Pure Maths Colloquium: Principal bundles in algebraic geometry
22 June 2015 16:00 in CM221
I will discuss the notion of principal bundles in algebraic geometry. Roughly speaking, a principal G-bundle is a map X -> X/G, where the group G acts freely on a space X. I will give more precise
definitions and examples. In particular, we will see that in many
cases a principal bundle can be interpreted as a vector bundle with
some extra structure.
I will introduce a very natural conjecture of Grothendieck and Serre
providing a condition for a principal bundle to be locally trivial. Then I will discuss the recent progress in the conjecture. I will also briefly talk about the moduli spaces of principal bundles and their importance in the Langlands program.
No special knowledge in algebraic geometry is expected.
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