Dr. Juan Orendain
Visiting Assistant Professor at Case Western Reserve University
E-mail juan.orendain[ at] case [dot] edu
Teaching
Math 308
Math 227
List of past courses
Research interests
Category theory and its applications to the following areas
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/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.
- Length one double cateogries via End-indexigs.
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
Activities
Past activities
List of past activities
Books, papers, etc.
Bookshelf
Resources
Resources in applied category theory