# Ranks, lines, progressions, sets (Click here to view video of this lecture)

## April 11, 2019 8:00 PM Jadwin Hall A10

“Set” is a popular card game developed by a researcher in genomics to help her students think combinatorially. It’s a very simple game — there’s just one rule! — but it conceals a lot of complexity. There’s a well-known question all players of this game arrive at, which is: how many cards can be out on the table without there being any legal play to make? This sounds like a piece of recreational mathematics, but in fact it’s a special case of the “cap set problem" in additive combinatorics, and to other deep questions in number theory, analysis, and beyond. I’ll talk about the sudden resolution of the cap set problem in 2016 after years of stasis, and what it all has to do with “ranks” of nxnxn “matrices” and the optimization problem of visualizing a set of objects in Euclidean space given only a set of comparisons between their distances