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Mathematics Department

Operator Algebras and Dynamics Seminar

Fall 2021

Dates subject to change depending on the colloquia schedule.

  • Nov
    10
  • Vrej Zarikian
    USNA
    Time: 03:45 PM
  • Sep
    29
  • Complexity of Elevated Staircase Transformations
    ENS Shaun Rodock
    USNA
    Time: 03:45 PM

    View Abstract

    We introduce elevated staircase transformations, a type of rank-one transformation. The classical staircase transformation was shown to attain quadratic complexity and it was conjectured in 1995 that this was minimal among all mixing rank one transformations. We show that elevated staircase transformations are mixing and attain complexity q(log q)^(1+eps) sharply disproving the conjecture.
  • Sep
    22
  • Compressions and Operator Systems
    Ben Passer
    USNA
    Time: 03:45 PM

    View Abstract

    The matrix range of two tuples of operators can be identical even if the tuples themselves have very different structure. Using a notion of extreme point for operator systems, we show that the spatial structure of a tuple T can be determined from the matrix range under minimality conditions. This generalizes work in the literature on free spectrahedra, matrix convex sets, and compact operators.
  • Sep
    13
  • Dilation Scales and the Structure of Operator Systems
    Ben Passer
    USNA
    Time: 03:45 PM

    View Abstract

    The structure of a compact convex set K is determined by affine functions, and the extreme points of K are detectable in the embedding of affine functions on K into the continuous functions on K. The noncommutative analogue of this is to examine an operator system inside a unital C*-algebra. I will discuss some basics of operator systems and show how this framework leads into dilation problems for noncommuting operators and problems about the spatial structure of operator systems.
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