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Kakeya problem over (Z/NZ)^n for general N

The runaway seminar:
The runaway seminar:
When Jun 03, 2024
from 02:30 PM to 03:30 PM
Where LH-111, First Floor
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Speaker: Manik Dhar (MIT)
Abstract: A Kakeya Set in (Z/N Z)^n is a set that contains a line in every direction.  It has been known for over a decade that such sets must be large when N is prime (or more generally over any finite field).  This goes back to Dvir's proof of the finite field Kakeya conjecture as posed by Wolff.
In this talk, we will cover the polynomial method techniques for finite fields and recent developments, including some works by the speaker, which resolve this problem over (Z/NZ)^n.  The proofs involve several extensions/modifications to the polynomial method (as used by Dvir for the finite field case) which may be of independent interest.
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