In C*-algebras, there is an invariant of interest called the "radius of comparison", and in the case of $C*$-algebras associated to dynamical systems, the radius of comparison is conjectured to be equal to half of the dynamical system's mean dimension. However, this problem has been difficult to approach, with the best current upper bound of the radius of comparison (as of two years ago) being roughly 36 times the mean dimension. In 2020, Hirshberg and Phillips defined the notion of mean cohomological independence dimension, which has proved useful in refining this upper bound. It is a cohomological variant of mean dimension, and it is likely that it agrees with mean dimension in most cases. In addition to helping the radius of comparison question for $C*$-algebras, mean cohomological independence dimension is easier to work with in a variety of ways. For example, the proof for the product formula $mcid ( X^n , G ) = n \cdot mcid ( X , G )$ is much simpler than what is known in the mean dimension case.

Meeting ID: 852 4277 3200 Passcode: 103121