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Wednesday, April 27, 2016

**Abstract:** Suppose you are given an unknown polynomial $f$ about which you know nothing except that its degree is $d$ and that it has $n$ variables. If you are allowed to sample the values $f$ takes on a finite set $X$, when does that data allow you to recover $f$? When $n=1$ this question has a simple answer; yes, as long as $X$ contains $d+1$ or more points. When $n>1$ the question becomes much more complicated and depends intimately on the geometry of the set $X$. We will survey some results and conjectures in this area. This talk will be extremely accessible.