Saraí Hernández-Torres
Investigadora Asociada C
Instituto de Matemáticas, UNAM
email: saraiht
[AT] im.unam.mx
I am a tenure-track researcher in the Instituto de Matemáticas at the National Autonomous University of Mexico (UNAM) in Ciudad Universitaria, Mexico City.
Previously, I was a postdoctoral fellow at the Technion – Israel Institute of Technology. My hosts were Eviatar Procaccia and Ron Rosenthal. I obtained my Ph.D. with the probability group in the Department of Mathematics at the University of British Columbia (UBC). I worked under the supervision of Omer Angel and Martin Barlow. Before that, I completed my M.Sc. in Mathematics at UBC and my B.Sc. in Mathematics at the Universidad de Guanajuato / CIMAT in Mexico. More details on my academic background and activities are available on my CV.
I am interested in discrete probability. I study stochastic models defined over combinatorial structures, such as random walks, random trees, and competitive growth processes. My work describes the large-scale behaviour of discrete random processes and their rigorous connections to continuous models through the scaling limit.
Recent and upcoming events
- January 13-17, 2025. The changing of times: a conference in honour of María Emilia Caballero. Merida, Mexico.
- January 23-24, 2025. Connections Workshop: Probability and Statistics of Discrete Structures. SLMath, Berkeley, USA.
- February 21, 2025. Seminario del Departamento de Matemáticas. ITAM, CDMX, Mexico.
- February 25-27, 2025. Workshop on Probability and Machine Learning. CIMAT, Guanajuato, Mexico.
- March 20, 2025. Duke Probability Seminar. Duke University, Durham, NC, USA.
- April 3, 2025. Coloquio de Profesores. CINVESTAV, CDMX, Mexico.
I'm one of the organizers for:
-
Seminario de Probabilidad y Procesos Estocásticos.
UNAM, Mexico. Together with Laura Eslava and Liliana Peralta. -
Red de Mujeres Latinoamericanas en Probabilidad y Estadística: Aleatorias y Normales.
Together with Laura Eslava, Alejandra Fonseca-Morales and Lizbeth Peñaloza. -
Seminar: Random walks and Hecke algebras.
Instituto de Matemáticas, UNAM. Together with José Simental. -
Workshop: Mixtures of probability and geometry.
Casa Matemática Oaxaca (CMO). Together with Noé Bárcenas, Raquel Perales y Ron Rosenthal.
Research
Below there is a list of research papers, a list of talks with videos available online, and other writing.
Papers
Papers are listed in reverse chronological order by appearance on the arXiv. See also publication list on the arXiv.
Sharp one-point estimates and Minkowski content for the scaling limit of three-dimensional loop-erased random walk
With Xinyi Li and Daisuke Shiraishi
Preprint, arXiv:2403.07256.
Distance-dependent chase-escape on trees
With Matthew Junge, Naina Ray* and Nidhi Ray*
New Zealand Journal of Mathematics, 2024, Vol. 55, 31–41.
The chemical distance in random interlacements in the low-intensity regime
With Eviatar B. Procaccia and Ron Rosenthal
Communications in Mathematical Physics, 2023, Vol. 400, 1697–1737.
Scaling limits of the three-dimensional uniform spanning tree and the associated random walk
With Omer Angel, David Croydon, and Daisuke Shiraishi
The Annals of Probability, 2021, Vol. 49, No. 6, 3032–3105.
The number of spanning clusters of the uniform spanning tree in three dimensions
With Omer Angel, David Croydon, and Daisuke Shiraishi
Advanced Studies in Pure Mathematics, 2021: 403-414 (2021)
(Stochastic Analysis, Random Fields and Integrable Probability — Fukuoka 2019. Vol. 87).
Chase-escape with death on trees
With Erin Beckman, Keisha Cook, Nicole Eikmeier, and Matthew Junge
The Annals of Probability, 2021, Vol. 49, No. 5, 2530-2547.
Survey articles
Crossing bridges between percolation models and Bienaymé-Galton-Watson trees
With Airam Blancas and María Clara Fittipaldi
XIV Symposium on Probability and Stochastic Processes, to appear.
Crossing bridges between percolation models and Bienaymé-Galton-Watson trees
With Airam Blancas and María Clara Fittipaldi
XIV Symposium on Probability and Stochastic Processes, to appear.
Distance-dependent chase-escape on trees
With Matthew Junge, Naina Ray* and Nidhi Ray*
New Zealand Journal of Mathematics, 2024, Vol. 55, 31–41.
The chemical distance in random interlacements in the low-intensity regime
With Eviatar B. Procaccia and Ron Rosenthal
Communications in Mathematical Physics, 2023, Vol. 400, 1697–1737.
Scaling limits of the three-dimensional uniform spanning tree and the associated random walk
With Omer Angel, David Croydon, and Daisuke Shiraishi
The Annals of Probability, 2021, Vol. 49, No. 6, 3032–3105.
The number of spanning clusters of the uniform spanning tree in three dimensions
With Omer Angel, David Croydon, and Daisuke Shiraishi
Advanced Studies in Pure Mathematics, 2021: 403-414 (2021)
(Stochastic Analysis, Random Fields and Integrable Probability — Fukuoka 2019. Vol. 87).
Chase-escape with death on trees
With Erin Beckman, Keisha Cook, Nicole Eikmeier, and Matthew Junge
The Annals of Probability, 2021, Vol. 49, No. 5, 2530-2547.
Sharp one-point estimates and Minkowski content for the scaling limit of three-dimensional loop-erased random walk
With Xinyi Li and Daisuke Shiraishi
Preprint, arXiv:2403.07256.
Coauthors:
Omer Angel. Erin Beckman. Airam Blancas. Keisha Cook. David Croydon. Nicole Eikmeier. María Clara Fittipaldi. Matthew Junge. Xinyi Li. Eviatar B. Procaccia. Naina Ray*. Nidhi Ray*. Ron Rosenthal. Daisuke Shiraishi. (* highlights high school or undergraduate students.)
Talks
Videos of recorded talks
Minkowski content of the scaling limit of 3D loop-erased random walk.
Institute for Pure & Applied Mathematics (IPAM). May 2024.
Generalized chase-escape models and weighted Catalan numbers.
BIRS workshop: Analytic and Probabilistic Combinatorics. November 2022.
Three-dimensional uniform spanning trees.
Joint Israeli Probability Seminar. January 2021.
Scaling limits of uniform spanning trees in three dimensions.
UBC Probability Seminar. September 2020.
Un tour alrededor de los árboles generadores uniformes.
Coloquio Interinstitucional de Matemáticas (UDG-UNISON-UAGro). Diciembre 2023.
Caminando al azar entre fractales.
Día Internacional de la Mujer y la Niña en la Ciencia. Febrero 2023.
De un volado a la evolución de Schramm-Loewner.
Hablando de Matemáticas, IM-UNAM. Septiembre 2022.
Coloquio de Orientación Matemática, Ciencias TV. Agosto 2022.
Acercándose a las caminatas aleatorias.
Seminario Virtual de Matemáticas, Universidad de Colima. Febrero 2022.
Espacios métricos generados por caminatas aleatorias.
Quinta Reunión de Matemáticos Mexicanos en el Mundo. Diciembre 2021.
Atrápame si puedes: un sistema de partículas interactivas.
Coloquio de ex-estudiantes CIMAT-DEMAT. Febrero 2021.
La geometría de los fenómenos críticos.
Coloquio Oaxaqueño de Matemáticas. Octubre 2020.
David Croydon: Scaling limits of the two- and three-dimensional USTs.
Oxford Discrete Mathematics and Probability Seminar. October 2020.
Other writing
A macroscopic view of two discrete random models
PhD thesis. Supervisors: Omer Angel and Martin Barlow.
UBC library SlidesIntroducción a los espacios de Bergman (Introduction to Bergman spaces).
Undergraduate thesis. Supervisor: Fernando Galaz Fontes.
PDFTeaching
My teaching is guided by Federico Ardila's axioms.
Axiom 1. Mathematical potential is equally present among different groups, irrespective of geographic, demographic, and economic boundaries.
Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
Axiom 4. Every student deserves to be treated with dignity and respect.
-Axioms proposed by Federico Ardila on his AMS Notices article
"Todos Cuentan: Cultivating Diversity in Combinatorics".
Probabilidad en Estructuras Discretas
Posgrado en Ciencias Matemáticas, UNAM
Facultad de Ciencias, UNAM
Probabilidad I
- 2024. January - June (Term 2024-II)
- 2022. August - December (Term 2023-I)
Probabilidad II
- 2024. August - December (Term 2025-I)
- 2023. January - June (Term 2023-II)
Procesos Estocásticos I
- 2023. August - December (Term 2024-I)
Seminario de Probabilidad: Probabilidad en Estructuras Discretas
- 2024. January - June (Term 2024-II)
University of British Columbia
MATH 100:701 (Differential Calculus with Applications to Physical Sciences and Engineering)
Recitation instructor
- 2019. September - December (Winter Term 1)
MATH 180 (Differential Calculus with Physical Applications)
Recitation instructor
- 2018. September - December (Winter Term 1)
MATH 100:106 (Differential Calculus with Applications to Physical Sciences and Engineering)
Instructor
- 2017. September - December (Winter Term 1)
Teoremas de la forma en probabilidad (Shape theorems in probability).
Summer school: Geometría Prohibida . Universidad Autónoma de San Luis Potosí, July 2022.
PDFGroup
Masters
-
Jorge Emiliano Álvarez Gil Leyva.
Posgrado en Ciencias Matemáticas, UNAM
Under academic mentorship (tutoría académica).
Bachelor's
-
Jorge David López Maldonado.
Facultad de Ciencias, UNAM -
Jorge Emiliano Álvarez Gil Leyva.
Facultad de Ciencias, UNAM
Tesis: Simulación de la Evolución de Schramm-Loewner. (Under review) -
Juan Pablo Rodríguez Villagrán.
Facultad de Ciencias, UNAM
Tesis: Percolación FK en gráficas de Cayley. (Under review)
Bachelor's
-
Jeremai Reyes Garay.
Facultad de Ciencias, UNAM. May 3, 2024.
Bachelor's honours thesis: Exponente de crecimiento en caminatas aleatorias con ciclos borrados. -
Jorge Salvador Martínez Villafan.
Facultad de Ciencias, UNAM. February 1, 2024.
Co-director: Laura Eslava.
Bachelor's honours thesis: Redes de investigación en probabilidad y estadística en Latinoamérica:
desarrollo y análisis estadístico de una base de datos con perspectiva de género.
Links
This last section includes miscellaneous links to media appearances and some past events where I contributed to their organization.
Media
- October 18, 2024.
I was interviewed by journalist Eirinet Gómez for the Mexican newspaper La Jornada:
"Quien se dedica a los números tiene un mundo hermoso y fascinante por delante" (In Spanish).
- October 3, 2024.
I am deeply honored to have received a 2024 L’Oréal-UNESCO-AMC For Women in Science Fellowship at the national level (Beca para Mujeres en la Ciencia L’Oréal-UNESCO-AMC).
* Here is a note (in Spanish) written by Darío Alatorre for the Instituto de Matemáticas webpage. It was also featured in Gaceta UNAM and summarized in English for Global UNAM Weekly News.
* Wired Magazine published a note in Spanish introducing all the researchers recognized by L’Oréal-UNESCO-AMC in 2024, including both senior and young awardees. The article highlights the work, challenges, and achievements of the senior winners.
* This video showcases all the young researchers who were awarded the L’Oréal-UNESCO-AMC fellowship in 2024.
* The Communication Department of the Instituto de Matemáticas also created a video where I talk about the process of obtaining the fellowship while enjoying several cups of coffee around the institute.
Past events
Joint Summer School SLP-CDMX - Escuelas Conjuntas SLP-CDMX
The Escuelas Conjuntas SLP-CDMX de Dinámica, Combinatoria y Probabilidad is a joint effort between UNAM and the Instituto de Física at the Universidad Autónoma de San Luis Potosí, through the Dinámica Potosina research group. This series of summer schools offers mini-courses and conferences on symbolic dynamics, combinatorics, and discrete probability, with a focus on exploring the connections between these three areas. In addition to math, the Escuelas Conjuntas also feature sessions dedicated to personal development. The primary audience includes advanced undergraduate and graduate students.
There have been two editions of the Escuelas Conjuntas SLP-CDMX, and we look forward to continuing this series of events in the future. Stay tuned for more updates!
The Segunda Escuela Conjunta SLP-CDMX was hosted at the Universidad Autónoma de San Luis Potosí. In this edition, the mini-courses were taught by Raimundo Briceño, Jennifer Jones-Baro, Sandra Palau, and Gourab Ray. The Instituto de Matemáticas webpage has an overview of the summer school (in Spanish) and shows some pictures.
- Notes from the mini-course 'Random walks, electrical networks and circle packing' by Gourab Ray.
- Radio UASLP interviewed Felipe García-Ramos, Raimundo Briceño, and me to talk about the summer school at the Noticiario Conexión Universitaria (around minute 20).
The Primera Escuela Conjunta SLP-CDMX was hosted at the Instituto de Matemáticas, UNAM. In this first edition, the mini-courses were taught by Miklós Bona, María Isabel Cortez, and María Clara Fittipaldi. The Instituto de Matemáticas webpage has a brief account of the event (in Spanish) and some pictures.
- Notes from the mini-course 'Promediabilidad y medidas invariantes' by María Isabel Cortez.
- Notes from the mini-course 'Distribuciones cuasi-estacionarias para cadenas de Markov' by María Clara Fittipaldi.
PIMS-CRM Summer School in Probability and OOPS
- 2020, 2021: the Online Open Probability School (OOPS) presented several mini-courses throughout the summer. Recordings are available in BIRS and YouTube.
- 2017: UBC hosted the PIMS-CRM Summer School in Probability. Marek Biskup and Hugo Duminil-Copin taught one-month long courses. Sandra Cerrai, Christina Goldschmidt, and Martin Hairer taught mini-courses. All these lectures were taped and videos are posted on MathTube.
Fest
When I was younger, we occasionally organized small conferences among friends, covering various areas of mathematics. These events provided a glimpse into the speakers' work, and we all enjoyed talking about mathematics between friends. These events where called fest, and the main organizers were Malors Espinosa Lara and our admired late friend Mario Díaz.
I was part of the organizing committee of the following fests:
- 2020: The FEST 2020 took place online, where we celebrated mathematics in Spanish.
- 2016: the Sarai Fest -1 was held as my 25th birthday party.
I was also a speaker at the Francisco Fest -1 in March 2013 and the Malors Fest -1 in January 2014.