Report Title：Foundations of Galois Theory
Reporter：Pavel Kolesnikov
Affiliation:Sobolev Institute of Mathematics
Report Time:10:00-11:00 July 15-18, 20-23, 2026
Report Location: Zoom Id: 904 645 6677，Password: 2026
Abstract:
Galois theory links topics of ring theory and group theory to analyze the symmetry of polynomial roots. In this course, we observe the foundations of Galois theory to reach the main goal: a proof of generic unsolvability of polynomial equations in radicals. Indicative course program:
1. Symmetric groups: orders of elements, conjugation, solvability.
2. Polynomial rings, maximal ideals.
3. Simple algebraic extensions and their automorphisms.
4. First examples of Galois groups.
5. Normal extensions of fields.
6. The Fundamental Theorem of the Galois Theory.
7. Examples of the Galois correspondence.
8. (Un)Solvability of algebraic equations by radicals.
Bio:
Pavel Kolesnikov: PhD, a leading researcher of the Sobolev Institute of Mathematics and acting head of the department of algebra and mathematical logic of Novosibirsk State University.Pavel Kolesnikov specializes in the study of non-associative structures emerging in contemporary mathematics, like Rota-Baxter algebras, dendriform algebras, conformal and vertex algebras, etc.
