Harvard–MIT Algebraic Geometry Seminar: Complex variations of Hodge structures of rank 2 over curves


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May 23, 2023 3:00 pm - 4:00 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

Nicolas Tholozan - École Normale Supérieure

Through the work of Simpson, complex variations of hodge structures (C-VHS) play a central role in the study of the moduli space of local systems over a complex algebraic variety. In this talk I will consider one of the simplest examples, namely C-VHS of rank 2 over curves. These objects are known to hyperbolic geometers as « branched hyperbolic surfaces ».

I will review what is known about their monodromy, and discuss in particular a joint result with Bertrand Deroin: every PSL(2,R)-local system of Euler class 2g-3 over a curve of genus g admits an isomonodromic deformation that supports a C-VHS.