Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topics on mathematical crystallography   In July 2012 the General Assembly of the United Nations resolved that 2014
should be the International Year of Crystallography, 100 years since the award
of the Nobel Prize for the discovery of X-ray diffraction by crystals. On this
special occasion, we address several topics in mathematical crystallography.
Especially motivated by the recent development in systematic design of crystal
structures by both mathematicians and crystallographers, we discuss interesting
relationships among seemingly irrelevant subjects; say, standard crystal
models, tight frames in the Euclidean space, rational points on Grassmannian,
and quadratic Diophantine equations. Thus our view is quite a bit different
from the traditional one in mathematical crystallography.
  The central object in this article is what we call crystallographic tight
frames, which are, in a loose sense, considered a generalization of root
systems. We shall also pass a remark on the connections with tropical geometry,
a relatively new area in mathematics, specifically with combinatorial analogues
of Abel-Jacobi map and Abel's theorem.

12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys