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* Princeton Discrete Math Seminar *
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Speaker: Dmitrii Zakharov (MIT)
Thursday 27th April, 3:00 in Fine Hall 224.
Title: "Recent progress on the Erdos-Ginzburg-Ziv problem"
In 1961, Erdos, Ginzburg and Ziv showed that among any 2n-1 numbers one can
find n whose sum is divisible by n. Consider a higher dimensional
generalization of this fact: what is the smallest N such that among any N
points in Z^d one can find n whose sum is zero mod n? This turns out to be a
much more difficult question and the exact answer is only known when d =1 or
2 or n is a power of 2. I will talk about 2 new upper bounds substantially
improving previously known results for most parameters (d, n). Proofs use a
variety of tools coming from additive combinatorics, algebraic methods and
convex geometry. Joint work with Lisa Sauermann.
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