Topology Seminar - Michael Dougherty

Ohio State Garden of Constants
April 17, 2025
1:50 pm - 2:50 pm
JR0387

Date Range
2025-04-17 13:50:00 2025-04-17 14:50:00 Topology Seminar - Michael Dougherty Michael DoughertyLafayette CollegeTitleCell Structures for Braid Groups from Complex PolynomialsAbstractIn this talk, I will describe a new geometric and combinatorial structure for the space of complex polynomials with a fixed number of roots. In particular, I will define a metric on the space of monic polynomials with d distinct centered roots, and I will introduce a finite cell structure for the metric completion. Each cell in this complex is a product of two Euclidean simplices, and the combinatorial structure comes from the dual presentation for the d-strand braid group. In particular, this provides a concrete connection between two classifying spaces for the braid group. This is joint work with Jon McCammond. JR0387 America/New_York public

Michael Dougherty
Lafayette College

Title
Cell Structures for Braid Groups from Complex Polynomials

Abstract
In this talk, I will describe a new geometric and combinatorial structure for the space of complex polynomials with a fixed number of roots. In particular, I will define a metric on the space of monic polynomials with d distinct centered roots, and I will introduce a finite cell structure for the metric completion. Each cell in this complex is a product of two Euclidean simplices, and the combinatorial structure comes from the dual presentation for the d-strand braid group. In particular, this provides a concrete connection between two classifying spaces for the braid group. This is joint work with Jon McCammond.

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