SMRI Seminar: Treumann -- Deligne-Lusztig varieties or irregular connections

**Please note this seminar is in-person only 

SMRI Seminar: 
’Deligne-Lusztig varieties or irregular connections’
David Treumann (Boston College)

Thursday 19 October
1:00-2:00pm (AEDT) 
Carslaw 375 

Abstract: I will give an introduction to Deligne-Lusztig theory, and a second 
introduction to the theory of irregular singularities of linear ODEs, and make some 
comparisons. Deligne-Lusztig theory organizes most of the irreducible characters of a 
finite group G of Lie type of into "series," that are indexed by conjugacy classes of 
maximal abelian subgroups T of G. The representations in one series are those that 
appear in the cohomology of an F_p-bar-variety X equipped with an action of the finite 
group G x T. A basic result of Deligne and Lusztig is "orthogonality", which tells e.g. 
that representations in the series corresponding to T are different from representations 
in the series corresponding to T-prime, when T is not conjugate to T-prime. It is proved 
by analyzing a stratification of the quotient (X times X-prime)/G. I will explain how 
the varieties X and (X times X-prime)/G, and this stratification, arise as moduli spaces 
of constructible sheaves on a topological annulus. They have a lot in common with moduli 
spaces of connections on C^* with irregular singularities at zero and infinity.
 

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Please join us after the seminar for SMRI afternoon tea, 2:00-2:45pm every Thursday on
the SMRI Terrace (accessed through A14-04-L4.36) 

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