Alex Barrios
Assistant Professor of Mathematics
Undergraduate Research
I regularly work with undergraduate students on research projects in algebraic geometry and number theory. I was previously one of the directors of the Pomona Research in Mathematics Experience (PRiME) and also supervised undergraduate research as part of the Mathematical Sciences Research Institute Undergraduate Program (MSRI-UP). Below is a list of undergraduate research projects that I have directed:
University of St. Thomas
Center for Applied Mathematics Summer 2024 Research
On good abc triples
Students: Juan Cañas Garcia and Aspen Erickson (University of St. Thomas)
Center for Applied Mathematics Fall 2024 Research
Minimal discriminants and primes of additive reduction for elliptic curves with a 8-isogeny
Student: Jewel Aho (University of St. Thomas)
PRiME 2023
Minimal discriminants and primes of additive reduction for elliptic curves with a 4-isogeny
Students: Jewel Aho (University of St. Thomas), Louis Burns (Pomona College), Thea Nicholson (Xavier University of Louisiana), and Fabian Ramirez (University of California Irvine)
PRiME 2022
Good ABC Triples and Good Elliptic Curves
Students: Elise Alvarez-Salazar (University of California, Santa Barbara), Barry Henaku (Washington University in St. Louis), and Summer Soller (University of Utah)
Recipients of the MAA MathFest 2022 Poster Presentation Award
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)
Recipients of the MAA MathFest 2021 Number Theory Undergraduate Research Presentation
MSRI-UP 2020
Automorphism and Monodromy Groups of Classical Modular Curves (co-advised 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 (co-advised with Edray Goins)
Students: Ra-Zakee Muhammad (Pomona College), Javier Santiago (University of Puerto Rico, Río Piedras), Eyob Tsegaye (Stanford University)
Dessin d’Enfants from Cartographic Groups (co-advised 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 4-isogeny
Student: Abigail Loe (Carleton College)
PRiME 2019
Minimal Discriminants of Rational Elliptic Curves with a non-trivial 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