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Mission:
Mission:
Our goal is to foster the development of mathematician researchers in global southern countries. While many poor countries specialize in exporting raw materials and providing manufacturing labor, most leading scientific and humanistic developments occur elsewhere. We observe that this model alone will not develop the poor regions to acceptable XXI century standards. OMR seeks to ameliorate this growing development gap by spreading, guiding and sponsoring the transfer of techniques, skills and knowledge to third-world-based young researchers and students, and to help them connect with leading research institutions. We acknowledge that most of the population --and most talented minds-- currently have no generalized access to higher education, not to say research opportunities and funding. So, we intend to shrink that shortage by directly mentoring and sponsoring talented youth in need for opportunities. (English and Spanish spoken!)
Current and past activities:
Fall2024-Spring2025-Summer2025: Research & Learning Programs
Fall2024-Spring2025-Summer2025: Research & Learning Programs
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
Image source here
2024 Summer Research Program
2024 Summer Research Program
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
Image source here
2023-2024 OMR: Mentorship and Sponsorship
2023-2024 OMR: Mentorship and Sponsorship
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)
2022 Summer Research Program
2022 Summer Research Program
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)
If you want to learn more about OMR, please reach out: robertohp.math@gmail.com
Sponsors and mentors welcomed!
Questions, comments and sponsorship:
Questions, comments and sponsorship:
Roberto Hernández Palomares,
robertohp.math@gmail.com
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