Sheaves and schemes
From 1940-1945 Jean Leray was a prisoner of war in Edelbach, Austria. In order to conceal is expertise in differential equations and mechanics from the Germans, he taught a series of lectures on algebraic topology. In the process, he invented sheaves, sheaf cohomology, and spectral sequences. In my series of two talks, I will explain what sheaves are, and how they are related to continuous, smooth, analytic, and algebraic geometry. Then I will extend this line of thinking to explain what schemes are. There will be several examples from all four geometries to illustrate the connections. While I will use category theoretic language, I will explain the terminology as it arises.