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SUMMARY:The polynomial method in combinatorial incidence geometry - Tao\, 
 T (University of California\, Los Angeles)
DTSTART:20110217T140000Z
DTEND:20110217T150000Z
UID:TALK29878@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Combinatorial incidence geometry is concerned with controlling
  the number of possible incidences between a finite number of geometric ob
 jects such as points\, lines\, and circles\, in various domains.  Recently
 \, a number of breakthroughs in the subject (such as Dvir's solution of th
 e finite field Kakeya conjecture\, or Guth and Katz's near-complete soluti
 on of the Erdos distance problem) have been obtained by applying the _poly
 nomial method_\, in which one uses linear algebra (or algebraic topology) 
 to efficiently captures many of these objects inside an algebraic variety 
 of controlled degree\, and then uses tools from algebraic geometry to unde
 rstand how this variety interacts with the other objects being studied.  I
 n this talk we give an introduction to these methods.\n
LOCATION:Seminar Room 1\, Newton Institute
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