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 Juan Orendain, PhD      
                                                                                                                                          

VAP at the MAMS department 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 1 internalizations via End-indexing.


Teaching

Fall 2023

Math 308 Abstract Algebra
Math 401 Graduate Abstract Algebra I

Spring 2023

Math 402 Abstract Algebra II
Math 462 Algebraic Topology
Math 601 Reading seminar on Markov categories, with Mark Meckes


List of past courses


Recent talks

2023


Organization

Spring 2023

co-organizer of Math 601, reading seminar on categorical probability, with Mark Meckes.

Previous events and seminars organized



Mentoring

  • Rubén Maldonado, PhD, CCM, UNAM
  • Iván Sánchez Silva, PhD, co-mentoring with José Antonio Zapata, CCM, UNAM
  • Brian Zhang, Capston project. Case Western Reserve University.
  • Sam Reeder, Capston project. Case Western Reserve University.




Activities





Past activities

List of past activities



Books, papers, etc.

Bookshelf



Resources

Resources in applied category theory