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{\Large Department of Mathematics, BGU}

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{\Huge Noncommutative Analysis}\\[0.2\baselineskip]

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\textbf{On} \emph{Monday, April  4, 2022}
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\textbf{At} \emph{11:00 -- 12:00}
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\textbf{In} \emph{32/114}

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{\large\scshape Chris Phillips 
  %
  (University of Oregon)
}
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will talk about
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{\Large\bfseries The Radius of Comparison of a Commutative C*-algebra\par}
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\textsc{Abstract:}
The radius of comparison of a C\emph{-algebra is one measure of
the generalization to C}-algebras of the dimension of a compact
space. Part of the Toms-Winter conjecture says, informally, that a
simple separable nuclear unital C*-algebra satisfying the UCT is
classifiable if and only if its radius of comparison is zero.
Nonzero radius of comparison played a key role in one of the main
families of counterexamples to the original form of the Elliott
classification program.

It has been known for some time that the radius of comparison of
C (X) is, ignoring additive constants, at most half the covering
dimension of X. (The factor 1/2 appears because of the use of
complex scalars in C*-algebras.) In 2013, Elliott and Niu used Chern
character arguments to show that the radius of comparison of C (X)
is, again ignoring additive constants, at least half the rational
cohomological dimension of X. This left open the question of which
dimension the radius of comparison is really related to. The
rational cohomological dimension can be strictly less than the
integer cohomological dimension, and there are spaces with integer
cohomological dimension 3 but infinite covering dimension.

We show that, up to a slightly worse additive constant, the radius
of comparison of C (X) is at least half the covering dimension of X.
The proof is fairly short and uses little machinery.








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