Department of

June 2020 July 2020August 2020Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su MoTuWe Th Fr Sa 1 2 3 4 5 6 1 2 3 4 1 7 8 9 10 11 12 13 5 6 7 8 9 10 11 2 3 4 5 6 7 8 14 15 16 17 18 19 20 12 13 14 15 16 17 18 9 101112 13 14 15 21 22 23 24 25 26 27 19 20 21 22 23 24 25 16 17 18 19 20 21 22 28 29 30 26 27 28 29 30 31 23 24 25 26 27 28 29 30 31

Wednesday, February 5, 2020

**Abstract:** A Polish group $G$ is displayable in a Banach lattice $(X, \|\cdot \|)$ if there exists a group homomorphism $\rho$ from $G$ into the lattice isometries of $X$ such that 1) $G$ is homeomorphic to $\rho(G)$, and 2) $X$ can be renormed with an equivalent lattice norm $\|| \cdot |\|$ so that $\rho(G)$ is the group of lattice isometries on $(X, \| | \cdot | \| )$. When is a group $G$ displayable in a Banach lattice $X$? This question has been explored in the context of Banach spaces and surjective linear isometries. In this talk based on ongoing work, we first survey some the known results and techniques for displays in Banach spaces to provide context. We then prove displayability results for certain classes of Banach lattices. In particular, if $X$ is either order continuous or an $AM$ space, $X$ can be renormed using various techniques, so that the identity is the only lattice isometry on $X$. Finally, we expand on these techniques to give general conditions sufficient for $G$ to be a display on $X$. This talk will be accessible to grad students of all levels.

Monday, March 2, 2020

Wednesday, April 1, 2020