NTSGrad Fall 2015/Abstracts

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Sep 02

Lalit Jain
Monodromy computations in topology and number theory

The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required.


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Organizer contact information

Sean Rostami (srostami@math.wisc.edu)



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