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

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

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.

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.

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)

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.