Alex Barrios
Assistant Professor of Mathematics
Research publications and submitted articles
Tamagawa numbers of elliptic curves with an l-isogeny, submitted (with John Cullinan).
Prime isogenous discriminant ideal twins, submitted (with Alyson Deines, Maila Brucal-Hallare, Piper Harris, Manami Roy).
Reduced minimal models and torsion, submitted.
Symmetric tensor powers of graphs, Sci. Ser. A Math. Sci. (N.S.) 36 (2026), 12–34. (with Weymar Astaiza, Henry Chimal-Dzul, Stephan Ramon Garcia, Jaaziel de la Luz, Victor H. Moll, Yunied Puig, Diego Villamizar)
Local data of elliptic curves under quadratic twist, Res. Number Theory 11 (2025), no. 3, Paper No. 75, 39 pp. (with Manami Roy, Nandita Sahajpal, Darwin Tallana, Bella Tobin, Hanneke Wiersema). DOI
On abc triples of the form (1,c-1,c), Integers 23 (2023), Paper No. A65, 22 pp. (with Elise Alvarez-Salazar, Calvin Henaku, Summer Soller). DOI
Lower bounds for the modified Szpiro ratio, Acta Arithmetica 208 (2023), 51-68. DOI
Explicit classification of isogeny graphs of rational elliptic curves, Int. J. Number Theory 19 (2023), no. 4, 913–936. DOI
Good elliptic curves with a specified torsion subgroup, Journal of Number Theory 242 (2023), 21–43. DOI
Representations attached to elliptic curves with a non-trivial odd torsion point, Bull. London Math. Soc. 2022;54:1846–1861 (with Manami Roy). DOI
Local data of rational elliptic curves with non-trivial torsion, Pacific J. Math. 318 (2022) 1-42 (with Manami Roy). DOI
Minimal models of rational elliptic curves with non-trivial torsion, Res. Number Theory 8 (2022), no. 1, Paper No. 4., 39 pp. DOI
A constructive proof of Masser’s Theorem, Contemp. Math., Vol 759, pp. 51-61, 2020. DOI
Minimal models of rational elliptic curves with non-trivial torsion, Ph.D. Thesis - Purdue University, 2018, 372 pp., ProQuest LLC, Ann Arbor, MI.
Expository publications
(w. Ranthony A.C. Edmonds, Roberto Soto) Book chapter in Math Alliance: Investing in Tomorrow Today. Count Me In: Community and Belonging in Mathematics by Della Dumbaugh and Deanna Haunsperger, MAA Press, 2022.