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The U.S. Naval Academy
Mathematics Department

Operator Algebras and Dynamics Seminars

Spring 2024

All talks are from 3:45-4:45 p.m. in the Seminar room, unless otherwise specified.

  • Apr
    15
  • Spanning Problems in Free Spectrahedra (part 2)
    Ben Passer
    US Naval Academy
    Time: 03:45 PM

    View Abstract

    Free spectrahedra are matrix convex sets that are determined by linear matrix inequalities. There are various notions of extreme point in the matrix convex setting, which are useful for different purposes. While real free spectrahedra are spanned by "free extreme points" (essentially, finite-dimensional boundary representations), as shown by Evert and Helton, this result does not extend to the complex coefficient case to any extent. I will discuss how the operator system point of view is helpful in these discussions and highlight some differences between the real and complex cases.
  • Apr
    08
  • Spanning Problems in Free Spectrahedra (part 1)
    Ben Passer
    US Naval Academy
    Time: 03:45 PM

    View Abstract

    Free spectrahedra are matrix convex sets that are determined by linear matrix inequalities. There are various notions of extreme point in the matrix convex setting, which are useful for different purposes. While real free spectrahedra are spanned by "free extreme points" (essentially, finite-dimensional boundary representations), as shown by Evert and Helton, this result does not extend to the complex coefficient case to any extent. I will discuss how the operator system point of view is helpful in these discussions and highlight some differences between the real and complex cases.
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