Posts Tagged ‘AndreasHolmsen’

Andreas Holmsen, Nerves, minors, and piercing numbers

Friday, April 28th, 2017
Nerves, minors, and piercing numbers
Andreas Holmsen
Department of Mathematical Sciences, KAIST
2017/5/08 Mon 4PM-5PM
We will give a topological generalization of the planar (p,q) theorem due to Alon and Kleitman. In particular we will show that the assertion of the (p,q) theorem holds for families of open connected sets in the plane under the hypothesis that the intersection of any subfamily is empty or connected. The proof is based on a surprising connection between nerve complexes and complete minors in graphs. This is join work with Minki Kim and Seunghun Lee.

On the Erdős-Szekeres convex polygon problem

Wednesday, May 25th, 2016
On the Erdős-Szekeres convex polygon problem
Andreas Holmsen
Department of Mathematical Sciences, KAIST
2016/05/27 4PM (Room 2411 of Bldg E6-1)
Very recently, Andrew Suk made a major breakthrough on the Erdos-Szekeres convex polygon problem, in which he solves asymptotically this 80 year old problem of determining the minimum number of points in the plane in general position that always guarantees n points in convex position. I will review his proof in full detail.

Andreas Holmsen, Topological methods in matching theory

Sunday, March 1st, 2015
Topological methods in matching theory
Andreas Holmsen
Department of Mathematical Sciences, KAIST
2015/4/7 Tue 4PM-5PM
Around 15 years ago, Aharoni and Haxell gave a wonderful generalization of Hall’s marriage theorem. Their proof introduced topological methods in matching theory which were further developed by Berger, Meshulam, and others. Recently, motivated by some geometric questions, we extended these methods further, and in this talk I’ll explain the ideas and some of our results.

Andreas Holmsen, On the Erdős-Szekeres Problem

Monday, September 10th, 2012
On the Erdős-Szekeres Problem
Andreas Holmsen
Department of Mathematical Sciences, KAIST
2012/9/21 Fri 4PM-5PM
In 1935 Erdős and Szekeres showed that every “sufficiently large” set of points in general position in the plane contains a “large” subset which is in convex position. Since then many mathematicians have tried to determine good bounds for “sufficiently large” in  terms of “large”, as well as given numerous generalizations and refinements. In this talk I will survey this famous problem and extend it to a natural object which we call generalized wiring diagram. This unifies several proposed generalizations, and as a result we will settle several conjectures in this area. This is joint work with Michael Dobbins and Alfredo Hubard.

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.