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Local monodromy of constructible sheaves  

Deepam Patel (Purdue)
Tuesday, October 10, 2023 - 2:30pm
PDL C-38
Deepam Patel
Main talk (2:30pm)
Title: Local monodromy of constructible sheaves
Abstract: Let X be a complex algebraic variety, and X-->D a proper morphism to a small disk which is smooth away from the origin. In this setting, the higher direct images of the constant sheaf form a local system on the punctured disk, and the Local Monodromy Theorem (due to Brieskorn-Grothendieck-Griffiths-Landsman) asserts that the eigenvalues of local monodromy are roots of unity. In this talk, we will discuss generalizations of this result to the setting of arbitrary morphisms between complex algebraic varieties, and with coefficients in arbitrary constructible sheaves. If there is time, I'll discuss applications to variation of monodromy in abelian covers, and applications to the monodromy of alexander modules.
This is based on joint work with Madhav Nori.
Pre-talk (1:45pm)
Title: What is monodromy?
Abstract: I’ll try to explain how the study of solutions to differential equations leads naturally to the notion of mondromy of local systems. If there’s time we’ll look at the classical example of a degeneration of elliptic curves.
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