I have worked in the field of Euclidean Ramsey Theory.  Recently I have been spending a lot of time on various polymath projects so a lot of the content here has been devoted to that. I also have spent some time on Math Overflow.

Euclidean Ramsey theory involves Ramsey theory and geometry. Let me give two sample problems. One is if the plane is two colored and we have an isoceles triangle is there a monochromatic copy of that triangle?

The other is if we have set K that lies on a sphere for any number of colors r is there a space of dimension n such that for any partition of that space into r colors there is a monochromatic set congruent to K?

These two problems are open. They are examples of the type of problems that come up in this field.

5 Responses to “About”

  1. Hiroki Says:


    I’ve been working on my M.S. thesis about Euclidean Ramsey Theory. I just found your blog and I wonder if you can give me some articles about the new in this field. I red the articles of Ron Graham and Kriz, but I’m very interested in new results.

  2. kristalcantwell Says:

    I have answered this question in a post here:

  3. konradswanepoel Says:

    Hi, Kristal,

    Could you perhaps make a copy of your paper Edge-Ramsey Theory available?

    • kristalcantwell Says:

      I have thought about putting some of my papers online. That particular one would be more difficult than others. Some of my earlier papers were not written in TeX. That is one of them. I don’t think I have the files for that one either. I also have to work through the approval process for Arxiv. If I get the approval I would probably start with a recent papers and work backward and see what I could do with the earlier papers.

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