Dr. Juan Orendain
Visiting Assistant Professor at Case Western Reserve University
E-mail juan.orendain [at] case [dot] edu
Research interests
Higher category theory and its applications to:
- Topology
- Quantum field theory
- Operator algebras
- Representation theory
Online profiles
Publications/preprints
- w/R. Oeckl. Compositional Quantum Field Theory: An axiomatic presentation. Pereprint vers.
- Free globularly generated double categories II: The canonical double projection. Cahiers de topologie et géometrie différentielle catégoriques Vol. LXII (2021) Issue 3. pp 243-302 Preprint vers. Journal vers.
- Free globularly generated double categories I. Theory and Applications of Categories Vol. 34 No.42, pp 1343-138. Preprint vers. Journal vers.
- Lifting bicategories into double categories: The globularly generated condition. Theory and Applications of Categories, Vol. 34, No. 4, pp 80-108. Preprint vers. Journal vers.
- Combinatorial dimensions: Indecomposability of certain local trivial extension algebras. Journal of Algebra an Applications, 13, No. 06. Preprint vers. Journal vers.
- On direct sum decompositions of Krull-Schmidt artinian modules. Journal of Algebra and Applications, 13, No. 03. Preprint vers. Journal vers.
- Lifting bicategories through the Grothendieck construction. Submitted. Preprint vers.
- Cylinder topological quantum field theory: A categorical presentation of classical field theory and its symmetries. Preprint vers.
- A note on the existence of essential indecomposable submodules of Ore domains. Preprint vers.
In preparation
- w/Nick Gurski and David Yetter. Compact closed bicategories.
- w/R. Oeckl. Compositional Quantum Field Theory II: State spaces and involutive symmetric monoidal functors
- w/J.A. Zapata. A cubical approach to higher lattice gauge theory.
- w/Rubén Maldonado. Length one double cateogries via End-indexigs.
Teaching
Fall 2022
Math 308 Abstract Algebra
Math 227 CalculusIII
Spring 2023
Math 402 Abstract Algebra II
Math 462 Algebraic Topology
List of past courses
Recent talks
2022
- Reconstructing double categories from End-indexings. Conference on Functor Categories, Model Theory, and Constructive Category Theory. University of Almería, Almería. Spain
- Equivariant Functorial Quantum Field Theory. BIRS CMO Workshop on Mathematical and Conceptual Apects of Quantum Theory
- Higher lattice gauge fields and cubical omega-groupods. Higher Structures Seminar, Feza Gürsey Center for Physics and Mathematics.
- Globularly generated double categories. Mathematics Colloquium Yeditepe University, Istambul, Turkey.
- Composicionalidad categórica: De modelos de epidemiología y diseño de software a gravedad cuántica. coloquio departamento de Matemáticas ITAM
- Quantum field theory in the GBF from TQFT. Quantum Foundations group meeting CCM UNAM
- Topological quantum field theory as symmetric monoidal functors quantum foundations group meeting CCM UNAM
- Categories, fields and information theory. quntum foundations group meeting CCM UNAM
- Operational semantics on Petri nets. Escuela Oaxaqueña de matemáticas. IMATE UNAM Unidad Oaxaca.
2021
- Globularly generated double categories: Then and now. CaTCat: Open House on Category Theory 2021. Mexico City, Mexico. Slides.
- Por qué y cómo categorificar una teoría cuántica de campos. Coloquio PCCM. CCM UNAM. Morelia Mexico. Slides.
- Length of framed bicategories. Category Theroy 2021. CT20->21. Genoa. Italy.
- Length 1 double categories via End-indexings. Special session on cateogries and topology, MCA2021 Buenos Aires. Argentina. Slides.
- Open Petri nets and symmetric monoidal double categories. [In Spanish] Petri nets reading seminar. Slides.
- How long does it take to frame a bicategory. New York City category theory seminar. Video. Slides.
- The rate equation and the master equation for stochastic Petri nets [In Spanish] Petri nets reading seminar. Slides.
- Operational semantics for Petri nets as commutative monoidal categories [In Spanish]. Petri Nets reading seminar. Slides.
- Remarks on the bicategory of von Neumann algebras. QSSS, Ohio State University. US. Slides
2020
- Remarks on the bicategory of von Neumann algebras. UFSC C*-algebras seminar. UFSC. Brazil. Slides. Video.
- Categorías dobles de álgebras de von Neumann. Segundo cíclo de conferencias. [In Spanish] Facultad de Ciencias UNAM. Slides. Video.
- Globularly generated double categories. MIT categories seminar. MIT. US. Slides. Video.
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Double categories of factors. Noncommutative Geometry Seminar at the University of Copenhagen. Denmark. Slides.
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Formal Haagerup standard form on infinite index morphisms of factors. Groups, Operators, and Banach Algebras Webinar. Lancaster University. UK. Slides.
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Internal categories of factors. Zagreb Workshop on Operator Theory. University of Zagreb. Zagreb, Croatia. Slides. Video.
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Formal Haagerup standard form on infinite index morphisms of factors. Canadian Operator Symposium, Fields Institute, Canada. Slides
Organization
Events and seminars organized
Mentoring
- Rubén Maldonado, PhD, co-mentoring with Raymundo Bautista, CCM, UNAM
- Iván Sánchez Silva, PhD, co-mentoring with José Antonio Zapata, CCM, UNAM
Activities
Nov 28-Dec 2. Talk at the Virtual double Categories Workshop
Past activities
List of past activities
Books, papers, etc.
Bookshelf
Resources
Resources in applied category theory