12:00 pm Friday, April 4, 2008
Sophex Seminar: Finite Field Kakeya Conjecture by Mark Lewko in RLM 9.166
Two weeks ago a simple combinatorial proof of the finite field Kakeya conjecture was published by Zeev Dvir. We will present his proof and discuss related results and conjectures. In 1928 Besicovitch showed that there exist bounded subsets of R^n containing a unit line segment in every direction with measure zero. The Kakeya conjecture asserts that these sets have full Hausdorff dimension. In 1999, Tom Wolff formulated an analog of this conjecture for finite fields. These conjectures have deep connections with problems in Fourier analysis, combinatorics, number theory and PDE. Our presentation will only assume elementary algebra. Submitted by
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