Title: Randomly Supported Independence Speaker: Per Austrin, KTH, Stockholm (Joint work with Johan Håstad) We study questions of the following flavor: given a random subset $S$ of $[q]^n$, what is the probability that there exists a $k$-wise independent distribution supported on $S$? These questions are motivated by the importance of $k$-wise independence in general, and by applications to hardness of approximation in particular. We prove that, with high probability, $\poly(q) n2$ random points in $[q]^n$ can support a pairwise independent distribution. Then, again with high probability, we show that $(\poly(q) n)^t \log(n^t)$ random points in $[q]^n$ can support a $t$-wise independent distribution. Finally, we show that every subset of $[q]^n$ with size at least $q^n(1-\poly(q)^{-t})$ can support a $t$-wise independent distribution.