Dr. Juan Orendain
Postdoctoral fellow, part of the project Quantum information Structure of Space Time QISS
QISS project Presentation
Centro de Ciencias Matemáticas CCM,
National University of Mexico UNAM. Campus Morelia.
jorendain[at]matmor.unam.mx
︎︎︎August 2022: VAP at Case Western Reserve University
Research interests
Category theory and its applications to the following areas
Online profiles
Publications/preprints
- 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. Local Functorial Quantum Field Theory: Axiomatic presentation
- w/R. Oeckl. Local Functorial Quantum Field Theory: Codimension 1 data and involutive functors
- w/J.A. Zapata. A cubical approach to higher lattice gauge theory.
- Length one double cateogries via End-indexigs.
Teaching
List of past courses
Recent talks
- 2022 Equivariant Functorial Quantum Field Theory. BIRS CMO Workshop on Mathematical and Conceptual Apects of Quantum Theory
- 2022 Higher lattice gauge fields and cubical omega-groupods. Higher Structures Seminar, Feza Gürsey Center for Physics and Mathematics.
- 2022 Globularly generated double categories. Mathematics Colloquium Yeditepe University, Istambul, Turkey.
- 2022 Composicionalidad categórica: De modelos de epidemiología y diseño de software a gravedad cuántica. coloquio departamento de Matemáticas ITAM
- 2022 Quantum field theory in the GBF from TQFT. Quantum Foundations group meeting CCM UNAM
- 2022 Topological quantum field theory as symmetric monoidal functors quantum foundations group meeting CCM UNAM
- 2022: Categories, fields and information theory. quntum foundations group meeting CCM UNAM
- 2022: 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.
- 2021: Por qué y cómo categorificar una teoría cuántica de campos. Coloquio PCCM. CCM UNAM. Morelia Mexico. Slides.
- 2021: Length of framed bicategories. Category Theroy 2021. CT20->21. Genoa. Italy.
- 2021: Length 1 double categories via End-indexings. Special session on cateogries and topology, MCA2021 Buenos Aires. Argentina. Slides.
- 2021: Open Petri nets and symmetric monoidal double categories. [In Spanish] Petri nets reading seminar. Slides.
- 2021: How long does it take to frame a bicategory. New York City category theory seminar. Video. Slides.
- 2021: The rate equation and the master equation for stochastic Petri nets [In Spanish] Petri nets reading seminar. Slides.
- 2021: Operational semantics for Petri nets as commutative monoidal categories [In Spanish]. Petri Nets reading seminar. Slides.
- 2021: 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.
- 2020: Categorías dobles de álgebras de von Neumann. Segundo cíclo de conferencias. [In Spanish] Facultad de Ciencias UNAM. Slides. Video.
- 2020: Globularly generated double categories. MIT categories seminar. MIT. US. Slides. Video.
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2020: Double categories of factors. Noncommutative Geometry Seminar at the University of Copenhagen. Denmark. Slides.
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2020: Formal Haagerup standard form on infinite index morphisms of factors. Groups, Operators, and Banach Algebras Webinar. Lancaster University. UK. Slides.
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2020: Internal categories of factors. Zagreb Workshop on Operator Theory. University of Zagreb. Zagreb, Croatia. Slides. Video.
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2020: Formal Haagerup standard form on infinite index morphisms of factors. Canadian Operator Symposium, Fields Institute, Canada. Slides
Organization
Co-organizer of the UNAM categories seminar
Organizer of the Symmetric monoidal framed bicategories seminar
Activities
- Conference on Functor Categories, Model Theory, and Constructive Category Theory. University of Almería, Almería. Spain
- ACT2022 Strathclyde. Glasgow, Scoland.
Past activities
List of past activities
Books, papers, etc.
Bookshelf
Resources
Resources in applied category theory