Roberto Hernández Palomares

Mathematician Researcher in quantum symmetires: operator algebras and tensor categories

Office: MC 5311

e-mail: robertohp (dot) math (at) gmail (dot) com, Teaching e-mail: r5hernan (at) waterloo (dot) ca

		About me: I am Postdoctoral Fellow at the University of Waterloo, Mathematics Department 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

• I study quantum symmetries via unitary tensor categories, C*-algebras, and subfactors, in the disciplines of operator algebras, category theory, and quantum algebra.

• Quantum symmetries is an interdisciplinary branch of mathematical physics that intersects fields such as non-commutative geometry, quantum groups and topology, with applications in conformal and topological quantum field theory, quantum information, and theoretical condensed matter physics.

• Copy of my CV/Resume (Last updated: 18 July 2023)

• My publications on the arXiv

• My Google Scholar site

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

  Our goal at OMR is to foster the development of mathematics researchers in the global southern countries. While many poor countries are specializing in exporting raw materials and outsourcing manufactoring 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 amileorate 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 the 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!)
  Some former/current students: Violeta Martínez Escamilla (CIMAT, Mexico) José Barrientos Lopez (CIMAT, Mexico) Héctor Iván Zepeda Santes (DEMAT, Mexico)

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

Current teaching:

Current Students:

• Violeta Martínez Escamilla (Masters in Pure Math, CIMAT, Mexico)
• José Barrientos Lopez (Masters in Pure Math, CIMAT, Mexico)

Publications and preprints:

• 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

Conferences and talks (Future and Past):

• 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