报告题目：Foundations of Galois Theory

报告人：Pavel Kolesnikov

所在单位：Sobolev Institute of Mathematics

报告时间：July 15-18, 20-23, 2026, 10:00-11:00

报告地点：Zoom Id: 904 645 6677，Password: 2026

报告摘要:

    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.

报告人简介：

    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.