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Crystallography and Cohomology of Groups

by Howard Hiller

Year of Award: 1987

Award: Lester R. Ford

Publication Information: The American Mathematical Monthly, vol. 93, 1986, pp. 765-779

Summary: This article starts with a problem motivated by crystal patterns and tilings:  the lattice and the point group are not enough to determine the space group. In pursuit of a sufficient algebraic invariant, the author takes us into the realm of cohomology of groups and explains how the missing invariant plays a role in the modern solution to Hilbert's eighteenth problem.

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About the Author: (from The American Mathematical Monthly, vol. 93 (1986), Howard Hiller was born in Brooklyn, New York, and educated at Cornell University and MIT. His research interests have varied from mathematical logic to algebraic K-theory to differential geometry. He has spent a year at Oxford University under an American Mathematical Society Research Fellowship, a year at Gottingen under an Alexander von Humboldt Fellowship, and taught at Yale University and Columbia University. Currently he is an assistant vice-president at Citicorp Investment Bank.


Subject classification(s): Groups | Abstract Algebra | Algebra and Number Theory | Index
Publication Date: 
Tuesday, September 23, 2008