At the third Mathematical Crystallography session, there will be a discussion of future mathematical crystallography plans. Here are some things to think about.

First of all, I don’t see a real “mathematical crystallography” community. There seem to be a number of groups scattered amidst a much larger community of crystallographers who are quite happy with their software packages but otherwise might ask what mathematics is *for*. And there are several branches of mathematics (itself the most fragmented of the natural sciences – if you can call mathematics a natural science) that would be involved, from discrete geometry and graph theory to geometric group theory and Riemann manifolds to cohomology theory and algebraic topology, etc., many of whom may regard mathematical crystallography as an antiquarian activity.

And I haven’t even mentioned the physicists, biologists, nanoscientists and assorted engineers. Mathematical crystallography seems to be a panoply of villages scattered across several empires. From this panoply, how do we create a community?

One of the initiatives is this blog, where I am hoping to start a discussion. Blogs live or die by participation, which means that we need people to join the discussion. Hopefully, this posting is a start: how do we want to build the community?

Face-to-face meetings, attracting colleagues *and students* would be a likely mechanism. So conferences are a possibility. Next year is the International Year of Crystallography, so that is a good time for an event or two. Possible events include:

- While the schedule of the XXIIIrd Congress of the International Union of Crystallography (in July, 2014) has been set, we may be able to set up a little something just outside the gates.
- SIAM has two possibilities, the SIAM Conference on Discrete Mathematics in June, 2014 and the much larger Annual Meeting in July, 2014. But the problem with SIAM minisymposia is that they are smaller: this year, we arranged for only twelve speakers, which is half as many as at last year’s AMS meeting, which suggests another possibility.
- The AMS has eight sectional meetings next year, during weekends during the academic year. We could organize a special session at one of them, and that would give us space for twenty speakers or so.
- We could try descending on an area besides mathematics. The American Chemical Society is having two national meetings next year as is the American Physical Society; we could find out how to crash their parties.

Two things about the longer term.

- One very likely consumer of mathematical crystallography is metal-organic frameworks, and the biggest MOF community is in China. In 2015, SIAM will not hold its regular annual meeting, and instead it will set up shop in the gigantic 8th International Congress on Industrial and Applied Mathematics in Beijing. I have no idea what the ICIAM is like, but if it is at all like the International Congress of Mathematicians (and the ICIAM is modeled after the ICM), it will require a serious proposal to get in.
- At the business meeting today, the SIAM SIAG on Mathematical Aspects of Materials Science decided that their next meeting will be in 2016 – in Europe.

One last point, following up on the business meeting. The SIAG is itself trying to get entry into the Materials Research Society, which I understand is a vast group of scientists and engineers who regard mathematicians as aliens from the planet Vulcan. During the discussion of what kind of minisymposia the SIAG might organize in a MRS meeting, one person said, “If you don’t have a hook to an existing MRS community, you will have an empty room.” Another said, “No one is going to come to a meeting on ‘Mathematical Methods’.” Since attendance at our minisymposia is smaller than attendance at the 2010 minisymposium (where the title was ‘Crystal Design using Discrete Structures in Geometry’ rather than ‘Mathematical Crystallography’), the fellow at the business meeting may have a point.

So now, comments, suggestions, criticism…?

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