Fall workshop on Surface Matching and Space Tessellations
12:00 - 14:00 Lunch
14:00 - 15:00 Invited Talk 1 - Andreas Holmsen
15:00 - 15:20 Coffee break
15:20 - 16:40 Session 2
16:40 - 17:00 Coffee break
17:00 - 18:00 Invited Talk 2 - Sang Won Bae
18:00 - 20:00 Dinner
09:00 - 10:00 Invited Talk 2 - Michael Dobbins
10:00 - 10:20 Coffee break
10:20 - 12:00 Session 3
12:00 - 13:30 Lunch
1) The intersection of a matroid and an oriented matroid - Andreas Holmsen
I will present a combinatorial result about the intersection of a matroid and an oriented matroid which implies, among other things, Barany's colorful Caratheodory theorem. All the necessary notions will be introduced during the talk.
2) A point in a $nd$-polytope is the barycenter of $n$ points in its $d$-faces. - Michael Dobbins
In this talk I show that for any positive integers $n,d$ and any target point in a $(nd)$-dimensional convex polytope $P$, it is always possible to find $n$ points in the $d$-dimensional faces of $P$ such that the center of mass of these points is the given target point. Equivalently, the $n$-fold Minkowski sum of the $d$-skeleton of $P$ is a copy of $P$ scaled by $n$. This verifies a conjecture by Takeshi Tokuyama, and may be viewed as loosely analogous to Carathéodory's Theorem. The proof uses equivariant topology.
3) Title: Diameters and Radii of Polygons - Sang Won Bae
Among parameters describing a planar figure are its diameter and radius.
In the literature, the diameter means the maximum distance between any two points in the figure and the radius the minimum of the maximum distance from a point to its farthest point.
Varying the shape of the figure and the distance function on it, the diameter and radius enjoy a variety of flavor and computational complexity.
In this talk, we restrict the planar figure to be a polygon with or without holes,
and mainly consider the shortest path metric in it as the distance function.
Some basic ideas on the diameter and radius in that sense, recent progress in the computational point of view, and open research problems will be discussed.
*****Poster is Click here.