Geometry & Geometric Analysis Seminar
The Geometry and Geometric Analysis (GAGA) Seminar is an opportunity for geometers, topologists, and others from TCU and other campuses to learn about new topics of mutual interest. GAGA meets most weeks during the school year. You can find notes from past talks at the GAGA Note Repository, located in a secure off-campus location.
The next meeting of GAGA will be Tuesday, January 21 from 4 to 5 pm in Tucker Technology Center (TUC) 243. Henson Graves will speak on "A Mathematical Formalism to Bridge Between Category Theory and Engineering."
Abstract: This talk is a case study of a bridge between category theory and engineering. The bridge is bidirectional. The talk traces how an initial quest to find constructive axioms that generate toposes evolved into the development of a mathematical formalism, called Algos. I could only solve the problem with insight from work on modeling and simulation in industry. The solution enabled a language independent of set theory, but with defined membership and subtype relations. Axiom sets which contain these axioms generate a topos, called an Algos topos. Algos toposes can be implemented within a proof assistant. An Algos topos with additional axioms can represent the meta theory of categories (a 2-category of categories and functors). An Algos meta theory used within a proof assistant can be used to develop models and simulations for an engineering context. Physical systems that occur in engineering are defined at a meta level. These concepts make use of category constructions such as limits and Grothendieck topologies. The system concepts can be used to design or analyze interacting physical systems.