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Journals and Conferences
Given a convex compac t set K C [~2 w h a t is the la rges t n such t h a t K conta ins a convex la t t ice n-gon? We answer th i s ques t ion asympto t ica l ly . I t t u rns out t h a t the max ima[ n is re la ted to the larges t affine pe r ime te r t h a t a convex set conta ined in K can have. This, in turn , gives a new charac te r iza t ion of /4o,… (More)
In 1979 Vaaler proved that every d-dimensional central section of the cube [−1, 1]n has volume at least 2d. We prove the following sharp combinatorial analogue. Let K be a d-dimensional subspace of Rn. Then, there is a probability measure P on the section [−1, 1]n ∩K, so that the quadratic form∫ [−1,1]n∩K v ⊗ v dP (v) dominates the identity on K (in the… (More)
What is the minimum perimeter of a convex lattice n-gon? This question was answered by Jarńık in 1926. We solve the same question in the case when perimeter is measured by a (not necessarily symmetric) norm.
What is the minimum perimeter of a convex lattice n-gon? This question was answered by Jarník in 1926. We solve the same question, and prove a limit shape result, in the case when perimeter is measured by a (not necessarily symmetric) norm.
The workshop on Discrete Geometry was attended by 53 participants, many of them young researchers. In 13 survey talks an overview of recent developments in Discrete Geometry was given. These talks were supplemented by 16 shorter talks in the afternoon, an open problem session and two special sessions. Mathematics Subject Classification (2000): 52Cxx.… (More)
Several significant new developments have been reported in many branches of discrete geometry at the workshop. The area has strong connections to other fields of mathematics for instance topology, algebraic geometry, combinatorics, and harmonic analysis. Discrete geometry is very active with hundreds of open questions and many solutions. There was a large… (More)