Waring's Problem: the number $G(k)$
The stack of L-parameters
Line bundles and Cartier divisors on families of twistor-P^1's
Families of twistor-P^1's
Analytic Beilinson-Bernstein
Representations of real groups [ARGOS Seminar]
Analytic Riemann-Hilbert
Analytic Stacks
Organizational Meeting for the Summer Term [Math-Phys Seminar]
We discuss the schedule for the summer term: Please think of topics that you would like to discuss in the group and a talk that you could present.
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The non-abelian Hodge locus
Given a family of smooth projective varieties, one can consider the relative de Rham moduli space, of flat vector bundles of rank n on the fibers. The flat vector bundles which underlie a Z-polarized variation of Hodge structure form the “non-abelian Hodge locus”. Simpson proved that this locus is closed and analytic, and he conjectured it is algebraic. Simpson's conjecture would imply a conjecture of Deligne that only finitely many representations of the fundamental group underlie a Z-PVHS on some fiber. I will discuss a proof of Deligne’s and Simpson’s conjectures, under the additional hypothesis that the Z-Zariski closure of monodromy is a cocompact arithmetic group. This is joint work with Salim Tayou.
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