Another successful open problem session! 🙂 Thank you to everyone who attended and a special thank you to our presenters. The slides are posted below.
Date: Tuesday, December 14
Time: 1:30-4:00pm EST (6:30-9:00pm GMT, 7:30-10:00am Wed NZDT)
Schedule:
Session 1: 1:30-2:30pm EST
Session 2: 3:00-4:00pm EST
Social Time: 4:00pm EST – ??
Format:
In each session, several open problems will be presented. For each problem, we’ll have ~5 minutes for the presentation followed by ~5 minutes for discussion. There may be time at the end of each session for more discussion or unplanned open problem contributions.
Session 1:
1. Nathan Bowler – slides
2. Rose McCarty – slides
3. James Davies – slides
4. MichaÅ‚ Pilipczuk – slides
5. Nicholas Anderson – slides
6. Ben Moore – slides
Session 2:
1. Bruce Richter – slides
2. Michael Wigal – slides
3. Dillon Mayhew – slides
4. Zach Walsh – slides
5. Jorn van der Pol – slides
6. Jim Geelen – slides
Joe Bonin and Jorn van der Pol both pointed out that the following conjecture is very-much off the mark.
False conjecture: Every simple rank-4 matroid with no lines of length 4 or more contains a plane with at most 4 points.
By results of Keevash on the existence of designs, for each k and infinitely many n there exists a Steiner systems S(3,k,n); this is a collection of k-element subsets of an n-element set such that each triple is contained in exactly one of the subsets in the collection. These k-element subsets define the planes of an n-element rank-4 paving matroid. That matroid is triagnle-free and all of its planes have exactly k points.