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Motives and categorifications of quantum statistical mechanics

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Speaker: 
Matilde Marcolli
Affiliation: 
Caltech
Date: 
Tue, 23/12/2014 - 14:00 - 15:00
Location: 
MPIM Lecture Hall

The talk is based on joint work with Goncalo Tabuada (arXiv:1411.3223). We show that the Bost-Connes quantum statistical mechanical system admits a natural categorification in terms of orbit categories of Tate motives. This construction is then further generalized to include a large class of Bost-Connes-type data, which have similar categorifications, obtained through the Tannakian formalism, and which give rise to interesting quantum statistical mechanical systems. These include a quantum statistical mechanical system associated to Weil numbers and the category of motives over finite fields.

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