Ben Wallis (Northern Illinois University) Garling sequence spaces Abstract: By generalizing a construction of Garling, for each $1\leqslant p<\infty$ and each normalized, nonincreasing sequence of positive numbers $w\in c_0\setminus\ell_1$ we exhibit an $\ell_p$saturated, complementably homogeneous Banach space $g(w,p)$ related to the Lorentz sequence space $d(w,p)$. Using methods originally developed for studying $d(w,p)$, we show that $g(w,p)$ admits a unique (up to equivalence) subsymmetric basis, although when the weight $w$ satisfies a certain biregularity condition, it does not admit a symmetric basis. We then discuss some additional properties of $g(w,p)$ related to uniform convexity and superreflexivity. Joint work with Fernando Albiac and J. L. Ansorena. 
