Capsets, Sunflower-free sets in {0,1}^n, and the slice rank method

Capsets, Sunflower-free sets in {0,1}^n, and the slice rank method

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Eric Naslund, Princeton University
Fine Hall 110

In this talk we will look at the recent breakthrough of Ellenberg and Gijswijt and Croot, Lev and Pach, which used polynomial method to obtain exponential upper bounds for the Capset problem, that is upper bounds for the size of the largest set in F_3^n which contains no three term arithmetic progressions. In particular we will look at Tao's reformulation of this approach using the so called "Slice Rank Method," and how it can be used to give exponential upper bounds for the Capset and Sunflower-free problems.