Seminar Event Detail


Combinatorics

Date:  Friday, October 07, 2016
Location:  4088 East Hall (3:10 PM to 4:00 PM)

Title:  Positivity and canonical bases for surface skein algebras

Abstract:   We investigate whether surface cluster algebras have positive canonical bases, natural linear bases for which the structure constants for multiplication are all positive. There are three natural bases we consider. We restrict to the subalgebra spanned by closed loops. (In particular, this subalgebra does not contain the cluster variables, which correspond to arcs.) On this subalgebra, which is also the skein algebra of the surface, one of the bases (the bangles basis) is almost never positive and another basis (the bracelets basis) is always positive.

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Speaker:  Dylan Thurston
Institution:  Indiana U.

Event Organizer:   Sergey Fomin   

 

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