Cohomology in algebra, geometry, physicsand statistics

Deformed Donaldson-Thomas connections

The deformed Donaldson-Thomas (dDT) connection is a Hermitian connection of a Hermitian line bundle over a $G_2$-manifold satisfying certain nonlinear PDEs. This is considered to be the mirror of a calibrated (associative) submanifold via mirror symmetry. As the name indicates, the dDT connection can also be considered as an analogue of the Donaldson-Thomas connection ($G_2$-instanton). 
In this talk, after reviewing these backgrounds, I will show that dDT connections indeed have properties similar to associative submanifolds and $G_2$-instantons. I would also like to present some related problems. This is joint work with Hikaru Yamamoto. 
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