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Borel regulator, zeta-motives and moduli of abelian varieties (tropical or otherwise)

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KA2W02 - Arithmetic geometry, cycles, Hodge theory, regulators, periods and heights

I will try to describe a rich landscape of ideas which relates the symmetric spaces for the general linear group, and the moduli spaces of topical curves and abelian varieties.  A classical result due to Siegel interprets the volume of the former as a product of Riemann zeta values.  As explained in the abstract of the workshop, this underpins the interpretation of zeta values as Borel regulators.  After reviewing this I will explain how to interpret a single odd zeta value as a piece of a regulator integral (joint with Schnetz and Yeats) and define the associated motive.  Applications include the construction of infinitely many new cohomology classes in the moduli space of abelian varieties, both tropical and classical. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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