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Joint Algebra and Geometry/Geometry and Topology Seminar

Wednesday, April 10, 2019
4:00pm to 5:00pm
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Linde Hall 387
Cohomology of the space of polynomial morphisms on A^1 with prescribed ramifications
Oishee Banerjee, Department of Mathematics, University of Chicago,

In this talk we will discuss the moduli spaces Simpmn of degree n + 1 morphisms A1K with "ramification length <m" over an algebraically closed field K. For each m, the moduli space Simpmn is a Zariski open subset of the space of degree n + 1 polynomials over K up to Aut(A1K). It is, in a way, orthogonal to the many papers about polynomials with prescribed zeroes - here we are prescribing, instead, the ramification data. We will also see why and how our results align, in spirit, with the long standing open problem of understanding the topology of the Hurwitz space.

For more information, please contact Math Dept. by phone at 626-395-4335 or by email at [email protected]caltech.edu.