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

I'm also one of the organizers for:

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.

Distance-dependent chase-escape on trees

With Matthew Junge, Naina Ray* and Nidhi Ray*

Preprint, arXiv:2209.09876.

The chemical distance in random interlacements in the low-intensity regime

With Eviatar B. Procaccia and Ron Rosenthal

Preprint, arXiv:2112.13390.

Scaling limits of the three-dimensional uniform spanning tree and the associated random walk

With Omer Angel, David Croydon, and Daisuke Shiraishi

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

Annals of Probability, 2021, Vol. 49, No. 5, 2530-2547.

Scaling limits of the three-dimensional uniform spanning tree and the associated random walk

With Omer Angel, David Croydon, and Daisuke Shiraishi

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

Annals of Probability, 2021, Vol. 49, No. 5, 2530-2547.

Distance-dependent chase-escape on trees

With Matthew Junge, Naina Ray* and Nidhi Ray*

Preprint, arXiv:2209.09876.

The chemical distance in random interlacements in the low-intensity regime

With Eviatar B. Procaccia and Ron Rosenthal

Preprint, arXiv:2112.13390.

Coauthors:

Omer Angel. Erin Beckman. Keisha Cook. David Croydon. Nicole Eikmeier. Matthew Junge. Eviatar B. Procaccia. Naina Ray*. Nidhi Ray*. Ron Rosenthal. Daisuke Shiraishi. (* highlights undergraduate students.)

Talks

Videos of recorded talks

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.

Paseos al azar en gráficas.

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 Slides

Introducción a los espacios de Bergman (Introduction to Bergman spaces).

Undergraduate thesis. Supervisor: Fernando Galaz Fontes.

PDF

Teaching

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".

2019. September - December (Winter Term 1).

MATH 100:701 (Differential Calculus with Applications to Physical Sciences and Engineering)

Recitation instructor

2018. September - December (Winter Term 1).

MATH 180 (Differential Calculus with Physical Applications)

Recitation instructor

2017. September - December (Winter Term 1).

MATH 100:106 (Differential Calculus with Applications to Physical Sciences and Engineering)

Instructor

Teoremas de la forma en probabilidad (Shape theorems in probability).

Summer school: Geometría Prohibida . Universidad Autónoma de San Luis Potosí, July 2022.

PDF

Links

Online Seminars

These are some seminars I like. Many thanks to the organizers for uploading their recordings.

Courses and Mini Courses in Probability

Fest

Once in a while, we organize short conferences for our friends in different areas of mathematics. Speakers offer a glimpse of their current work, and we all enjoy talking about mathematics between friends.

  • 2020: the FEST 2020 took place online. We celebrated mathematics in Spanish.
  • 2016: the Sarai fest -1 was my 25th birthday party.