Research Project: Construction of highly-regular Quantum Graphs
Objectives:  Construct highly-regular Define higher regularity for quantum graphs, build examples and relate them to spin models and quantum invariants for knots.
Fields of study: Operator algebra, combinatorics, low-dimensional topology, quantum information.
Participants:
- Nestor Bravo Hernández (Universidad de Guanajuato, MX),
- Fabio Viales Solis (Universidad de Costa Rica, CR),
Lead by:
Roberto Hernández Palomares (U Waterloo, CAN)

Learning Program: Head start into  Operator Algebras
- Pólya enumeration theorem: using symmetries to count graphs
-  Classifying wallpaper patterns (Notas: Los grupos cristalográficos planos, by Manuel L. N.)
-  The Cantor Set:  topological vs measure-theoretic aspects
- The Banach-Tarski Paradox
- Rudiments of operator algebras (following GOALS Notes)
Participants:
- Manuel Liu Ng  (University of Panama, PA)
Lead by:
Roberto Hernández Palomares 

Project: Construction of highly-regular Quantum Graphs
Objectives:  Define higher regularity for quantum graphs, build examples and relate them to spin models and quantum invariants for knots.
Fields of study: Operator algebra, combinatorics, low-dimensional topology, quantum information.

Participants:
- Iván Ortiz Arana  (Universidad de Guanajuato, MX),
- Nestor Bravo Hernández (Universidad de Guanajuato, MX),
- Sergio Ching Heredia (Universidad Autónoma de Yucatán, MX),
- Fabio Viales Solis (Universidad de Costa Rica, CR),
- Emmanuel Silva Amaya (Universidad Nacional de Colombia, COL).

Mentors:
José Manuel Barrientos López (Purdue University, USA),
Violeta Martínez Escamilla (University of Waterloo, CAN).
Lead by:
Roberto Hernández Palomares (U Waterloo, CAN)

Seminar Series:
- Speaker: Michael Brannan (University of Waterloo) (19-Ago, 2024)
Title: Quantum functions, correlations, and operator algebras
-Speaker: Jorge Castillejos (UNAM)  (12-Ago, 2024)
Title: La simbiosis entre algebras de von Neumann y C*-álgebras
-Speaker: Makoto Yamashita (Univeresity of Oslo) (5-Ago, 2024)
Title: Graphs to quantum groups through Kauffman brackets

Master thesis advising
- José Manuel Barrientos López (CIMAT, MX)
Topic: Classification of Irrational Rotation C*-algebras
Highlights:  Promoted funding obtention to attend GOALS 2023 (Purdue U, USA), and
Twinned Conference on C*-Algebras and Tensor Categories (Fields Institute, CAN)
Adviser: Roberto Hernández Palomares (U Waterloo, CAN)  

Master thesis advising
- Violeta Martínez Escamilla (CIMAT, MX)
Topic: Classification of AF C*-algebras
Highlights:  Promoted funding obtention to attend GOALS 2023 (Purdue U, USA), and
Twinned Conference on C*-Algebras and Tensor Categories (Fields Institute, CAN)
Adviser: Roberto Hernández Palomares (University of Waterloo, CAN)

Academic Mentorship
- Héctor Iván Zepeda Santes (Universidad de Guanajuato, MX)
Mentorship: Winter 2023, Sponsorship: received stipends sponsored by OMR.  
Travel Sponsorship: Partial OMR funding to compete in CIIM Bogotá, Colombia 2022
Adviser: Roberto Hernández Palomares (U Waterloo, CAN)

Project: Looking for a projection
Objective: Construct Hilbert C*-module admitting no orthogonal Pimsner-Popa basis.
Fields of study: Operator algebra, K-theory, category theory, Hilbert C*-modules, Functional analysis.

Participants:
José Manuel Barrientos López (Universidad de Guanajuato, MX),
Violeta Martínez Escamilla (Universidad de Guanajuato, MX)
Sponsorship: Both participants received summer stipends sponsored by OMR.

Lead by:
Roberto Hernández Palomares (U Waterloo, CAN)