Santiago Arango-Piñeros
Curriculum Vitae
- Department of Mathematics, UMass Amherst, LGRT 1238, Amherst, Massachusetts, USA
santiago.arango.pineros@gmail.com,sarangopiner@umass.edu- https://sarangop1728.github.io
- arXiv, MathSciNet, GitHub
- PDF version
Appointments
- 2025–present
- UMass Amherst
Visiting Assistant Professor (Postdoc)
Education
- 2025
- Ph.D. Mathematics, Emory University
Advised by David Zureick-Brown and John Voight. - 2019
- M.S. Mathematics, IMPA, Rio de Janeiro, Brazil
- 2017
- B.S. Mathematics, Universidad de los Andes, Bogotá, Colombia
- 2017
- B.S. Environmental Engineering, Universidad de los Andes, Bogotá, Colombia
Research interests
- Broad
- Number theory and arithmetic algebraic geometry.
- Specific
- Elliptic curves and abelian varieties, Galois representations, Honda–Tate theory, low degree points on curves, modular curves, generalized Fermat equations, stacky curves, arithmetic statistics, computational and algorithmic aspects.
Articles
- Appendix to: On \(p\)-adic solubility of \(Ax^{\ell} + By^{m} + Cz^{n} = 0\),
with Christopher Keyes and Andrew Kobin. - Counting number fields of fixed degree by their smallest defining polynomial,
with Fabian Gundlach, Robert J. Lemke Oliver, Kevin J. McGown, Will Sawin, Allechar Serrano López, Arul Shankar, and Ila Varma. - Counting primitive integral solutions to spherical generalized Fermat equations.
Canadian Mathematical Bulletin FirstView (2026). - Fermat descent.
- Galois groups of simple abelian varieties over finite fields and exceptional Tate classes,
with Sam Frengley and Sameera Vemulapalli. - Counting 5-isogenies of elliptic curves over the rationals,
with Changho Han, Oana Padurariu, and Sun Woo Park. Journal of the London Mathematical Society 113 (2026), no. 5, e70572. - Bounds for the relative class number problem for function fields,
with María Chara, Asimina S. Hamakiotes, Kiran S. Kedlaya, and Gustavo Rama. Journal of Number Theory 278 (2026), 977–1010. - Galois groups of low dimensional abelian varieties over finite fields,
with Sam Frengley and Sameera Vemulapalli. To appear in Transactions of the American Mathematical Society. - Frobenius distributions of low dimensional abelian varieties over finite fields,
with Deewang Bhamidipati and Soumya Sankar. International Mathematics Research Notices 2024 (2024), no. 16, 11989–12020. - Mertens' theorem for Chebotarev sets,
with Daniel Keliher and Chris Keyes. International Journal of Number Theory 18 (2022), no. 8, 1823–1842. - The global field Euler function,
with Juan Diego Rojas. Research in the Mathematical Sciences 7 (2020), no. 3, Paper No. 19, 21 pp.
Teaching
UMass Amherst, Instructor of Record
- Fall 2026
- Math 714: Arithmetic of Elliptic Curves
- Fall 2026
- Math 132: Calculus II
- Spring 2026
- Math 411: Introduction to Abstract Algebra 1
- Fall 2025
- Math 411: Introduction to Abstract Algebra 1
Arizona Winter School
Emory University, Instructor of Record
- Fall 2023
- Math 111: Calculus I
- Fall 2022
- Math 111: Calculus I
Emory University, Teaching Assistant
- Spring 2022
- Math 116: Calculus for life sciences
- Fall 2021
- Math 221: Linear Algebra
Universidad de los Andes, Teaching Assistant
- Spring 2020
- Mate 1203: Cálculo Diferencial
- Fall 2019
- Mate 1203: Cálculo Diferencial
- Spring 2019
- Mate 1207: Cálculo Vectorial
Invited seminar talks
- 2025
- Harvard University, Number theory seminar
- 2025
- Wesleyan University, Algebra seminar
- 2025
- Amherst College, Five college number theory seminar
- 2025
- University of California San Diego, Number theory seminar
- 2024
- University of Illinois Chicago, Number theory seminar
- 2024
- Tufts University, Number theory seminar
- 2024
- Boston University, Algebra and number theory seminar
- 2024
- Brown University, Algebra seminar
- 2024
- Emory University, Algebra and number theory seminar
- 2024
- Amherst College, Five college number theory seminar
- 2024
- Dartmouth College, Algebra and number theory seminar
- 2024
- University of Georgia, Athens, Algebra and number theory seminar
- 2023
- University of South Carolina, Number theory seminar
Organization
Special sessions
- 2026
- Arithmetic Statistics of Rational Points and Number Fields,
AMS Spring Eastern Sectional Meeting, Boston College.
With Niven Achenjang and Sameera Vemulapalli. - 2024
- Explicit Computation with Stacks (MRC special session),
Joint Mathematics Meetings, San Francisco.
With Jonathan Love and Sameera Vemulapalli.
UMass Amherst
- 2025–present
- Five College Number Theory Seminar, co-organizer
Emory University
- 2024–2025
- Algebra and Number Theory Seminar, main organizer
- 2022–2024
- Graduate student algebra and number theory seminar, co-organizer
Referee work
Mathematische Zeitschrift, Proceedings of the American Mathematical Society, Rocky Mountain Journal of Mathematics, Sixteenth Algorithmic Number Theory Symposium.
Selected conference and workshop participation
- 2025
- Algebraic points on curves, ICERM, Providence, RI.
- 2024
- Nilpotent counting problems in arithmetic statistics, AIM, Pasadena, CA.
- 2024
- Number theory in the Americas 2, Casa Matemática Oaxaca, Oaxaca, México.
- 2024
- XVI Algorithmic Number Theory Symposium. MIT, Boston, MA.
- 2024
- The Mordell conjecture 100 years later. MIT, Boston, MA.
- 2024
- Hypergeometric motives in the LMFDB. MIT, Boston, MA.
- 2024
- Shimura curves in the LMFDB. Dartmouth, Hanover, NH.
- 2024
- Arizona Winter School: Abelian Varieties. Tucson, AZ.
- 2023
- PAlmetto Number Theory Series XXXVII. UGA, Athens, GA.
- 2023
- LuCaNT: LMFDB, Computation, and Number Theory. ICERM, Providence, RI.
- 2023
- MRC: Explicit computations with stacks. Buffalo, NY.
- 2023
- Conference in Arithmetic Statistics. CIRM, Marseille, France.
- 2023
- Spring school in Arithmetic Statistics. CIRM, Marseille, France.
- 2023
- Arizona Winter School: Unlikely Intersections. Tucson, AZ.
- 2023
- Introductory Workshop: Diophantine Geometry. MSRI, Berkeley, CA.
- 2023
- Connections Workshop: Diophantine Geometry. MSRI, Berkeley, CA.
- 2022
- PAlmetto Number Theory Series XXXV. U of SC, Columbia, SC.
- 2022
- AGNES: Summer school in higher dimensional moduli. Brown, Providence, RI.
- 2022
- PCMI: Number theory informed by computation. Park City, UT.
- 2022
- CTNT: Connecticut summer school in number theory. UCONN, Storrs, CT.
- 2022
- GAGS: Georgia Algebraic Geometry Symposium. Emory, Atlanta, GA.
- 2022
- Arizona Winter School: Automorphic forms beyond \(\mathrm{GL}_2\). Tucson, AZ.
- 2021
- PCMI: Inverse Galois Problem. Online.
Software and databases
- 2023
- \(L\)-functions and Modular Forms Database (LMFDB), https://www.lmfdb.org
I have made modest contributions. Most recently:- I developed the Zigzag pictures for the hypergeometric motives pages. See this random family.
- I updated the Newton polygon pictures for abelian varieties over finite fields, see this random isogeny class.
Skills
- Language
- Spanish (native speaker), English, Portuguese.
- Computer
- Python, Magma, SageMath.
Awards
- 2025
- Graduate Student Research Award, Emory University Math Department