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Title:
The monodromy of meromorphic projective structures
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Abstract:
The notion of a complex projective structure is fundamental in low-dimensional geometry and topology. The space of projective structures on a surface is closely related to the space of holomorphic quadratic differentials, and there is a natural map from the space of projective structures to the character variety of the surface, sending a projective structure to its monodromy representation. In this talk, I will describe joint work with Tom Bridgeland in which we introduced the notion of a "meromorphic projective structure" with poles at a discrete set of points. In the case of a meromorphic projective structure, the monodromy can be viewed as a point in a moduli space introduced by Fock and Goncharov in their work on cluster varieties. This appears to be a manifestation of a general relationship between cluster varieties and spaces of stability conditions on 3-Calabi-Yau triangulated categories.
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