Monday, March 28, 2022
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All day |
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10am |
03/28/2022 - 10:30am The moduli space of Anosov representations of a surface group in a group $\mathsf G$, which is an open set in the character variety, admits many more natural functions than the regular functions: length functions, correlation functions. We compute the Poisson bracket of those functions using some combinatorial device, show that the set of those functions is stable under the Poisson bracket and give an application to the convexity of length functions, generalizing the result of Kerckhoff on Teichmüller space. We shall start by giving an introduction to Anosov representations, define precisely what are the functions we consider and explain the combinatorial device involved. This is a joint work with Martin Bridgeman. Location:
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4pm |
03/28/2022 - 4:30pm Abstract: I will talk about the problem of classifying local systems of geometric origin on algebraic varieties over complex numbers, from the point of view of arithmetic. Conjecture: For a smooth algebraic variety S over a finitely generated field F, a semi-simple Q_l-local system on S_{\bar{F}} is of geometric origin if and only if it extends to a local system on S_{F'} for a finite extension F'\supset F My main goal will be to provide motivation for this conjecture arising from the properties of the p-adic Riemann-Hilbert correspondence and the Fontaine-Mazur conjecture, and survey known partial results. Location:
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