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                * Princeton Discrete Math Seminar *
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Speaker: Cosmin Pohoata (IAS)

Thursday 10th November, 3:00 in Fine Hall 224.

Title: Convex polytopes from fewer points

Finding the smallest integer N=ES_d(n) such that in every configuration of N points in R^d in 
general position there exist n points in convex position is one of the most classical problems 
in extremal combinatorics, known as the Erdős-Szekeres problem. In 1935, Erdős and Szekeres 
famously conjectured that ES_2(n)=2^{n−2}+1 holds, which was nearly settled by Suk in 2016, 
who showed that ES_2(n)≤2^{n+o(n)}. We discuss a recent proof that ES_d(n)=2^{o(n)} holds 
for all d≥3. Joint work with Dmitrii Zakharov.


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