March 3

Elias Katsoulis, East Carolina UniversityOperator algebras for multivariable C*dynamicsI will present various algebras associated with multivariable dynamical systems over arbitrary C*algebras. These algebras demonstrate a strong rigidity that allows them to encode well the dynamical system from which they originate. This is reflected in their classification theory, which I will discuss in detail. If time permits, I will also describe a promising direction for obtaining computable invariants through the use of local maps, e.g., local derivations. 
March 17 
Aon seimineár. Sláinte! 
March 24 
Bill Ross, University of RichmondThe range of a Toeplitz operatorIn this joint work with Emmanuel Fricain and Andreas Hartmann, we explore the range of a coanalytic Toeplitz operator. In particular, we examine the boundary behavior of functions in the range as well as a natural orthogonal decomposition of the range with respect to the range norm. 
March 31 
David Sherman, UVaTwo new theorems about similar matricesIt is wellknown that if A and B are selfadjoint complex matrices, AB and BA are similar. Is this still true if A and B are merely normal? We say that a matrix V is a partial isometry if V*V is a projection; which matrices are similar to partial isometries? Somewhat to my surprise, I have coauthored a paper with Stephan Garcia and Gary Weiss that answers these two questions. I'll present solutions, examples establishing sharpness of the results, and some open problems. 
April 7 
No seminar  Fields Medalist Vaughan Jones (Vanderbilt University) will give a threelecture series April 68. 
April 14 
Kristin Courtney, UVaIsometries of the Toeplitz matrix algebra
I will discuss some results from the titular paper by Farenick, Mastnak,
and Popov, which was posted to arXiv in February of this year. The paper
follows along a common theme in analysis/linear algebra of characterizing
"preserver" maps on (subalgebras of) M_{n}(C). The two primary
results of the paper are a characterization of continuous multiplicative
isometries and a characterization of linear isometries on the Toeplitz
subalgebra. I will present some background and a proof of the
second result, namely:
a linear isometry from the Toeplitz subalgebra of M_{n}(C) into M_{n}(C) is
multiplication on the left and right by unitaries.
The remaining time will be dedicated to corollaries and consequences.

April 21 
Scott Atkinson, UVaA tubular characterization of hyperfiniteness, part 1 of 2These talks will roughly follow the narrative of Kenley Jung's celebrated 2006 paper titled "Amenability, tubularity, and embeddings into R^{ω}." The main result states that a (separable) von Neumann algebra is hyperfinite if and only if there is exactly one embedding into an ultrapower of the hyperfinite II_{1}factor R up to unitary conjugacy. In the first talk, we will introduce the relevant definitions (including 'tubular'the mathematical notion, not the adjective used by Teenage Mutant Ninja Turtles) and then proceed with the proof of this characterization. In the second talk, we will complete the proof and discuss some of the consequences of this result in the literature and in my current research. 
April 28 
Scott Atkinson, UVaA tubular characterization of hyperfiniteness, part 2 of 2These talks will roughly follow the narrative of Kenley Jung's celebrated 2006 paper titled "Amenability, tubularity, and embeddings into R^{ω}." The main result states that a (separable) von Neumann algebra is hyperfinite if and only if there is exactly one embedding into an ultrapower of the hyperfinite II_{1}factor R up to unitary conjugacy. In the first talk, we will introduce the relevant definitions (including 'tubular'the mathematical notion, not the adjective used by Teenage Mutant Ninja Turtles) and then proceed with the proof of this characterization. In the second talk, we will complete the proof and discuss some of the consequences of this result in the literature and in my current research. 