Quantum expanders and applications
Gilles Pisier, Texas A&M University (cartel)
Viernes 22 de mayo, Módulo 17, aula 520, 12:00h.
\[\]We will explain the notion of quantum expander, a sort of non-commutative analogue of expanding families of graphs, where an n-regular finite graph with N vertices admitting a spectral gap
\[\varepsilon>0\]is replaced by an n-tuple of unitary matrices of size N
\[\times\]N with an analogous spectral gap
\[\varepsilon>0\]. Here n,
\[\varepsilon\]should remain fixed while N
\[\to\infty\]. The talk will relate such questions with the non-separability of the set of finite dimensional (actually even of 3-dimensional) operator spaces which goes back to joint work with Marius Junge, and several more recent "quantitative" refinements obtained using an estimate of the metric entropy of the set of quantum expanders. We will show how the presence of a quantum expander restricts the number of distinct irreducible representations, in analogy with a well known question of Wigderson for expanders.