Soft packings, nested clusters, and condensed matter
September 19 to September 23, 2016
American Institute of Mathematics,
San Jose, California
and Marjorie Senechal
This workshop will be devoted to modeling the
geometry of condensed matter. The workshop will focus on "soft packing" and
"nested clustering" phenomena in discrete geometric structures and their
applications to understanding the internal atomic structure of solids and
fluids. In particular, the workshop seeks to integrate the theories of tilings,
coverings, and packings, and to develop new discrete geometric concepts and
tools needed to study aperiodic structures such as aperiodic crystals.
The main problems for the workshop include:
These three problem areas are interrelated and arise in applications.
- Nested clustering in aperiodic structures in Euclidean space. Structure
theory for nested
clusters; local rules for building global structures; local
characterizations of global
structures; and creating a catalogue of nested clusters.
- Soft sphere packing and its relationship with classical sphere packing.
Optimal soft packings;
density estimates; and soft packing analogues of the kissing number and
- Delaunay point sets in Euclidean space. Classification of Delaunay sets;
over Delaunay sets; local theorems; and Delaunay graphs.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.
Papers arising from the workshop: