Walter Whiteley's Home Page
Walter Whiteley's Home Page
Coordinator, Graduate Diploma
in Mathematics Education
Directtor, Mathematics for Education Program
Office Ross S 518; Extension 22598.
In 201314, I am teaching Math 3050. This course has a moodle site http://webct.math.yorku.ca/course/view.php?id=147
Work for the York University Faculty Association
 YUFA Chief Steward.

YUFA nominated trustee of the York Pension Fund.

Trustee YUFA Trust Fund

Trustee YUFA Retirees Benefits Trust
Areas of Current Research
Discrete Applied Geometry
I currently hold an NSERC grant for research in discrete
applied geometry. This covers a range of problems related
to geometric constraints: rigidity of frameworks, CAD programming,
scene analysis, ... .
This May, Bernd Schulze completed his Ph.D. Thesis on Combinatorial and Geometric Rigidity with Symmetry Constraints. It is available for download
Recent work, available only in preprint form, includes:
 Generic rigidity of frameworks with Symmetry:
preprint with Robert Connelly, Patrick Fowler, Simon Guest, Bernd Schulze.
Further results on rigidity of symmetric frameworks  work of Bernd Schulze, are in his thesis linked above. .
 Swapping blocks and holes in spherical frameworks with Elissa Ross and Wendy Finbow Singh. An investigation based on the duality of stresses and motions for spherical polyhedra
 The analysis of 'Assur Graphs' from mechanical engineering of linkages, with Brigitte Servatius and Offer Shair.
 Work on global rigidity of powers of graphs in dimensions 2 and 3, with Matthew Cheung.
 Computing the segmental motions and variable loop flexibility of Immunoglobulins with Sean Law (Biology) and Dean Gill Wu.
 Comparing the bar and body and bar and joint molecular models, with TiongSeng Tay (National University of Singapore).
 Independent direction and parallel drawing constraints in 3D, with
Natalie Stoianov, and now with Elissa Ross;
 Isostatic Almost Spherical Frameworks vis Disc Decomposition (preprint), with Wendy FinbowSingh: a study of the rigidity and inductive constructions for 'corals': triangulated spheres
with added edges, holes, etc. in specific patterns, with Wendy Finbow Singh;
 translation of firstorder rigidity and rigidity averaging results
among metrics derived from projective geometry (Euclidean, spherical,
hyperbolic, Minkowski, ... ) with Franco Saliola;
 inductive techniques
for plane rigidity using tree covereings; rigidity of generalized
grids, with Laura Chavez and Lily Moshe;
 connections between the firstorder rigidity of planar graphs and pseudo triangulations.
with a long list of coauthors (see below)
 rigidity of generalized grids in the plane, with Joseph Aiken and Sandra Gregov.
Protein Flexibility
I am also a senior researcher on a team
four year National Institute of Health grant through Arizona State University and Michigan State
University on New algorithms for protein flexibility. My collaborators
there are Professor Michael Thorpe and Professor Leslie Kuhn . Some of the materials from the work are now available for downloading or for use from the web, at flexweb.asu.edu
Recently, we organized a workshop at BIRS (Banff) on this topic. From the workshop, there is a Web Comptes Rendus site with a number of papers which are freely available for downloading by the public. The site also includes some 'problems' (and solutions) from the discussions around the workshop.
I am working with a Masters Student in Computer Science, two Ph.D students
in mathematics, and several undergraduate students in mathematics and computer science on problems in bioinformatics, molecular flexibility and rigidity, etc..
We are now informally gathering researchers at York who are interested in
bioinformatics, including protein structure and classification.
If you share this interest, get in touch with me. There is a graduate
course in bioinformatics COSC 5290 which is
taught in the Computer Science Graduate
Program. More information is available from
the web pages of Mariana Kant, the course director.
Localization in a multiagent network
For several years I have been collaborating with a group centered in computer science at Yale. Two of the senior researchers are Professor Stephen Morse and Professor Yang (Richard) Yang . Working in particular with a recent Ph.D. student (now a postdoc at Columbia)
Tolga Eren, we have a number of conference papers published, and some journal articles being submitted.
Pseudo Triangulations and Rigidity of planar graphs.
Following from a workshop on rigidity in Barbados a few years ago, there have been a number of joint papers connecting planar graphs which are generically rigid in the plane, with pseudotriangulations. Some of these papers can be found at the sites of some members of this collaboration: Professor Ileana Streinu and Professor Gunter Rote . One of these papers can be downloaded from
arXiv:math.CO/0307347, and a second one can be downloaded from arXiv:math.MG/0309156.
A specific project, with Ileana Streinu, applied the analysis of convexifying simple polygons in the plane to onevertex origami: when can a folded paper with one vertex (a folded cone) be flattened, or made into a convex cone, without any new folds?
Research Background
I was a student of GianCarlo Rota, at MIT. My thesis was on
logic and invariant theory  really the background of analytic geometry
and its connections to matroid theory. If people are interested
in more information about this remarkable individual, there is
further information available at
Rota.Org
Recent Preprints
 with Franco Saliola, Contraining Plane Configurations in CAD: circles
lines and angles; preprint, accepted for publication.
Avialable in PDF format from Franco Saliola's site
 with Laura Chavez and Lily Moshe,
Basis and Circuits for 2rigidity by
Tree Coverings, 2002
 Constraining Plane Configurations in CAD: geometry of lengths and directions; March 1996.
 with H. Crapo, 3stresses in 3space and projected 4polytopes: reciprocals liftings and parallel configurations, preprint (1993).
 with J. Owen (DCubed Ltd, Cambridge England), Constraining Plane Geometric Configurations in CAD: directions and distances, 1994.
Recent Publications
 To see like a mathematician, to be presented at the Visual
Representation and
Interpretation conference in Liverpool England in September 2002.
download
 Dynamic Geometry and the Practice of Geometry,
for distribution at ICME9 Tokyo, July 2000.
download a PDF file of this paper.
 The Decline and Rise of Geometry, to appear in the Proceedings of
the 1999 CMESG Conference
download a PDF file of this paper.
 with Brigitte Servatius, Constraining Plane Configurations in CAD: combinatorics of lengths and directions; SIAM J. Discrete Math. 12 (1999), 136153.
 Modeling Molecular Structures, in P. Duxbury and M. Thorpe (eds.), Rigidity Theory and Applications, Birkhauser Boston.
 An analogy in geometric homology: rigidity and cofactors on geometric graphs; Accepted for the Proceedings of the RotaFest, 1997.
 Matroids from Discrete Geometry, in Matroid Theory, J. Bonin, J. Oxley and B. Servatius (eds.), AMS Contemporary Mathematics, (1997), 171313.
 Rigidity and Scene Analysis; in the Handbook of Discrete
and Computational Geometry, J. Goodman and J. O'Rourke (ed.),
CRC Press, 1997, 893916.
 with Robert Connelly, Secondorder rigidity and prestress stability for tensegrity frameworks; SIAM J. on Discrete Methods 9 (1996), 453491.
 Representing geometric objects, Learning and Geometry: Computational Approaches, D. Kueker and C. Smith (eds.), Birkhauser 1996, 143178.
 Analytic vs synthetic geometry for computers, Learning and Geometry: Computational Approaches, D. Kueker and C. Smith (eds.), Birkhauser 1996, 121141.
 with TiongSeng Tay and Neil White, Skeletal rigidity of simplicial complexes: I; European J. of Combinatorics 16 (1995), 381403.
 with TiongSeng Tay and Neil White, Skeletal rigidity of simplicial complexes: II; European J. of Combinatorics 16 (1995), 503523.
 with H. Crapo, Spaces of stresses, projections, and parallel drawings for spherical polyhedra, Beitraege zur Algebra und Geometrie / Contributions to Algebra and Geometry 35 (1994), 259281.
 How to design or describe a polyhedron, J. of Intelligent and Robotic Systems 11 (1994), 135160.
 with Peter Alfeld and Larry Schumaker, The generic dimension of the space of C1 splines of degree d>8 on tetrahedral decompositions, SIAM J. Numerical Analysis (1993), 889920.
 with H. Crapo, Plane stresses and projected polyhedra I: the basic pattern, Structural Topology 20 (1993), 5568.
Walter Whiteley
email address:
whiteley@mathstat.yorku.ca
Department of Mathematics and Statistics.
York University
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