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DG:= <Galois Theory, Covering Spaces and Grothendieck Topologies>

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This week's DG is by Ben Briggs (last year's Academic Support officer if you didn't already know) and will be on Galois Theory, Covering Spaces and Grothendieck Topologies. We are in a new room as well: B3.03 but at the same time of Tuesday at 6pm.

A lot of constructions in set theory and geometry can be done by thinking about sets (or groups or rings...) varying continuously over a topological space. Grothendieck wanted to be able to consider sets varying nicely over other things. What was needed was a good notion of 'covering' in a much more general setting than topological spaces.

An analogy between Galois theory for fields and covering space theory in topology led Grothendieck to define a new notion of topology. We'll look at this analogy, and a few other examples, to get to the moral of the story: 'geometry and algebra go in opposite directions'. All of this leads to awesome new maths.

Suitable for third/fourth years and keen second years, but having heard of Galois theory and covering spaces will make things more interesting.