Séminaires : Séminaire Groupes, Représentations et Géométrie

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BPS invariants naturally appear in the enumerative geometry of sheaves with one-dimensional support on a Calabi-Yau threefold. Toda conjectured that these invariants are independent of the appearing Euler characteristic $\chi$. I will talk about work in progress with M. Groechenig and D. Wyss proving this conjecture in the K3 case.  We argue by relating BPS cohomology to p-adic integration on moduli stacks of sheaves, for which $\chi$-independence was shown by Carocci-Orecchia-Wyss. For this, we use a local description of these moduli stacks of sheaves in terms of moduli stacks of quiver representations.

I will start with an introduction to the various concept appearing here.