Noncommutative geometry via quivers with relations

Quivers with relations and their path algebras appear in many guises throughout algebra and geometry. I will sketch how to give a workable combinatorial description of their deformation theory. This allows one to give quite explicit descriptions of deformations of Abelian or enhanced triangulated categories such as categories of coherent sheaves or Fukaya categories. This talk is based on a series of papers joint with Zhengfang Wang.

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