Positivity of Kac polynomials

Ben Davison (University of Glasgow)

Wednesday 1st March, 2017 16:00-17:00 Maths 515


The talk concerns Kac's conjecture from the early 80s, that the coefficients of his polynomial, counting absolutely indecomposable quiver representations, are positive integers.  This was proved some years ago by Hausel, Letellier and Villegas, using Nakajima quiver varieties.  The positivity conjecture turns out to also be a consequence of the integrality theorem in cohomological Donaldson-Thomas theory.  The end the proof uses algebra/complex geometry, despite being a result in representation theory/combinatorics - I'll explain in broad outline how this goes.

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