Posts Tagged ‘AndreasHolmsen’

Andreas Holmsen, Convex representations of Oriented Matroids

Thursday, September 1st, 2011
Convex representations of Oriented Matroids
Andreas Holmsen
Department of Mathematical Sciences, KAIST
2011/09/16 Fri 4PM-5PM
Many combinatorial problems and arguments concerning finite point sets in the Euclidean plane (or higher dimensions) often do not use the linear structure. A more general concept is that of an Oriented Matroid (OM). It is well-known that every OM can realized by pseudolines, and in fact most oriented matroids can not be realized by straight lines.
Recently, Alfreod Hubard (Courant Institute) and myself have found a new way to represent an OM by convex sets which retains much more of the “straightness” of the Euclidean plane. Interestingly, in our model the isotopy conjecture holds in a very strong sense, and it unifies several aspects of pseudoline arrangements.

Andreas Holmsen, Points surrounding the origin

Monday, August 25th, 2008
Points surrounding the origin
Andreas Holmsen
Div. of Computer Science, KAIST, Daejeon, Korea.
2008/10/09 Thu, 3PM-4PM

Many problems in discrete and computational geometry can be reduced to combinatorial questions concerning systems of segments or triangles in the plane. In spite of what (little) we can say about these planar questions, much less is known in higher dimensions. In this talk we will survey some of these questions and classical results, and present the following theorem: Let d>2 and n>d+1 and P a set of n points in d-dimensional Euclidean space. Then P contains a subset Q of d points such that for any point p in P, the simplex spanned by Q and p does not contain the origin in its interior. This answers a question by R.Strausz, and along the way we strengthen the Colored Helly and Caratheodory theorems, due to L. Lovász and I. Bárány, respectively.

Joint work with János Pach and Helge Tverberg.