报 告 人（Speaker）：Andrey Lazarev，Lancaster University

报告地点(Location)：吉林大学数学楼第五研讨室

Abstract: This course covers the definition and basic properties of homotopy groups of topological spaces, a fundamental notion of algebraic topology. The special role of the first homotopy group (called the fundamental group) is explained. One of the most efficient methods of computing the fundamental group relies on the construction of a universal covering and a theory of covering spaces is developed up to and including their classification. Various concrete examples of computation are given.

（1）10:00-11:00, June 25, 2025，Reminder on homotopy groups, examples. Commutativity of higher homotopy groups.

（2）9:00-10:00, June 26, 2025，Covering spaces and their connection with the fundamental group of the base.

（3）9:00-10:00, June 27, 2025，Computation of the fundamental group using the method of the universal covering. Examples: wedges of circles, tori, the Klein bottle, real projective spaces.

(4) 9:00-10:00, June 28, 2025，Classification of covering spaces.

报告人简介：Andrey Lazarev，英国兰卡斯特大学教授，从事代数拓扑与同伦论的研究，曾担任 Bull. Lond. Math. Soc.杂志主编，在Adv. Math.、 Proc. Lond. Math. Soc.、 J. Noncommut. Geom.等杂志上发表多篇高水平论文。