Mathematics Sin Fronteras

Bilingual Math Outreach
Brown University
Mar 10-May 26, 2021

What is Mathematics Sin Fronteras?

Mathematics Sin Fronteras (MSF) is a Pan-American (virtual) bilingual (English-Spanish) extracurricular weekly math outreach lecture series spread over a 3-month period. The goal of MSF is to introduce (1st and 2nd year) undergraduate students from diverse backgrounds across South, Central and North America to mathematics and its applications in an engaging and inclusive way that complements the usual university/college math curriculum. The aim is also to promote cross-cultural communication by connecting students across the Americas with a passion for math, and provide them with the opportunity to interact with leading researchers in their fields in a bilingual environment. Underrepresented and economically disadvantaged groups are particularly encouraged to apply.

Organizing committee:

Maria Isabel Cortez (Pontificia Universidad Católica de Chile)
Alicia Dickenstein (University of Buenos Aires and CONICET – Argentina)
Gabriela Ovando (Universidad Nacional de Rosario and CONICET, Argentina)
Andrea Vera-Gajardo (Instituto de Mathematicas of Universidad de Valparaiso, Chile)
Alicia Prieto Langarica (Youngstown State University, Ohio, US)
Kavita Ramanan (Brown University, Rhode Island, US)

This conference is an initiative of the Math CoOp at Brown University, with support from the Division of Applied Math at Brown University, the National Science Foundation's (NSF's) "Mathematical Science Institutes Diversity Initiative" (MSIDI) and the Society for Industrial and Applied Math (SIAM). In particular, we would like to gratefully acknowledge financial support from MSIDI and SIAM.


Brown Logo

Brown University Department of Applied Mathematics


Society for Industrial and Applied Mathematics (SIAM)

NSF Logo

NSF Mathematical Science Institutes Diversity Initiative (MSIDI)

Application Form

Applications for the third and fourth minicourses are now being accepted. Applications submitted by April 8th will be given full consideration. Students who apply are expected to be able to attend all 6 lectures on Zoom (see schedule), and thus should have good internet access to be able to participate actively. Each lecture will be held on a Wednesday from 15--16:30 NYC time (-4 GMT).

The lecture series is targeted towards first and second year undergraduate students in South, Central and North America, and open to all, regardless of gender identity or background. Underrepresented and economically disadvantaged groups are particularly encouraged to apply.
If you have any further questions, email

Speakers and Schedule

The series consists of weekly lectures from March 10--May 26, 2021. Each lecture will be held on a Wednesday from 15:00-16:30 Eastern Time (ET), and will be conducted virtually via Zoom. All four lecturers are bilingual, and can ask and answer questions in both English and Spanish. Mini Courses 1 and 3 will be delivered in English and Mini Courses 2 and 4 will be delivered in Spanish. But, in all cases, slides of the lectures and (optional) homework assignments will be available in both English and Spanish. Thus, students need be fluent in only one language, and not both.

Details of the schedule, speakers and lectures are given below, and are also available in the following pdf file.

Mini Course 1

Re-Imagining the World Through Linear Algebra
Dates and Time: Mar 10, Mar 17, Mar 24, each Wednesday 15-16:30 hours Eastern Time

Note that on Mar 10, this will correspond to 15-16:30 hours Eastern Standard Time (20--21:30 GMT)
But from Mar 17 onwards, this will correspond to 15--16:30 Eastern Daylight Time (19--20:30 GMT)

Language: In English, with slides in Spanish
Malena Espanol

Abstract: In these lectures we will explore basic linear algebra concepts that are used in the processing of digital images. We will start by seeing how images are represented in computers and TV monitors. Then, we will explore how we can use linear algebra to deblur, denoise, and compress digital images.

Biography: Dr. Malena I. Espanol is an Argentine-American applied mathematician, currently an Assistant Professor at the School of Mathematical and Statistical Sciences at Arizona State University (ASU). She earned a B.S. in mathematics from the University of Buenos Aires, Argentina, and M.S. and Ph.D. in mathematics from Tufts University, USA. After graduation, Dr. Espanol was a postdoctoral scholar at the California Institute of Technology. In 2012, she started a faculty position at The University of Akron where she stayed until 2019 when she joined ASU. Dr. Espanol works on the development, analysis, and application of mathematical models and numerical methods for solving problems arising in science and engineering, with a focus on problems related to materials science, image processing, and medical applications. Dr. Espanol has given hundreds of presentations at national and international seminars, workshops, and conferences. In 2016, she helped create a research community for Women in Math of Materials by organizing networking luncheons, workshops, and special sessions at the main conferences in the area. Dr. Espanol has supervised more than 30 undergraduate and graduate students in research projects and has been a mentor for several more as part of the AWM mentor program and the Math Alliance.
Teaching Assistant (TA) Victoria Uribe
Victoria Uribe is a Mexican-American PhD student in Applied Mathematics at Arizona State University. Her current research interests include inverse problems, numerical linear algebra, and machine learning.

Mini Course 2

Geometric flows: Deforming geometry in time
Dates and Time: Mar 31, Apr 7, Apr 14, each Wednesday 15:00-16:30 Eastern Daylight Time (19--20:30 GMT)
Language: In Spanish, with slides in English
Mariel Saez

Abstract: In this course I will describe what is a geometric flow and how they have been used to address problems in several areas of mathematics. In the last two lectures I will concentrate on the particular case of "Curve shortening flow" and connect it with the main ideas in the field.

Biography: Mariel Saez received her Ph.D. in 2005 from Stanford University, under the supervision of Rafe Mazzeo. Between 2005 and 2008, she held a postdoctoral position at Max Plack instute for Gravitational Physics (Albert Eintein's institute) in Gerhard Huisken's group and currently she is Associate Professor at the mathematics department of Pontificia Universidad Católica de Chile. Her research interests are geometric analysis, with an emphasis on geometric flows and conformal geometry.
Teaching Assistant (TA) Sebastián Muñoz
Sebastián Muñoz is a Chilean Master's student in Mathematics at Pontificia Universidad Católica de Chile. His current research interests are geometric flows, in particular, the study of the existence and the singularities of the harmonic map heat flow.

Mini Course 3

The isoperimetric problem
Dates and Time: Apr 21, Apr 28, May 5, each Wednesday 15:00-16:30 Eastern Daylight Time (19--20:30 GMT)
Language: In English, with slides in Spanish
Tatiana Toro

Abstract: The isoperimetric problem dates back to the ancient Greeks. It can be stated as follows: Among all closed curves in the plane of fixed length, which curve (if any) maximizes the area of its enclosed region? Although it is easy to obtain a result intuitively, the first mathematically rigorous proof was only obtained only in the 19th century. In this series of lectures we will explore different approaches to this problem. This will give us the opportunity to study some geometry as well as some aspects of the Fourier transform.The isoperimetric problem opens the door to many interesting questions currently under study in an area of mathematics called Geometric Measure Theory. At the end of the course we will discuss some of them.

Biography: Professor Toro was born in Bogota, Colombia. Both of her parents were the first in their families to attend college. She received her B.S. from the Universidad Nacional de Colombia in Bogotá and her Ph.D. from Stanford University. She has been a member of the Institute for Advanced Study in Princeton, of the Mathematical Sciences Research Institute (MSRI) in Berkeley and a fellow at the Radcliffe Institute for Advanced Study. Her awards include a Guggenheim Foundation Fellowship, two Simons Foundation Fellowships, and the Landolt Distinguished Graduate Mentor Award, from the University of Washington. She is a Fellow of the AMS, and a “Miembro Correspondiente de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales”. In 2020 she was elected as a Member of the American Academy of Arts and Sciences, and she received the Blackwell-Tapia Award.
Teaching Assistant (TA) Ignacio Tejeda
Ignacio Tejeda is a PhD student in Mathematics at the University of Washington. His home country is Chile, where he earned a B.S and a M.S in Mathematics from Universidad Católica de Chile, before moving to the United States in September, 2020. His mathematical interests include differential equations, geometric measure theory and differential geometry. In his free time, he enjoys playing the cello and joining classical music ensembles.

Mini Course 4

An introduction to error correcting codes
Dates and Time: May 12, May 19, May 26, each Wednesday 15:00-16:30 Eastern Daylight Time (19--20:30 GMT)
Language: In Spanish, with slides in English
María Chara

Abstract: Error-correcting codes play an important role in many areas of science and engineering, as they safeguard the integrity of data against the adverse effects of noise in communication and storage. On the most basic level, good error-correcting codes are able to both transmit data efficiently and correct a large number of errors relative to their length. In this short course we will study the basic notions of the theory of error-correcting codes. We will see some classical examples of linear codes over finite fields such as the Hamming codes, Reed-Solomon codes, cyclic codes and BCH codes. We will study classical bounds for the parameters of these codes and their detection and error-correction capabilities.

Biography: María Chara is Associate Professor at Universidad Nacional del Litoral and Assistant Researcher at the National Council for Scientific and Technical Research in Argentina (Conicet). She obtained her PhD in 2012 at Universidad Nacional del Litoral, under the supervision of Dr. Roberto Miatello (UNC) and Dr. Ricardo Toledano (UNL), working on towers of function fields. Since then, she has been working not only on the theoretical aspects of the theory of function fields over finite fields but also on its applications to coding theory.
Teaching Assistant (TA) Saraí Hernández-Torres
Saraí Hernández-Torres is a postdoctoral fellow at the Technion – Israel Institute of Technology. She received her B.S. in mathematics from the University of Guanajuato, and in 2020, she obtained her Ph.D. in mathematics from The University of British Columbia. Her research interests are in probability theory and combinatorics.

Lecture Materials for Each Mini-Course

Mini Course 1

Mini Course 2

Mini Course 3

Other References

Mini Course 4

Other Materials


Will be updated after March 8, 2021.


If you have any questions, please e-mail