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 


2021


2020





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