Allechar Serrano López

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

I am a fourth-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".


Teaching


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

Outreach and Other Interests


I am very passionate about the promotion of women in mathematics and the participation of minorities in science.

Summer Mathematics Program for High School Students

I was a counselor for this four-week program in number theory for high school students in 2018 and 2017.



Latinos in Action at the University of Utah

I have been a member of LIA University of Utah Chapter and served as Academic co-Chair since 2015.


Eccles Beginnings
Summer Bridge Program

I was the instructor of the math portion of this four-week program. It consisted of a review of high school math and it was aimed at underrepresented groups.


AWM Research Symposium

The symposium will be held on April 6-7, 2019 at Rice University.


Infinite Possibilities Workshop

This is a conference for women of color in mathematics. I attended in April, 2018.

Algebraic Geometry Student Seminar


The Algebraic Geometry Student Seminar meets on Thursday, from 10:35 a.m. to 11:30 a.m., in 102 JFB. If you have any questions, please contact Allechar.


Schedule


August 23


Complements on surfaces and BAB
Speaker: Stefano Filipazzi

Abstract: Recently Birkar proved the famous BAB conjecture. A main tool in the proof is the theory of complements. In this talk, I will overview the notions involved in the formulation of the BAB conjecture and introduce what complements are. Then, I will focus on the case of surfaces, and highlight how complements are used in the proof of the conjecture.

Reference: https://www.dpmms.cam.ac.uk/~cb496/surfcomp.pdf


September 6


Matrix factorizations and Orlov's theorem
Speaker: Marin Petkovic

Abstract: The purpose of this talk is to give a brief introduction to matrix factorizations. We show some examples and sketch the construction of the triangulated category of curved dg-sheaves. We also state Orlov's theorem on hypersurfaces and give examples.



September 20


Torelli theorems
Speaker: Christian Klevdal

Abstract: How much information can you determine about an algebraic variety from its cohomology? In certain cases, quite a bit! In this talk, we will prove the classical Torelli theorem which states that a complex algebraic curve is determined up to isomorphism by its second cohomology. A key player is the Jacobian, which I will introduce along the way. If time permits, we will discuss generalizations of the Torelli theorem to complex K3 surfaces, hyperkahler varieties and possibly generalizations to other number fields. I'll try to keep the prerequisites for this talk low, basic knowledge of complex algebraic curves should be plenty for the bulk of the talk.



October 4


The average rank of elliptic curves
Speaker: Allechar Serrano López

Abstract: In 1979, Goldfeld conjectured that the average rank of elliptic curves over the rational numbers is 1/2. Theoretical results towards boundedness of the average rank were proven, assuming the Generalized Riemann Hypothesis and the Birch and Swinnerton-Dyer conjecture. However, the data did not support these results. In a joint work with Arul Shankar, Manjul Bhargava provided an unconditional proof of boundedness by studying the n-Selmer group. In this talk, I will give an outline of their proof.



October 18


Spectral sequences
Speaker: Matteo Altavilla

Abstract: Spectral sequences were developed in the 60s and since then they’ve become a central tool in algebra and geometry. We will review the definition and basic constructions, and the philosophy behind their application. I’ll then list a few examples and work out a very simple one in detail.



November 1


Speaker: Daniel Smolkin



November 15


Speaker: José Yañez



November 29


Speaker: Franco Rota


August 30


Strange duality for K3 surfaces via wall-hitting
Speaker: Huachen Chen

Abstract: We will first introduce a problem known as strange duality for moduli of sheaves on surfaces, then bring in moduli of complexes and wall-crossing, and explain how they can help to understand strange dualityfor K3 surfaces.






September 13


Minimal log discrepancies
Speaker: Joaquín Moraga

Abstract: We will introduce the minimal log discrepancy, which is an invariant to measure the singularities of an algebraic variety. This object is a central invariant in the study of birational geometry. Then we will discuss some conjectures and known results.



September 27


First hmology group of a closed Riemann surface
Speaker: Erjuan Fu

Abstract: In "primitive cohomology and the tube mapping", Schnell constructs the generators of the rational first homology group of a closed Riemann surface using all invariant vanishing cycles under the monodromy action. We will construct the generators using the tube classes over only finitely many vanishing cycles. We will see that the generator we constructed is the same as the difference of two cones over the same vanishing cycles, that is to say, we glue two thimbles with the same boundary along the same boundary.





October 11


Fall Break
(no seminar)













October 25


Frobenius Seshadri Constants
Speaker: Yen-An Chen

Abstract: In this talk, I will introduce a Frobenius variant of Seshadri constant defined by M. Mustata and K. Schwede, and then show that the lower bounds imply the global generation or very ampleness of the corresponding adjoint line bundle (in positive characteristic).



November 8


Speaker: You-Cheng Chou



November 22


Thanksgiving Break (no seminar)



December 6


Speaker: Seungsu Lee


Past seminars


Spring 2018
Fall 2017
Spring 2017
Fall 2016
Spring 2016
Fall 2015