##### Department of Mathematics,

University of California San Diego

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### Enumerative Geometry Seminar

## Andrea Ricolfi

#### SISSA

## Higher rank K-theoretic Donaldson-Thomas theory of points

##### Abstract:

Recently Okounkov proved Nekrasovs conjecture expressing the partition function of K-theoretic DT invariants of the Hilbert scheme of points Hilb($\mathbb C^3$, points) on affine 3-space as an explicit plethystic exponential. We generalise Nekrasovs formula to higher rank, where the Quot scheme of finite length quotients of the trivial rank $r$ bundle replaces Hilb($\mathbb C^3$,points). This proves a conjecture of Awata-Kanno. Specialising to cohomological invariants, we obtain the statement of Szabos conjecture. We discuss some further applications if time permits. This is joint work with Nadir Fasola and Sergej Monavari.

Host: Dragos Oprea

### April 21, 2020

### 9:00 AM

### Zoom (contact host for zoom link)

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