The Adjoint School 2018
The 2018 Adjoint School featured projects mentored by John Baez, Aleks Kissinger, Martha Lewis, and Pawel Sobocinski. It was organised by Brendan Fong and Nina Otter. The research week was held at the Lorentz Center, Leiden, The Netherlands, in May 2018.
Research Projects
Semantics for open Petri nets and reaction networks
Mentor: John Baez
Students: Fabrizio Genovese, Jonathan Lorand, Maru Sarazola
Petri nets and reaction networks are widely used to describe systems of interacting entities in computer science, chemistry and other fields, but the study of open Petri nets and reaction networks is new, and raise many new questions connected to Lawvere’s “functorial semantics”.
Readings
- A Compositional Framework for Reaction Networks , John C. Baez and Blake S. Pollard
- Decorated Cospans, Brendan Fong
Unification of the logic of causality
Mentor: Aleks Kissinger
Students: Pablo Andres-Martinez, Joseph Moelle, Sophie Raynor, Dmitry Vagner
We will employ the framework of (pre-)causal categories to unite notions of causality and techniques for causal reasoning which occur in classical statistics, quantum foundations, and beyond.
Readings
- A categorical semantics for causal structure , Aleks Kissinger and Sander Uijlen
- Theory-independent limits on correlations from generalized Bayesian networks , Joe Henson, Raymond Lal, and Matthew F Pusey
Compositional approaches to linguistics and cognition
Mentor: Martha Lewis
Students: Tai-Danae Bradley, Sarah Griffith, Jade Master, Brad Theilman
We will use compact closed categories to integrate compositional models of meaning with distributed, geometric, and other meaning representations in linguistics and cognitive science.
Readings
- Interacting Conceptual Spaces I : Grammatical Composition of Concepts , Joe Bolt, Bob Coecke, Fabrizio Genovese, Martha Lewis, Dan Marsden, and Robin Piedeleu
- Mathematical Foundations for a Compositional Distributional Model of Meaning, Bob Coecke, Mehrnoosh Sadrzadeh, and Stephen Clark
Modelling of open and interconnected systems
Mentor: Pawel Sobocinski
Students: Daniel Cicala, Jules Hedges, Eliana Lorch, Joshua Tan
We will use Carboni and Walters’ bicategories of relations as a multidisciplinary algebra of open and interconnected systems.
Readings
- The behavioral approach to open and interconnected systems, J.C. Willems
- Cartesian bicategories I , A. Carboni, and R.F.C. Walters