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Sheaves and schemes - the abstract structure of geometry

Graduate Student Colloquium

Sheaves and schemes - the abstract structure of geometry
Series: Graduate Student Colloquium
Seminar
Location: ENR2 S395
Presenter: David Taylor

 

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.
(Refreshments will be served.)