Higher-Arity Algebra via Hypergraph Rewriting
Abstract
In this talk I will present the state of the research on higher-arity algebras from the perspective of (labelled) hypergraph rewriting. Recent discoveries on ternary algebras enabled by the rewriting approach will be discussed and a proposal for computational foundations of formal objects generalizing diagrammatic calculi, such us the one in category theory, will be introduced. This presentation will be done using recently developed function paclets in Mathematica.
Please note that the meeting will be recorded and live-streamed to YouTube:
Carlos Zapata-Carratalá
Postdoctoral Fellow
Carlos has a background in physics and mathematics. He completed his undergraduate training at the University of Valencia and Imperial College London, and then pursued graduate studies in mathematical physics, receiving a masters from the University of Cambridge and a PhD from the University of Edinburgh. During his time in Edinburgh, Carlos has worked as a research assistant to Sir Michael Atiyah and a teaching fellow in the School of Mathematics, while also running the Society for Multidisciplinary and Fundamental Research, of which he is the founder and current president. Carlos is currently a Postdoctoral Fellow and Head of Strategy at the Wolfram Institute, a recently established research institution dedicated to the investigation of the mathematical foundations of computation and the legacy of Stephen Wolfram’s scientific ideas.
Carlos' research focuses on the mathematical foundations of science, particularly in physics and complexity. At present, he is investigating the realm of higher arity structures with a particular focus on ternary structures. This deeply multidisplinary project explores ideas with roots in simple algebraic objects that, due to their fundamental nature, manifest in fields as diverse as molecular biology, token economics, cognitive science, nuclear physics, data science, knot theory, music or game design. Recently he has developed Dimensioned Algebra, a formal mathematical framework that accounts for the dimensional analysis of physical quantities in mathematical models of science, providing an explicit point of contact between applied metrology and abstract mathematics. In the past he was worked on the foundations of classical and quantum mechanics, applications of symplectic/contact geometry to mechanics and thermodynamics, and generalizations of symmetry via Lie groupoids.
In his spare time, Carlos is a keen keyboard player, involved in historical baroque music performance and other forms of musical improvisation. Carlos is also the lead developer of an upcoming strategy card game. He has interests in kinetic art, cinematography, sound design and competitive gaming.