Polynomial Solving Seminar

Introduction to Alpha-theory 

Alpha-theory provides a rigorous way to certify approximate solutions for analytic equations. It was introduced by Steve Smale in the 80's, and is one of the main tools to produce robust path-following algorithms with rigorous complexity estimates.

In this first talk, I will introduce the main invariants and prove the "gamma theorem." The proof of the "alpha theorem" with optimal constant will be given in a subsequent lecture.

This is also the organizational meeting for this seminar.