Watch a 36-minute lecture by renowned mathematician Dana S. Scott as he shares personal insights and research experiences spanning seven decades of working with fixed-point theorems. Starting from his undergraduate exposure to fixed points, explore the journey through various mathematical applications, including the Knaster-Tarski Fixed Point Theorem, lattice theory, enumeration operators, and closure operators. Delve into advanced concepts like recursion models, universal closure operators, polymorphic types, and the category of types. Learn about potential future applications while following along with comprehensive slides that detail mathematical proofs and concepts. Originally presented at the Fixed Points in Computer Science 2023 workshop, this talk bridges fundamental mathematical principles with computer science applications, offering valuable insights for both mathematicians and computer scientists interested in fixed-point theory and its practical implementations.
Seventy Years Using Fixed Points in Computer Science and Logic
Overview
Syllabus
Intro
My First Research Experience
Knaster-Tarski Fixed Point Theorem
Tarski's Generalized Lattice-Theoretric Fixed-Point Theorem
The Easy Fixed-Point Theorem
Enumeration Operators
How to do Recursion in our Model?
The Category of Closure Operators
Products of Closures
A Universal Closure Operator
Using Fixed Points of Closures
Are There More General Types?
The Category of Types
Polymorphic Types
Some Conclusions
Taught by
Topos Institute
