Allechar Serrano López

University of Utah Mathematics Department
Email serrano at math dot utah dot edu
Office 328 JWB

I am a fifth-year graduate student at the University of Utah, supervised by Stefan Patrikis. I was born and raised in Costa Rica, where I completed bachelor's degrees in Mathematics and Economics at University of Costa Rica.

Before coming to Utah, I was an instructor at University of Costa Rica and worked for the research department of Central Bank of Costa Rica.

My last name is "Serrano López". It is composed of two words without a hyphen and it should be indexed by the letter "S".

My preferred pronouns are she/her/hers.


Fall 2019 and Spring 2020: I have received a fellowship from the University of Utah and I will not be teaching during this academic year. However, I will be working on my fellowship project Building an Inclusive Math Learning Environment to Support Student Retention in STEM.
Summer 2019: Math 2200, Discrete Math
                          TA for the RTG Pre-REU in Number Theory
                          Facilitator for the Math Instructor Training Workshop
Spring 2019: TA for Math 1310, Engineering Calculus I
Summer 2018: Counselor for the Summer Mathematics Program for High School Students
                          Instructor for Eccles Beginnings Summer Bridge Program
Spring 2018: Math 1090, Business Algebra Online
Fall 2017: Math 1220, Calculus II
Summer 2017: Counselor for the Summer Mathematics Program for High School Students
Spring 2017: Math 1100, Business Calculus
Fall 2016: Math 1100, Business Calculus
Spring 2016: TA for Math 1210, Calculus I
Fall 2015: TA for Math 2250, Differential Equations and Linear Algebra

Service and Other Interests

I am very passionate about the promotion of underrepresented groups in mathematics and STEM.

Association for Women in Mathematics, University of Utah Chapter (AWM)

I am Chair of the Outreach committee for our chapter, you can find some of our activities here. I am also co-organzining our Speaker Series and a conference.

Latinos in Action at the University of Utah

I have served as Academic Chair since 2015. You can learn more about our chapter here.


I am part of team that will be attending the SACNAS conference as part of a strategy to increase diversity in our graduate students.

Student Seminars

PANTS (Patrikis's Algebraic Number Theory Students) Seminar

I am co-organizing a student seminar in number theory. The seminar meets on Thursday from 4:00 p.m. until 5:30 p.m. in JWB 308. It is aimed at graduate students and advanced undergraduates.

During Spring 2020, we will work on elliptic curves following The Arithmetic of Elliptic Curves by Joseph H. Silverman. We will have talks and discuss exercises:

January 9 Organizational meeting
January 16 Allechar Chapter 3, The Geometry of Elliptic Curves
January 23 Chapter 3: 5, 8, 9, 22, 28
January 30 Hanlin Chapter 3, The Geometry of Elliptic Curves
February 6 Chapter 3: 15, 16, 18, 19, 24, 32
February 13 Departmental Colloquium: A gentle approach to crystalline cohomology
February 20 Christian Chapter 4, The Formal Group of an Elliptic Curve
February 27 AWM-RTG Colloquium: Isolated points on curves
March 5 Matthew Chapter 5, Elliptic Curves over Finite Fields
March 19 Chapter 5: 6, 10, 12, 14, 15
March 26 Brian Chapter 6, Elliptic Curves over the Complex Numbers
April 2
April 9 DCT Chapter 7 Elliptic Curves over Local Fields
April 16
April 23 Review of group cohomology and Chapter 8, Elliptic Curves over Global Fields

We also worked on Fourier Analysis on Number Fields by Dinakar Ramakrishnan and Robert J. Valenza. Here's a rough schedule of what we did during Fall 2019:

  • Kevin: Introduction and Riemann zeta function (8/26)
  • Dylan: Chapter 4, Structure of Arithmetic fields (9/9 and 9/16)
  • JJ: Chapter 5, Adeles, Ideles and the class groups (9/23 and 9/30)
  • Hanlin: Chapter 6, A quick tour of class field theory (10/14)
  • Matthew: Chapter 1, Topological groups (10/21)
  • Petar: Chapter 2, Some representation theory (10/28 and 11/4)
  • Christian: Chapter 3, Duality for locally compact abelian groups (11/11)
  • Kevin: Chapter 7, Tate's thesis and applications (11/18 and 11/25)

Number Theory Reading Group for Undergraduates

I am facilitating a number theory reading group for undergraduates. We meet on Tuesday from 2:00 p.m. until 3:00 p.m. in 323 LCB. We are working on elementary number theory.


I was the organizer of BAGELS (B(e creative!) Algebraic Geometry Eating and Learning Seminar) during the academic year 2018-2019. You can find more details here.

The organizer of BAGELS for the academic year 2019-2020 is José Ignacio Yáñez and this is the new seminar webpage.