##### Department of Mathematics,

University of California San Diego

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### Enumerative Geometry Seminar

## Yun Shi

#### Center of Mathematical Sciences and Applications, Harvard University

## D-critical locus structure for local toric Calabi-Yau 3-folds

##### Abstract:

Donaldson-Thomas (DT) theory is an enumerative theory which produces a virtual count of stable coherent sheaves on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory, originally introduced by Kontsevich-Soibelman, is a categorification of the DT theory. This categorification contains more refined information of the moduli space. In this talk, I will explain the role of d-critical locus structure in the definition of motivic DT invariant, following the definition by Bussi-Joyce-Meinhardt. I will also discuss results on this structure on the Hilbert schemes of zero dimensional subschemes on local toric Calabi-Yau threefolds. This is based on joint works with Sheldon Katz. The results have substantial overlap with recent work by Ricolfi-Savvas, but techniques used here are different.

### May 24, 2022

### 1:00 PM

https://ucsd.zoom.us/j/

Meeting ID: 964 3244 8457

Research Areas

Algebraic Geometry****************************