Education & Professional History
Brown University, ScB; Purdue University, MS, PhD
At Carleton since 2018.
Highlights & Recent Activity
National Science Foundation DMS2113782 ($548,786 — CoPI)
Codirector of the Pomona Research in Mathematics Experience (PRiME) (2019present)
Project leader (joint with Manami Roy) for the Rethinking Number Theory 2 Workshop during Summer 2021
Invited lecturer for the 2021 Arizona Winter School
Organizations & Scholarly Affiliations
Current Courses

Fall 2021
MATH 236:
Mathematical Structures

Winter 2022
MATH 210:
Calculus 3

MATH 400:
Integrative Exercise

Spring 2022
MATH 210:
Calculus 3

MATH 321:
Real Analysis I

MATH 400:
Integrative Exercise
My research interests are in Algebraic Number Theory, Class Field Theory, and Diophantine Geometry.
One of my primary focuses is on bridging the gap between our theoretical understanding of elliptic curves and the explicit construction of examples, and the calculation of data pertaining to elliptic curves. In this direction, my recent work includes the classification of minimal discriminants and local data (joint work with Manami Roy) of rational elliptic curves with a nontrivial torsion subgroup. The latter also explicitly classifies all rational elliptic curves with a nontrivial torsion point which have global Tamagawa number equal to one. The global Tamagawa number is one of the quantities that occur in the famed Birch and SwinnertonDyer conjecture. In addition, Roy and I have explicitly classified the cuspidal automorphic representation attached to rational elliptic curves with a nontrivial odd torsion point.
Part of my work on elliptic curves is motivated by the Modified Szpiro Conjecture, which is equivalent to Masser and Oesterlé‘s ABC Conjecture. To this end, I have shown that there are infinitely many good elliptic curves with a specified torsion subgroup. This generalizes Masser’s Theorem on the existence of infinitely many good elliptic curves with full 2torsion. I have also established lower bounds for the modified Szpiro ratio. In fact, these lower bounds are sharp if the ABC Conjecture holds.
Undergraduate Research
I am also passionate about introducing undergraduates to research topics in algebraic geometry and number theory. Through the Pomona Research in Mathematics Experience (PRiME) and the Mathematical Sciences Research Institute Undergraduate Program (MSRIUP), I have directed the following undergraduate research projects:
PRiME 2021
Minimal Discriminants of Rational Elliptics with Prescribed Isogeny Graphs
Students: Alyssa Brasse (Hunter College), Nevin Etter (Washington and Lee University), Gustavo Flores (Carleton College), Drew Miller (University of California, Santa Barbara), and Summer Soller (University of Utah)
MSRIUP 2020
Automorphism and Monodromy Groups of Classical Modular Curves (coadvised with Edray Goins)
Students: Samuel Heard (University of Oklahoma), Fabian Ramirez (Sonoma State University), Vanessa Sun (Hunter College)
Explicit Constructions of Finite Groups as Monodromy Groups (coadvised with Edray Goins)
Students: RaZakee Muhammad (Pomona College), Javier Santiago (University of Puerto Rico, Río Piedras), Eyob Tsegaye (Stanford University)
Dessin d’Enfants from Cartographic Groups (coadvised with Edray Goins and Sofía Martinez)
Students: Nicholas Arosemena (Morehouse College), Yaren Euceda (University of Minnesota, Twin Cities), Ashly Powell (University of the Virgin Islands)
Carleton College Towsley Fund for Winter Research 2019
Minimal Discriminants of Rational Elliptic Curves Separated by a 4isogeny
Student: Abigail Loe (Carleton College)
PRiME 2019
Minimal Discriminants of Rational Elliptic Curves with a nontrivial Rational Isogeny
Students: Alvaro Cornejo (University of California, Santa Barbara), Owen Ekblad (University of Michigan, Dearborn), Marietta Geist (Carleton College), Kayla Harrison (Eckerd College), and Abigail Loe (Carleton College)
Recipients of the MAA MathFest 2019 Number Theory Undergraduate Research Presentation
Works in preparation
 Reduced minimal models of rational elliptic curves, in preparation.
Published and submitted articles
 (w. Alyson Deines, Maila Hallare, Piper H, Manami Roy) Isogenous discriminant twins of prime degree over number fields, submitted.
 Explicit classification of isogeny graphs of rational elliptic curves, submitted.
 Lower bounds for the modified Szpiro ratio, submitted, preprint available at https://arxiv.org/abs/2104.10817
 Good elliptic curves with a specified torsion subgroup, submitted requested revisions, preprint available at https://arxiv.org/abs/2012.12475
 (w. Manami Roy) Representations attached to elliptic curves with a nontrivial odd torsion point, to appear in Bulletin of the London Mathematical Society, preprint available at https://arxiv.org/abs/2106.15722
 (w. Manami Roy) Local data of rational elliptic curves with nontrivial torsion, to appear in Pacific Journal of Mathematics, preprint available at https://arxiv.org/abs/2104.10337
 Minimal models of rational elliptic curves with nontrivial torsion, Res. Number Theory 8 (2022), no. 1, Paper No. 4., 39 pp. Article available at https://rdcu.be/cKxDl
 A constructive proof of Masser’s Theorem, Contemp. Math., Vol 759, pp. 5161, 2020. Preprint available at https://arxiv.org/abs/1908.04938
Expository Publications
 (w. Ranthony A.C. Edmonds, Roberto Soto) Math Alliance: Investing in Tomorrow Today, to appear as book chapter in Count Me In: Community and Belonging in Mathematics by Della Dumbaugh and Deanna Haunsperger, MAA Press