MIT Combinatorics Seminar
PointHyperplane Incidence Bounds And Applications
Csaba David Toth (Massachusetts Institute of Technology)
Wednesday, September 21, 2005 4:30 pm Room 2142
ABSTRACT

The celebrated SzemerediTrotter Theorem gives an asymptotically tight
bound for the number of incident pointline pairs among n points and m
lines in the Euclidean plane. No nontrivial tight bound is known in
general for the incidences of points and any other type of curves or
surfaces in the Euclidean space. All hyperplanes may be incident to
all points in a degenerate configuration where the points are
collinear. It turns out that one can give a tight incidence bound if
we disregard all degenerate and closetodegenerate hyperplanes. The
new incidence bound has several applications involving distance sets,
minimum volume simplices, and pointline configurations in 3D.


