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                * Princeton Discrete Math Seminar *
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Speaker: Alex Cohen (MIT)

MONDAY! 16th September, 4:30 in Fine Hall 214.

Title: Incidence lower bounds and applications

Lots of problems in combinatorics and analysis are connected to upper bounds
for incidences: given a set of points and tubes, how much can they intersect? 
We prove that if you choose n points in the unit square and a line through each
point, there is a nontrivial point-line pair with distance <= n^{-2/3+o(1)}.
It quickly follows that in any set of n points in the unit square, some
three form a triangle of area <= n^{-7/6+o(1)}, a new bound for this
problem. The main work is proving a more general incidence lower bound
result under a new regularity condition.

Joint with Cosmin Pohoata and Dimitrii Zakharov.

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