In this talk I will discuss some new applications of the polynomial method to some classical problems in combinatorics, in particular the Cap-Set Problem. The Cap-Set Problem is to determine the size of the largest subset A of Fpn having no three-term arithmetic progressions, which are triples of vectors x,y,z satisfying x+y=2z. I will discuss an analogue of this problem for Z4n and the recent progress on it due to myself, Seva Lev and Peter Pach; and will discuss the work of Ellenberg and Gijswijt, and of Tao, on the Fpn version (the original context of the problem).
Before the talk, at 3:10pm, there will be tea and cookies in Wean 6220.
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