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                * Princeton Discrete Math Seminar *
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Speaker: Hans Yu (Princeton)

Thursday 29th October, 3:00 in Fine Hall 224.

Title: The Erdős distinct distances problem in R^3

In 1946, Erdős proposed the distinct distances problem: what is the
least number of distances a set of N points in R^d spans? He computed that
integer grids give an upper bound of O(N/(log N)^(1/2)) for d=2 and N^(2/d) for
d at least 3. For d=2, a nearly matching lower bound cN/log N was obtained much
later in 2010 by Guth and Katz, who introduced influential tools such as
polynomial partitioning. In this talk, I will outline their proof and the extra
twists needed to prove a lower bound of N^(2/3-o(1)) for d=3. Time permitting, I
will briefly talk about the recent resolution of the distinct distances problem
for d>=3 by OpenAI. This is based on joint work with Jonathan Tidor and Dmitrii
Zakharov.


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