Another successful open problem session! ðŸ™‚ 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.