##### Department of Mathematics,

University of California San Diego

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### Conference on Tropical Geometry and Mirror Symmetry

## Masahito Yamazaki

## Amoeba, coamoeba and non-commutative Donaldson-Thomas invariants

##### Abstract:

I this talk I will discuss non-commutative Donaldson-Thomas invariants for a class of toric Calabi-Yau manifolds. The generating function of these invariants is computed by a crystal melting model, which is determined by the ``tropical limit'' of the coamoeba of the Newton polynomial of the toric diagram. In the thermodynamic limit, the limit shape of the crystal gives amoeba of the mirror Calabi-Yau manifold. If time allows, I will also discuss the wall crossing of Donaldson-Thomas invariants.\\ Talk time runs to 10:30 AM.

### February 14, 2010

### 8:30 AM

### AP&M 6402

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