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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
2
votes
differential of the characteristic polynomial
I'm not sure how explicit a formula is wanted here, but one can compute differentials if needed by relying on the usual concrete formula in affine algebraic geometry. (This is written down in variou …
39
votes
Accepted
Rep Theory Consequences of Bott--Weil--Borel
It's always a good idea to ask (as students typically do) why one is studying a particular subject or theorem. Here are some of my views, from the algebraic side of representation theory:
1) The or …
8
votes
homotopy type of connected Lie groups
I'm a bit skeptical as to how simple and low-tech a proof can be, since a fair amount of Lie group theory has to be in hand. Short of going into the full details of Iwasawa decomposition, you might fi …