Mixed Hodge Structures of Abelian Character Varieties

Room 0.29
Friday, 6 January, 2017 - 14:30

Introduced by Deligne, mixed Hodge structures provide a generalization of the Kähler decomposition of cohomology. They were motivated by Deligne’s attempt to assign “virtual” Hodge numbers to singular varieties, a problem in turn related to the Weil conjectures.

I will give a short introduction to mixed Hodge structures, and calculate them in some simple illustrative examples. Afterwards, I will present a sketch of how to obtain these structures for varieties given by quotients of diagonal actions and apply results to the free abelian character varieties of GL(n, C) and SL(n, C). Finally, these results and a result by J. Cheah will lead us to some interesting facts about the cohomology of such varieties, namely a duality based on the work by T. Hausel.

Speaker: 

Jaime Silva

Institution: 

Instituto Superior Técnico, Universidade de Lisboa / CAMGSD
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