讲座名称：Approximation Theory in Algebraic Contexts
Sergio Estrada，2003年毕业于西班牙Almería大学，获博士学位，现为穆尔西亚大学副教授。曾应邀到麻省理工学院和肯塔基大学合作研究。主要研究方向为同调代数、表示论和模型范畴，现为“Khayyam Journal of Mathematics”和“Research & Reviews: Discrete Mathematical Structures”杂志编委。已在Advance in. Math，J. Lond. Math. Soc.，Journal of Algebra，J. Pure App. Algebra，Comm. in Algebra等国际期刊上发表SCI论文50多篇。
The theory of covers and envelopes of modules has its origin at the beginning of the 80s in the works of Enochs and Auslander and Smalø. The theory is based on the intuitive idea of nicely approaching arbitrary objects that are difficult to study with other objects belonging to classes for which more information is available. In the talk we will give a brief historical review of the theory of covers and envelopes of modules leading to what has been known in the literature as the Flat Cover Conjecture. We will introduce the most significant tools that have allowed to give a positive solution to this conjecture (whose solution appeared published in 2001) as well as the impact of this result in other contexts which still today constitutes an active line of research in homological algebra.