Episodes from Quantitative Topology: 1. Variational problems, Morse and Turing.
This lecture will begin the series of discussing how effective solutions of topological problems are: and in particular, how large solutions to geometric topological problems are with various measures of complexity. Lecture one will show how one can use basic results about computability, algorithmic undecidability, and more general complexity measures to prove the existence of many solutions to certain variational problems. (This is largely based on joint work with Alex Nabutovsky.)