• Date: 1/17/25
  • Darren Creutz, Vanderbilt University
  • Title: Subshifts of non-superlinear complexity cannot be mixing
  • Abstract: I will present the companion result to my proof of the existence of mixing subshifts with word complexity arbitrarily close to linear, namely that any subshift which does not have superlinear word complexity must be partially rigid hence cannot be (strongly) mixing.
    More specifically, if p(q) is the number of words of length q appearing in a subshift and \liminf p(q)/q < infty then there exists a constant 0 < c \leq 1 such that every invariant probability measure \mu for the subshift, there is measure-theoretic partial rigidity of at least c: for all measurable sets B, \limsup \mu(T^{n} B \cap B) \geq c \mu(B). The tools involved range from graph theory and combinatorics to classical ergodic theory.

• Date: 1/24/25 (Zoom Meeting ID: 960 7137 8075)
  • Larissa Kroell, University of Waterloo
  • Title: The ideal intersection property for partial reduced crossed products
  • Abstract: Given a C*-dynamical system, a fruitful avenue to study its properties has been to study the dynamics on its injective envelope. This approach relies on the result of Kalantar and Kennedy (2017), who show that C*-simplicity can be characterized via the Furstenberg boundary using G-injective envelope techniques. In this talk, we will discuss consequences of this idea for partial C*-dynamical systems. In particular, we introduce partial G-injective envelopes and generalize techniques for ordinary C*-dynamical systems given in Kennedy and Schafhauser (2019) to partial C*-dynamical systems. As an application of this machinery, we give a characterization of the ideal intersection property for partial C*-dynamical systems. This is joint work with Matthew Kennedy and Camila Sehnem.

• Date: 1/31/25
  • Terry Adams, U.S. Government (retired)
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• Date: 2/7/25
  • Itamar Vigdorovich, UC San Diego
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• Date: 2/14/25
  • Caleb Eckhardt, Miami University
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• Date: 2/21/25
  • Behrang Forghani, College of Charleston
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• Date: 2/28/25
  • No Meeting

• Date: 3/7/25
  • Srivatsav Kunnawalkam Elayavalli, UC San Diego
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• Date: 3/14/25
  • No Meeting, Spring Break

• Date: 3/21/25
  • Scott Schmieding, Penn State University
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• Date: 3/28/25
  • Ronnie Pavlov, University of Denver
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• Date: 4/4/25
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• Date: 4/11/25
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• Date: 4/18/25
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• End of Spring Semester.

Past NCGOA and Subfactor seminars