Speaker: **Sorin Popa** (UCLA/Kyoto Univ.)

Title: Coarse decomposition of II_{1} factors

Time/Date: 1:00-2:30pm, April 19 (Fri.), 2019

Room: 128

Abstract: I will present a result showing that any deparable II$_1$ factor $M$ admits a {\it coarse decomposition} over the hyperfinite II$_1$ factor $R$, i.e., there exists an embedding $R\hookrightarrow M$ such that $L^2M\ominus L^2R$ is a multiple of the coarse Hilbert $R$-bimodule $L^2R \overline{\otimes} L^2R^{op}$ (equivalently, the von Neumann algebra generated by left and right multiplication by $R$ on $L^2M\ominus L^2R$ is isomorphic to $R\overline{\otimes}R^{op}$). Moreover, if $Q\subset M$ is an infinite index irreducible subfactor, then $R\hookrightarrow M$ can be constructed so that to also be coarse with respect to $Q$. This result implies existence of MASAs that are mixing, strongly malnormal, and with infinite multiplicity, in any separable II$_1$ factor.