Juan Orendain, PhD
MAMS department
Case Western Reserve University
Case Western Reserve University
I'm currently a VAP at the MAMS department at CWRU. I work on low dimensional category theory and its applications to topology, algebra, operator algebras, and mathematical physics. I'm especially interested in studying relations between models of higher categories and groupoids, and how differences between these models are expressed in terms of the way one draws higher morphisms and their composition. I'm also interested in coherence theorems, and how coherence data is used to construct interesting structures in mathematics and mathematical physics. I'm generally interested in any algebraic/compositional structure that has a good enough motivation and that can be expressed in terms of a bunch of little pictures. I'm in the job market 2024/2025.
Papers and preprints
Internalizations of decorated bicategories via π-indexings. J. Orendain, R. Maldonado. Appl Categor Struct 32, 16 (2024). Link.
A better space of generalized connections. J. Orendain, J. A. Zapata. To appear in Proceedings if the MGA conference 2024. Link.
Compositional Quantum Field Theory: An axiomatic presentation, w R. Oeckl. J. Math. Phys. 65, 012301 (2024). Link.
Free globularly generated double categories II: The canonical projection. Cahiers Vol. LXII (2021) Issue 3. pp 243-30. Link.
Free globularly generated double categories. TAC. Vol. 34, 2019, No. 42, pp 1343-1385. Link.
Internalizing decorated bicategories: The globularly generated condition. TAC, Vol. 34, 2019, No. 4, pp 80-108. Link.
On direct sums of Krull-Schmidt Artinian modules. J. Orendain. J. Algebra Appl. Alg, 13, 1350103 (2014). Link.
Combinatorial Dimensions: Indecomposability on Certain Local Finite Dimensional Trivial Extension Algebras. JAA Vol. 13, No. 06, 1450024 (2014). Link.
Length of fully faithful framed bicategories. J. Orendain. Submitted. Link.
Higher homotopy and lattice gauge fields. J. Orendain, J. A. Zapata. Submitted. Link.
Lifting bicategories through the Grothendieck construction. Link.
Cylinder topological quantum field theory: A categorical presentation of classical field theory and its symmetries. J. Orendain. Link.
A Note on the Existence of Indecomposable Essential Submodules of the Ring of Quotients of Ore Domains. J. Orendain. Link.
Current projects
Compact closed 2-categories monoids, with Nick Gurski and David Yetter.
State space functors, with Robert Oeckl.
Homotopy lattice gauge fields, with Jose Antonio Zapata
Book: Abstract algebra
Things I'm thinking about
A Markov category of partially ordered real vector spaces.
String objects in quantum field theory and tracial, involutive A_\infty-algebras.
Coherence for equipments.
Teaching
All teaching materials are on Canvas
Fall 2024
Math 308: Introduction to Abstract Algebra
Math 227: Calculus III
Spring 2024
Math 308: Introduction to Abstract Algebra
Math 228: Differential Equations
Math 352: Capstone project
Math 301: Undergraduate reading project
Fall 2023
Math 401: Abstract Algebra I
Math 308: Introduction to Abstract Algebra
Spring 2023
Math 462: Algebraic Topology
Math 402: Abstract Algebra II
Math 352: Capstone project
Fall 2022
Math 308: Introduction to Abstract Algebra
Math 227: Calculus III
Mentoring
PhD: Ruben Maldonado-Herrera
PhD: Ivan Sanchez Silva
Contact
Office: 2145 Adelbert Rd, Room B03
Email: juan.orendain (at) case (dot) edu