Abstract: This is a continuation of the talk from October 6. Details will be given of the proof that a Lagrangian surface $X\subset \mathbb C^2$ near an isolated singularity which is a Whitney umbrella is locally polynomially convex. In this talk I will discuss the connection between polynomial convexity of surfaces and their characteristic foliation.

Abstract: The aim of the talk is to prove the unsolvability by radicals of the quintic (in fact of the general \(n^{\text{th}}\) degree equation for \(n\geq 5\)). This famous theorem was first proved by N. Abel and P. Ruffini around 1821. However, a complete understanding of \(\textit{solvability}\) had to wait for Evariste Galois and his introduction of group theory in a 1831 manuscript that was miraculously found by Liouville in 1843. We will present a proof of the Abel-Ruffini theorem, very close to Galois's own exposition that uses only elementary properties of groups, rings, and fields as they are taught in a first course in abstract algebra.