J O N A T H A N L O R A N D
I am a mathematician working as a lecturer in the Mechanical Engineering Department at ETH Zurich, as part of the Frazzoli group in the Institute for Dynamic Systems and Control.
My focus is applied category theory, a branch of mathematics that formalizes general-purpose patterns of interconnection, composition, relation and translation, and puts these to use across a wide range of disciplines. This mathematics is particularly well-suited to systemic thinking, and it accomodates both rigorous, proof-based analysis as well as diagrammatic representations that are accessible to non-experts.
Currently I am working on monotone co-design theory. This is a flexible mathematical framework for modelling and optimizing complex systems built up of interconnected components which each require and provide resources. For an introduction to monotone co-design, see this talk by it's inventor Andrea Censi, or the PhD thesis of his former student, Gioele Zardini, or Chapter 4 in Spivak and Fong's book An Invitation to Applied Category Theory.
Before becoming inspired about applied category theory, I worked in (pure) category theory, representation theory, and symplectic & Poisson geometry.
Teaching, Mentoring, Advising, Outreach
I teach the following two classes at ETH Zurich each year: Applied Category Theory for Engineering I (fall semester) and Applied Category Theory for Engineering II (spring semester).
I also (co)mentor semester theses, master's thesis, and reading courses.
Creating supportive environments for learning and collaboration is important to me; see my teaching statement and diversity statement, as well as Eugenia Cheng's manifesto for inclusivity.
Andrea Censi, Gioele Zardini, and I are writing a textbook on applied category theory which is aimed towards practitioners and learners in applied fields, in particular in engineering. We have also created a website with a selection of useful resources for learning about applied category theory.
I serve on the scientific board advising the CODEWIND research project about community-oriented co-design for wind-energy.
Publications & Preprints
Applied category theory
- Categorification of Negative Information using Enrichment (paper with A. Censi, E. Frazzoli, G. Zardini)
Duality involutions on categories and bicategories
- Duality Involutions, Representations, and Geometry (my PhD thesis)
- Morita bicategories of algebras and duality involutions (paper with A. Valentino)
Classification problems in symplectic geometry
- (Co)isotropic triples and poset representations (paper with C. Herrmann, A. Weinstein)
- Decomposition of (co)isotropic relations (paper with A. Weinstein)
- (Co)isotropic pairs in Poisson and presymplectic vector spaces (paper with A. Weinstein)