About me

I am a tenure-track assistant professor at Montana State University. I completed my Ph.D. in Summer 2021 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 the University of Costa Rica and worked for the research department of the 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".


What I Do

I work on number theory.

I am interested in arithmetic statistics.



Fall 2020 - Spring 2021

University Teaching Assistantship

Critical History of Mathematics: Redefining What Is and Who Does Mathematics

I was awarded another fellowship from the University of Utah. I will be designing content for MATH 3010 Topics in the History of Mathematics during Fall 2020 and you can find more details about it here.

Fall 2019 - Spring 2020

University Teaching Assistantship

Building an Inclusive Math Learning Environment to Support Student Retention in STEM

I was awarded a fellowship from the University of Utah. I will not be teaching this academic year, but I will be working on my project.


Spring 2021

Topics in the History of Mathematics

MATH 3010

Summer 2020

Introduction to Number Theory

MATH 4400

Summer 2019

Discrete Mathematics

MATH 2200

Spring 2018

Business Algebra

MATH 1090, online

Fall 2017

Calculus II

MATH 1220

Spring 2017

Business Calculus

MATH 1100

Fall 2016

Business Calculus

MATH 1100

Other Teaching

Summer 2020

Math Instructor Training Workshop


Fall 2019

Reading group


Organizer and facilitator for reading group on number theory with four undergraduate students. Weekly meetings to discuss assigned exercises and readings.

Summer 2019

RTG Pre-REU in Number Theory

Teaching assistant

Summer 2019

Math Instructor Training Workshop


Spring 2019

Special Projects Course


I supervised an undergraduate student's graduation project through weekly meetings. The project was on computational aspects of elliptic curve cryptography.

Spring 2019

MATH 1310 Engineering Calculus I

Teaching assistant

Summer 2018

Eccles Beginnings Summer Bridge Program


Service and Outreach

One of my goals is to build a more inclusive and equitable math community. As a grad student, I have been involved in several activities like the ones listed below to achieve this goal.

Association for Women+ in Mathematics
at the University of Costa Rica



Equity, Diversity, and Inclusion Committee

Committee member

2020 - 2021

Association for Women in Mathematics
University of Utah Student Chapter

Outreach Chair
Speaker Series Co-chair

2020 - 2021
2019 - 2020
2019 - 2020
2018 - 2020

BRIDGES Conference


2019 - 2021

SACNAS Conference


2019 - 2021

GSAC Peer Mentoring Program
for Incoming Graduate Students


2019 - 2020

Latinos in Action

Academic Co-chair

2015 - 2020

GSAC Retention, Promotion, and Tenure

Committee member

2018 - 2019


PANTS (Patrikis' Algebraic Number Theory Students) Seminar

Spring 2020 Elliptic Curves
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
Fall 2019 Fourier Analysis on Number Fields
August 26 Kevin Introduction and Riemann Zeta Function
September 9
September 16
Dylan Chapter 4, Structure of Arithmetic Fields
September 23
September 30
JJ Chapter 5, Adeles, Ideles and the Class Groups
October 14 Hanlin Chapter 6, A Quick Tour of Class Field Theory
October 21 Matthew Chapter 1, Topological Groups
October 28
November 4
Petar Chapter 2, Some Representation Theory
November 11 Christian Chapter 3, Duality for Locally Compact Abelian Groups
November 18
November 25
Kevin Chapter 7, Tate's Thesis and Applications
Spring 2019 Modular Forms


I was the organizer of BAGELS (B(e creative!) Algebraic Geometry Eating and Learning Seminar) during the academic year 2018-2019. The new organizer is José Ignacio Yáñez.


Where to find me

Montana State University
Department of Mathematical Sciences
Wilson Hall Room 2-233
Bozeman, MT 59715 US

Email Me At

allechar [dot] serranolopez [at] montana [dot] edu