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Positivity for quantum canonical bases for cluster algebras

Date: Thursday, October 10, 2019 13:30 - 15:30
Speaker: Ben Davison (University of Edinburgh)
Location: Heinzel Seminar Room / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Tamas Hausel

Abstract:

I will explain how, in recent work with Travis Mandel, we prove that skew-symmetric quantum cluster algebras have positive structure constants. This work combines the language of scattering diagrams arising in the Gross-Siebert approach to mirror symmetry with that of cohomological DT theory, and proceeds by considering the canonical basis constructed from quantum theta functions. I will try to relate this to the canonical bases that are more familiar from geometric representation theory.
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