Roberto Hernández Palomares

Mathematician Researcher in Operator Algebras, Quantum Symmetries and Quantum Information

Research only e-mail: robertohp (dot) math (at) gmail (dot) com --- Teaching only e-mail: r5hernan (at) uwaterloo (dot) ca

		About me: I am Postdoctoral Fellow at U Waterloo, Pure Math My research mentors are Michael Brannan and Matthew Kennedy Previously I was a Visiting researcher at Universität der Saarlandes during the Focus semester in quantum information visiting Moritz Weber (Sep- Dec 2022) I was a postdoc at Texas A&M University, Mathematics Department (Aug 2022- Dec 2023) My research mentor at Texas A&M was Eric Rowell I received my PhD degree from OSU in 2021 under the supervision of David Penneys

• Copy of my My CV/Resume (Last updated: 1 Oct 2024)

• My publications on the arXiv

• My Google Scholar site

• I proudly lead, support and sponsor the initiative Outsourcing Math Research, supporting third-world-based young mathematicians. (Sponsors & mentors welcomed!)

• I used to organize the inter-university Quantum Symmetries Student Seminar (QSSS)

Publications and preprints:

• Remarks on C*-discrete inclusions arXiv: 2409.18161 , joint with Brent Nelson
• Quantum graphs, subfactors and tensor categories I arXiv: 2409.01951 , joint with Michael Brannan
• Discrete inclusions of C*-algebras arXiv: 2305.05072 , joint with Brent Nelson
• Dynein localization and pronuclear movement in the C. elegans zygote, Cytoskeleton https://doi.org/10.1002/cm.21733 , with D. A. Dawes, J. Henry, D.Ignacio, and N. Kravtsova
• K-theoretic classification of inductive limit actions of fusion categories on AF-algebras arXiv: 2207.11854 , with Q. Chen and C. Jones
• Q-system completion for C* 2-categories J. Func. Analysis DOI 10.1016/j.jfa.2022.109524, arXiv: 2105.12010 , with Q. Chen, D. Penneys and C. Jones
• Realizations of Rigid C*-Tensor Categories over GJS C*-algebras J. Math. Phys. DOI: 10.1063/5.0015294, , arXiv: 2005.09821 preprint , with M. Hartglass
• Classifying module categories for generalized Temperley–Lieb–Jones ∗-2-categories Int. J. of Math. DOI: 10.1142/S0129167X20500275, arXiv: 1905.00471 with G. Ferrer
• Geometric Measure of Arens Irregularity Preprint , with E. Hu, G. Maierhofer, and P. Rao

Articles in preparation:

• Inclusions of Operator Algebras from Tensor Categories: beyond irreducibility, joint with Lucas Hataishi
• Quantum graphs, subfactors and tensor categories II, joint with Michael Brannan
• C*-discrete inclusions from Cuntz-Pimsner algebras, joint with Brent Nelson
• Highly-regular quantum graphs, joint with Outsourcing Math Research
• Complex Hadamard Matrices, Symmetries, and Quantizations, joint with Michael Brannan and Daniel Gromada

Current teaching:

Current and Past Students:

• Violeta Martínez Escamilla (Aug 2023- Aug2024, Masters in Pure Math, CIMAT, Mexico)
• José Barrientos Lopez (Aug 2023- Aug2024, Masters in Pure Math, CIMAT, Mexico)
• Laurent Costa (Fall 2023, Projet de Bachelor, EPFL, Switzerland)

Conferences and talks (Future and Past):

• 2025
• Highly-regular quantum graphs, Saarland U, Germany Abstract (17-21 Feb 2025)
• 2024
• OSU Quantum Symmetries Seminar, Columbus, OH USA Abstract (TBD Oct 2024)
• Graph Theory Seminar, University of Waterloo, ON CAN Abstract (28 Oct 2024)
• South Atlantic Noncommutative Geometry Seminar, Universidad de Buenos Aires, ARG Abstract (22 Oct 2024)
• Analysis Seminar U Waterloo, ON Canada Abstract (14 Mar 2024)
• Mathematical Physics and Operator Algebra Seminar, Michigan State U, MI USA Abstract (25 Jan 2024)
• 2023
• Mini-course Speaker: actions of tensor categories on operator algebras, Twinned Conference on C*-Algebras and Tensor Categories, The Fields Institute, Canada Website (6-10 Nov 2023)
• Discrete Inclusions of C*-algebras, Canadian Operator Symposium 2023, Western University, London, ON, CA Abstract (25 May 2023)
• Discrete inclusions of C*-algebras, Great Plains Operator Theory Symposium 2023, OSU, Columbus, OH, USA Abstract (15 May 2023)
• Discrete inclusions of C*-algebras, NCGOA 2023, Vanderbilt U, Nashville, TN, USA Website (10 May 2023)
• K-theoretic classification of inductive limit actions of fusion catsegories on AF-algs, Carleton-Ottawa Joint Analysis Seminar, Ottawa, ON, CA (22 March 2023)
• K-theoretic classification of inductive limit actions of fusion catsegories on AF-algs, Analysis Seminar University of Waterloo, ON CA (16 March 2023)
• 2022
• Quantum symmetries for operator algebras, Polish-German seminar on quantum groups, graphs and symmetries via representation theory, Saarbrucken Univeristy, Germany Abstract (24 Nov 2022)
• Discrete inclusions of C*-algebras, Quantum Symmetries Seminar, Ohio State University Mathematics, Columbus, OH USA Abstract (22 Nov 2022)
• Unitary tensor categories and their actions, Malý Seminar, Karlin Univeristy, Prague, Czech Republic (4 Nov 2022)
• K-theoretic classification of inductive limit actions of fusion categories on AF-algebras, NCG&T Seminar, Institute of Mathematics of the Czech Academy of Sciences, Prague, Czech Republic Abstract (1 Nov 2022)
• K-theoretic classification of inductive limit actions of fusion categories on AF-algebras, Operator algebras Seminar, Mathematics KU Leuven, Belgium Abstract (14 Oct 2022)
• K-theoretic classification of inductive limit actions of fusion categories on AF-algebras, Functional Analysis Seminar, University of Ofxord Mathematical Institute Abstract (4 Aug 2022)
• K-theoretic classification of inductive limit actions of fusion categories on AF-algebras, Operator Algebras: Subfactors, K-theory and CFT: David Evans 70th Birthday Program and slides (1 Aug 2022)
• Q-systems and higher unitary idempotent completion for C*-algebras, QGSQuantum Groups Seminar (27 Jun 2022)
• Qué son los espacios no-conmutativos y sus simetrías cuánticas, Coloquio FMAT-CIMAT, Yucatán, México (18 Mayo 2022)
• Q-System Completion for C*-algebras, JMM 2022, Skein Theory and Quantum Algebra (7th April 2022)
• Simetrías cuánticas y espacios cuánticos Universidad de Guanajuato, Seminario Jr. de estudiantes (23rd Mar 2022)
• Applications of subfactor and categorical techniques to C*-algebras, Arizona State University, ASUERAU C*-Seminar (9th Feb 2022)
• Q-systems and higher unitary idempotent completion for C*-algebras, University of Waterloo, Analysis Seminar (2nd Feb 2022)
• Applications of subfactor and categorical techniques to C*-algebras, Mathematical Institute, University of Oxford, Functional Analysis Seminar (28th Jan 2022)
• 2021
• Q-systems and higher idempotent completion for C* 2-categories, Algebra and Combinatorics Seminar, Texas A&M University (8 Oct 2021)
• Q-system completion for C*-Algebras, YMC*A 2021, slides (13 Aug 2021)
• C*-algebras, right correspondences, and Q-systems, GPOTS 2021, notes (10 May 2021)
• UNAM: Seminario de categorias: Actions of unitary tensor categories on C*-algebras, (27 Jan 2021) notes , video (17 March 2021)
• IPAM: Actions of Tensor Categories on C*-algebras: Actions of unitary tensor categories on GJS C*-algebras, slides , (27 Jan 2021)
• Joint Mathematics Meeting 2021: Advances in Operator Algebras: Representations of unitary categories on C*-algebras (7 Jan 2021)
• Joint Mathematics Meeting 2021: Hopf Algebrasand Tensor Categories: Classification of module categories for generalized TLJ *-2-categories (6 Jan 2021)
• 2020
• Texas A&M, Brazos Analysis Seminar: Realizing unitary tensor categories as bimodules over GJS C*-algebras and Hilbertification (7 Nov 2020) Abstract
• Indiana University Bloomington, Algebra Seminar: Classifying unitary modules for generalized TLJ *-2-categories (16 Nov 2020)
• Vanderbilt University, Subfactor Seminar: Representations of RC*TC over GJS C*-algebras Abstract
• OSU NCGOA seminar: Constructing the Jiang-Su algebra
• OSU-Ox:Realizations of RC*TC over GJS C*-algebras and Hilbertification Slides
• OSU Hayes Graduate Forum: Quantum symmetries of quantum spaces. Poster
• 2019
• QUASY-CON 2019. Realizing rigid C*-tensor categories as bimodules over C*-algebras. abstract slides
• Research school on quantum symmetries. Classifying Module Categories for Generalized Temperley-Lieb-Jones *-2-Categories Poster
• 2018
• OSU: NCGOA Seminar. Geometric measure of Arens Irregularity Abstract
• OSU: NCGOA Seminar. There exists a unique separable hyperfinite II1 factor Abstract
• 2017
• OSU: Quantum Algebra & Quantum Topology Seminar. Jones’ Index Rigidity Theorem Abstract
• OSU: Quantum Algebra & Quantum Topology Seminar. Jones’ Index Rigidity Theorem pt. II Abstract
• 2014
• Fields Institute: Undergraduate Summer Research Program 2014 Geometric Measure of Arens Irregularity Slides