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3 questions
21
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A Weak Form of Borsuk's Conjecture
Problem: Let P be a d-dimensional polytope with n facets. Is it always true that P can be covered by n sets of smaller diameter?
Background and motivation
The Borsuk conjecture (disproved in 1993) ...
12
votes
1
answer
504
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Tverberg's theorem in CAT(0) spaces
Does Tverberg's theorem hold for CAT(0) spaces of covering dimension $d<\infty$:
Is it true that for any $d$-dimensional $CAT(0)$-space $X$ and a subset $E\subset X$ of cardinality $(d + 1)(r - ...
12
votes
3
answers
707
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A "round" lattice with low kissing number?
Historically, the lattices with high density were studied intensively, e.g. E_8 lattice or Leech Lattice. However, there are situations that lattices with low kissing number are required. Specifically,...