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2023 Mini-Workshop on Discrete Geometry
Wednesday, August 9, 2023 @ 10:00 AM - 4:00 PM KST
2023 Mini-Workshop on Discrete Geometry will be held on August 9th at Room B332, Institute for Basic Science (IBS), Daejeon, Republic of Korea.
The workshop consists of three presentations on recent results and an open problem session.
Researchers who are highly interested in this field are welcome to attend.
Tentative schedule
- 10:00-10:50 Michael Dobbins (SUNY Binghamton): Colorful intersections, Tverberg partitions, and geometric transversals
- 11:00-11:30 Andreas Holmsen (KAIST): The topology of the complex of ordered partitions
- 11:30-13:30 Lunch and free discussion
- 13:30-14:10 Minki Kim김민기 (GIST): Some variants of the colorful Helly theorems
- 14:20-16:00 Open problem session
- 16:30-17:30 Discrete Math Seminar: R. Amzi Jeffs (Carnegie Mellon University)
Organizers
- Andreas Holmsen (KAIST)
- Jinha Kim김진하 (IBS Discrete Mathematics Group)
- Minki Kim김민기 (GIST)
- Sang-il Oum엄상일 (IBS Discrete Mathematics Group / KAIST)
Abstracts
Michael Dobbins (SUNY Binghamton): Colorful intersections, Tverberg partitions, and geometric transversals
Given three red convex sets and three blue convex sets in three-dimensional space, suppose every red set intersects every blue set. Montejano’s theorem says there is a line that intersects all the red sets or all the blue sets. This was generalized to k-transversals in
Andreas Holmsen (KAIST): The topology of the complex of ordered partitions
The set of partitions of {1,…,n} into k nonempty ordered parts can be equipped with a natural cell-complex structure which we denote by P(n,k). Here we use discrete Morse theory to show that P(n,k) is homotopy equivalent to a wedge of (n-k)-dimensional spheres, where the number of spheres is given in terms of Stirling numbers of the second kind. Our result has applications related to geometric transversals and Tverberg partitions.
Minki Kim (GIST): Some variants of the colorful Helly theorems
Given a finite family