Invited Speakers and Special Events
 Fall Workshop:
 Greg Chirikjian:
Computational Structural Biology and the Kinematics of Macromolecular Machines
In this talk it is shown how methods originally developed to address
problems in the field of robot kinematics have been applied to
biophysical problems such as the analysis of conformational entropy of
biopolymers and the animation of conformational transitions in
multidomain proteins. In addition, it will be shown how techniques from
differential geometry and noncommutative harmonic analysis can be used
to analyze statistical patterns in the threedimensional structure of proteins in the
protein data bank. Open problems and future directions of the
speaker's work will also be discussed.

Branko Grunbaum:
Configurations  combinatorial, topological, and geometric.
This would be a survey covering, on the one hand, the history of the topic (starting about 130
years ago) with its abundant errors, as well as the recent (say last twenty years) revival and the
very active developments and challenging open problems at the present time.
 Igor Pak:
Inflating polyhedral surfaces:
Can you have a convex polyhedron of a smaller volume than a nonconvex
polyhedron with isometric surface? Imagine you start blowing air into
a cube with a bendable but nonstretchable surface. What can be said
about the limiting shape? These are the key questions we will consider.
I will start the talk by discussing the history of the problem, present
the examples and survey the earlier work on realization of surfaces.
In the second part of the talk I will discuss my recent results on
volumeincreasing deformations of polyhedral surfaces.
 Marjorie Senechal
A point set puzzle revisited
Two discrete point sets S1 and S2 are said to be homometric if, relative to some arbitrarily
chosen origin, their difference sets S1' and S2' coincide, where S'={xy : x,y in S}. Determining
S' from S is entirely trivial, but the converse is not.
Homometric point sets were first defined and studied in the 1930s, in connection with the
interpretation of Xray diffraction patterns. Later they were characterized algebraically.
Recently, surprising examples have been found in aperiodic sequences. I hope that studying these
different approaches together will shed light on their underlying geometry.
 Special event: Joe O'Rourke 3D printer demo
I will demonstrate the operation of a 3D printer, the ZPrinter 310, and a laser cutter, the Versa
Laser 200. Both act as printers in the sense that, within a software application, the user selects
File/Print, and they produce an object. The 3D printer is sent a file in .STL format, a special
stereolithography representation of triangles in space. It "prints" the object on thin layers of
powder, which it binds during the printing process. The result (after several hours!) is a solid
3D object. The laser cutter is something like a pen plotter, except with a 50 watt laser beam in
place of the pen. One prepares a drawing in, say, Adobe Illustrator, and it is cut out of material
(paper, plastic, wood) inside the cutterquickly, accurately, and amidst flame and smoke.
 Rigidity Theory Day
 Bob Connelly:
Rigidity from Cauchy to granular material
In 1813 A. L. Cauchy proved that convex polyhedra are rigid, even among convex polyhedra with given
facets. Since then, this result has been looked at infinitesimally, lemmas extended globally, in
higher dimensions, metrically, at secondorder, and even extended to nearby nonconvex polyhedra.
The infinitesimal theory of rigidity has a wide range of applications, and there are some
interesting difficulties in modeling problems concerning how it is used for packings and granular
materials. I will give an overview of these questions from my point of view.
 Henry Crapo: Rigidity as Homology
 Bob Norton: Kinematics in Engineering
Kinematics is fundamental to the design of all mechanisms and machinery.
Engineers create linkages, cams, and gear trains to perform a multitude of tasks.
We all use their mechanisms every day without realizing so. Our automobiles are full of them,
as are our households. Most of the consumer products we buy are manufactured with mechanisms of this type.
This talk will describe a few of the mathematical techniques (both geometric and algebraic) that
mechanical engineers typically use to synthesize linkages and create mechanisms for practical applications.
While the mathematical basis of linkage synthesis has been fairly well developed, there still remain
unsolved problems in kinematics. Some of the mathematical techniques recently developed require
cpuhours of computer time to calculate. This makes them impractical for any real engineering problem
solutions and useful only as academic exercises. There is still a great deal of experiential art
and intuition needed to successfully design kinematic devices.
Some of the fundamental precepts of linkage analysis will be briefly reviewed. A few geometrical
synthesis techniques will be described and their algebraic analogues introduced. Very little
engineering design is now done without extensive use of computers and commercial software, and these
typically require algebraic methodology. A few ComputerAidedDesign (CAD) tools will be described
in respect to their use in this context. Finally, a case study of the redesign of a typical mechanism
using modern CAD techniques will be presented.
 Rudi Penne: Instant centers in planar mechanisms
 Brigitte Servatius: The molecular conjecture in 2d
Given a graph whose vertices represent rigid bodies in 2space and whose edges represent pins holding their
endpoints together, polarity translates the graph into a system of straight line segments pinned
appropriately. The straight line segments can be interpreted as the rigid bodies with collinear pins.
We will discuss the JacksonJordan proof that the collinearity of the pins does not decrease the rank.
 Herman Servatius: Constrained Position Vector Configurations
We examine general systems of vectors constrained by mutual inner products, and show how such a
system is related to various geometric and combinatorial constructions.
 Meera Sitharam:
Rigidity and Geometric Constraint Decomposition
Geometric Constraint Systems (GCSs) arise in numerous applications
from mechanical computer aided design to molecular modeling.
``Good'' decompositions of GCSs are crucial
not just for efficient solving and updates, but also for describing
and sampling the solution space, simulating motion,
autoconstraining of underconstrained systems, constraint system
reformulation, appropriately dealing with overconstraints, etc.
This talk will show the close connection between obtaining a
``good'' decomposition and obtaining a combinatorial characterization
of generic rigidity.
 Special event: There will be an additional talk by
Branko Grunbaum on Thursday, 5:00pm  joint
event of the Math and CS departments at Smith College. If
you plan to arrive on Thursday, you may catch it, too.
The unexplored world of nonconvex polyhedra
An examination of the two main misdirections taken in the theory of
polyhedra (courtesy of Poinsot and Bruckner), and a presentation of some of the many exciting and
unexpected classes of "new" polyhedra and their properties.
