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Some deformation problems in the theory of Donaldson-Thomas invariants

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Theory of Donaldson-Thomas invariants, developed recently in our joint work with Kontsevich, produces collections of integers (more generally, elements of some rings of motives) which in many examples ``count” semistable objects in 3-dimensional Calabi-Yau categories. The collections depend on parameters and can jump when parameters cross codimension one walls (``wall-crossing phenomenon”). I am going to discuss a way to produce DT-invariants from the deformation theory of the ``wheel” of projective lines in a formal toric Poisson variety. This approach is related to so distant topics as Hitchin integrable systems, nonabelian Hodge theory and cluster algebras.

This talk is part of the Isaac Newton Institute Seminar Series series.

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