# Jerusalem Mathematics Colloquium

Thursday, 9th June 2005, 4:00 pm

Mathematics Building, Lecture Hall 2

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ZOKHOVITZKY PRIZE LECTURE

Evelyn Magazanik

(HU)

"Staircase Visibility"

** Abstract: **

A staircase is a polygonal path in R² that is x-monotone
and y-monotone and whose edges are alternately horizontal
and vertical. A subset S of R² is staircase connected
if every two points a,b in S are connected by a staircase
within S. Denote by ξ(a,b) the smallest number of edges
of such a connecting staircase. If S is a compact and
staircase connected subset of R², then ξ(.,.) is a
bounded integer valued metric on S. We say that a point x
belongs to the staircase k-kernel of S if ξ(x,y)≤ k
for all y in S. We study these kernels and determine the
possible values of their diameters.

Joint work with M.A. Perles.

Light refreshments will be served in the faculty lounge at 3:30.

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