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                * Princeton Discrete Math Seminar *
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Date: Thursday 1st December, 3:00 in Fine Hall 224.
 
Speaker: Eric Naslund, Princeton

Title: Capsets, sunflower-free sets in {0,1}^n, and the slice rank method.

We call a family of sets F ``sunflower-free'' if for every three of its 
sets, some element belongs to exactly two of them. 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 GF(3)^n which contains no three term arithmetic progression. In 
particular we will look at Tao's reformulation of this approach using the 
so-called "Slice Rank Method," and apply it directly to the Erdos-Szemeredi
sunflower problem, proving an exponential upper bound for the size of
any sunflower-free family of subsets of {1,2,…,n}.


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Next week:  Sergey Norin

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