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Abstract
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In 1957, Alexander Grothendieck published a long paper in
two parts in the Tohoku Mathematical Journal, Japan,
whose title can be translated as `On some points of homological
algebra'. This paper revolutionized the subject of homological
algebra and it sheds unifying light on topics in diverse areas such as group theory, Lie theory, number theory, algebraic topology, etc. It had profound applications to Algebraic Geometry, which were made apparent by Grothendieck and his school in the next few decades. The ideas of abelian categories and additive functors between them, and their derived functors, come from this paper. The famous `Grothendieck spectral sequence' first appeared here. I will give a series of two talks, introducing this paper's ideas and reporting some subsequent developments.
The first talk will assume no prior knowledge except of the basics of groups, rings, and modules at an undergraduate level. In it,
I will explain the historical context, and introduce the paper's themes in simple terms. The second talk will assume some
acquaintance with Algebraic Geometry.
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