Dec 252012

If I may be permitted a bit of self-promotion, Massimo Nespolo and I have set up a sequence of three minisymposia on Mathematical Crystallography at the upcoming Society for Industrial and Applied Mathematics’ (SIAM) conference on Mathematical Aspects of Materials Science during 9 – 12 June, 2013.

SIAM is one of the four leading mathematical organizations in the United States (the other three being the American Mathematical Society, the Mathematical Association of America, and the National Council of Teachers of Mathematics. As its name suggests, SIAM is the organization most concerned with applications of mathematics to, say, crystallography.

This is the third crystallography get-together I’ve been helped organize, and like the other two, it is part of my campaign to promote mathematical crystallography. I was brought into the subject by one of our invited speakers, Mike Zaworotko, who has been working on the problem of making materials science more like … architecture: you design the desired structure prior to building it, and the structure that you wind up building is the structure you set out to build. So I came into the subject from the crystal design side of the subject.

Even for architecture, design was a non-trivial mathematical problem. We may regard the geometry developed by people like Filippo Brunelleschi, Albrecht Durer, Gerard Desargues, and Gaspard Monge as old hat, but projective and descriptive geometry brought us forward from the old architectural design process we inherited from Romans like Marcus Vitruvius.

But even Vitruvius was ahead of modern chemists: his On Architecture included floorplans for houses. Vitruvius would never propose that a builder through some materials together in the hope that they would assemble themselves into a building. He wouldn’t even have proposed that people assemble a building bit by bit, fitting in bits that felt like they belonged (the way ants and termites build their nests). But by the time that Vitruvius wrote his book, about two thousand years after the construction the palace of Knossos, geometry had become a critical component of architectural design.

Materials science is at least two millennia behind, probably several times that. And that’s just the design side; while we’ve been able to look inside buildings for millennia, we only developed the ability to look inside a crystal about a century ago. And “quasicrystals” show that we are still working on how to tell what we are looking at.

So I am marketing mathematical crystallography. The problems are not only challenging, but also socially significant (crystallography will provide many critical components of the technological fixes of the coming century). If you can, come to the SIAM conference and check us out. Ours will be but one of many parallel series of minisymposia (the complete list will be posted sometime in January), so you can browse around and check out what mathematicians are doing in materials science these days.