Santiago Arango-Piñeros

 

(he/him/his)

santiago.arango.pineros@gmail.com

santiago.arango@emory.edu

Office: MSC W431

CV

I am a 5th year PhD candidate in the mathematics department at Emory University, in Atlanta.

My advisors are David Zureick-Brown and John Voight.

My research interests lie broadly in number theory and arithmetic geometry.

Here are my arXiv papers, MathSciNet profile, and GitHub profile.

Activities

• I am organizing Emory's algebra and number theory seminar.
• I will be a project assistant for Abbey Bourdon's project on Modular curves and Galois representations at the Arithmetic geometry workshop at UNT (The application deadline is March 25).

Research Articles

Counting 5-isogenies of elliptic curves over the rationals,
with Changho Han, Oana Padurariu, and Sun Woo Park.
(pdf, code)

Bounds for the relative class number problem for function fields,
with María Chara, Asimina S. Hamakiotes, Kiran S. Kedlaya, and Gustavo Rama.
(arXiv 2412.12467, code)

Galois groups of low dimensional abelian varieties over finite fields,
with Sam Frengley and Sameera Vemulapalli.
(arXiv 2412.03358, code)

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.
(arXiv 2306.02237, code)

Mertens' theorem for Chebotarev sets,
with Daniel Keliher and Chris Keyes.
International Journal of Number Theory 18 (2022), no. 8, 1823-1842.
(MR 4439576, arXiv 2103.14747)

The global field Euler function,
with Juan Diego Rojas.
Research in the Mathematical Sciences 7 (2020), no. 3, Paper No. 19, 21 pp.
(MR 4123394, arXiv 2005.04521)

In preparation

• Generalized Fermat equations and stacky curves,
  my PhD thesis.

Teaching and Mentoring

• Instructor of record for Math 111: Calculus 1, at Emory University. (Fall 2022 and 2023)
  • Here is a sample test (with my solution) that I helped design.
  • Here is a sample of the personal notes I wrote to prepare for my lectures. I shared these with my students as well.
• I was a Study Group Leader at the Arizona Winter School 2024.
• I was a Problem Set Leader at the Preliminary Arizona Winter School course on Abelian varieties over finite fields.
  • Here are the problem sets I helped create: PSET0, PSET1, PSET2, PSET3, PSET4, PSET4, PSET5, PSET6
• TWOPLES directed reading program.
  • Fall 2023: I mentored Sergio Maciel. We read about sheaf cohomology, mainly following Vakil's book and Hartshorne.
  • Fall 2020: I mentored Leonardo Méndez and Camilo Martinez. We read about algebraic number theory, following Milne's notes.
• Here is a note that LATHISMS wrote about me for Hispanic Heritage Month.

(hits since August/03/2024)