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Hyperbolicity, determinants, and reciprocal linear spaces

Geometric and topological combinatorics: Modern techniques and methods October 09, 2017 - October 13, 2017

October 12, 2017 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Cynthia Vinzant (University of Washington)
Location: MSRI: Simons Auditorium
  • hyperbolicity

  • stable polynomials

  • determinantal representation

  • matroid

  • hyperplane arrangment

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



A reciprocal linear space is the image of a linear space under coordinate-wise inversion. This nice algebraic variety appears in many contexts and its structure is governed by the combinatorics of the underlying hyperplane arrangement. A reciprocal linear space is also an example of a hyperbolic variety, meaning that there is a family of linear spaces all of whose intersections with it are real. This special real structure is witnessed by a determinantal representation of its Chow form in the Grassmannian. In this talk, I will introduce reciprocal linear spaces and discuss the relation of their algebraic properties to their combinatorial and real structure

29718?type=thumb Vinzant Notes 1.27 MB application/pdf Download
Video/Audio Files


H.264 Video 14-Vinzant.mp4 124 MB video/mp4 rtsp://videos.msri.org/data/000/029/602/original/14-Vinzant.mp4 Download
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