Explore a comprehensive lecture on the application of Newton's Method to semirings, presented by Javier Esparza from Technische Universität München. Delve into the speaker's decade-long research on solving systems of polynomial fixpoint equations over omega-continuous semirings. Discover how Newton's method, a well-known technique from numerical analysis, can be generalized to this algebraic setting. Examine the characterization of information contained in Newton approximants to the fixpoint and learn about various applications of this approach. Gain insights from key publications on the topic, including works on Newton's Method for omega-Continuous Semirings, Newtonian program analysis, and derivation tree analysis for accelerated fixed-point computation.