theory

March 2018, University of Arizona, Tucson, AZ

  • Maine-Québec Number Theory

October 2017, University of Maine, Orono, ME

  • MSRI Summer School: Automorphic Forms and Langlands Program

July/August 2017, MSRI, Berkeley, CA

  • Seventh Upstate New York Number Theory Conference

May 2017, Binghamton University, Binghamton, NY

  • Arizona Winter School: Perfectoid Spaces

March 2017, University of Arizona, Tucson, AZ

  • Connecticut Summer School in Number Theory

August 2016, University of Connecticut, Storrs, CT

  • Arizona Winter School: Arithmetic Geometry

March 2016, University of Arizona, Tucson, AZ

  • BU/Keio University Workshop 2015

September 2015, Boston University, Boston, MA

  • Elliptic Curves @ UConn

May 2014, University of Connecticut, Storrs, CT

  • Advanced Technological Education (ATE) 2013 Conference

Fall 2013American Association of Community Colleges, Washington DC