Research
Please note that depending on how much I have on my hands, this page may not be up-to-date.
My main area of research is Partially Ordered Sets, but I'm interested in many other areas, especially Graph Theory, and Geometry. Here are a few (somewhat random) things I am interested in.
- Ramsey Theory. I'd like to point out two papers of mine, one is very recent with my current PhD student, and one is somewhat older. There are plenty of unsolved questions in both.
- Random graphs and posets. The first paper is long one with some deep techniques, but also more problems to work on. The second has an easy and elegant first part, and a much harder second part. The model is barely studied at all. The third one is is an elegant paper in the area of pure probability theory.
- If you like discrete geometry, check out the chapter on Segment Orders in my thesis. If that's too long, or not peer reviewed enough, you can read the paper on the subject, though there are results in the thesis that are not in the paper. The problem if p_1 (sometimes referred to as "triangle orders") and p_2 (referred to as "shoe orders" or "boot orders") are distinct is still open. I started offering money for the solution in 2010, offering $50. The current prize is $200, but if I make full professor, I'll double it. (So maybe it is a good strategy to wait.)