[Colloquium] Talk by Zeev Dvir, IAS on April 27, 2009
Katie Casey
caseyk at cs.uchicago.edu
Tue Apr 14 13:45:12 CDT 2009
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF CHICAGO
Date: Monday, April 27, 2009
Time: 3:45 p.m.
Place: RY 251
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Speaker: Zeev Dvir
From: IAS
Website: http://www.math.ias.edu/%7edvir/
Title: Recent Progress on Kakeya Sets, Mergers and Extractors
Abstract: Kakeya sets (in vector spaces over finite fields) are
sets that contain a line in every direction. It was conjectured by
Wolff in 1999 that every Kakeya set has positive density (its size is
a constant fraction of the whole space). This conjecture is motivated
by several problems in mathematics and in computer science. In
particular, it has a tight connection with explicit constructions of
‘extractors’ and ‘mergers’ which are efficient procedures that
transform weak sources of randomness into stron ones and have many
applications. In this talk I will show the recent proof of Wolff’s
conjecture [D. 08], the application of the proof technique to the
construction of mergers and extractors [D. Wigderson 08] and a new
work [D. Kopparty Sudan Saraf 09] that extends the methods in earlier
papers to derived near optimal bounds on Kakeya sets and mergers.
Refreshments will be served prior to the talk in RY 255.
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