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Presented By: Combinatorics Seminar - Department of Mathematics

Chow Vanishing and Motives of Cluster Varieties

Josie Hlavinka (UC Berkeley)

Progress over the last decade has shown that the cohomologies of full rank, locally acyclic cluster varieties enjoy remarkable combinatorial structures. Crucial in this program has been the observation that these cohomology groups are, in certain Hodge theoretic senses, about as simple as possible. In this talk we will discuss a motivic lift of this observation. In particular we establish that the Voevodsky motives of really full rank sink-recurrent cluster varieties are mixed Tate and split over Q (strengthening results of Lam and Speyer), and we prove that their integral Chow groups are all trivial.

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