Brigitte Servatius

Mathematics Department, Worcester Polytechnic Institute
100 Institute Road, Worcester, MA 01609-2280
Tel: (508) 831-5361
Fax: (508) 831-5824

MQP Topics.

HyperTriangle 2

HyperTriangle 3

HyperTriangle 3B

HyperTriangle6

HyperTriangle 6B

Geometric Series.

A vector field up close.

Power Point

PDF

Tensegrity Workshop at les Moutons Matheux -- Centre de recherche du Larzac méridional, July 2007.

• Proving Desargues from Pappus
• spdechedron01
• spdechedron03
• Today's lecture
• Molecular Conjecture in 2D
  • (at 16th Fall Workshop on Computational and Combinatorial Geometry - Smith College 2006 )
• Rigidity, Connectivity, and Graph Decompositions
  • (at Workshop: Flexibility of Polyhedra and Frameworks, E.Schrödinger Inst., 2006 )
• Rigidity and Global Rigidity
  • (at Discrete Mathematics Day at Mt. Holyoke College - April 2005 )
• Combinatorics catalogs Geometry - Geometry generates Combinatorics
  • (at MD-DC-VA Section of the MAA Fall 2005 Meeting )
• The State of U.S. Science as reflected in restored 18'th century patents
  • (at Vega Days - Slovenia, 2004 )

• Editorial Work
• Fields of Interest
• Books
• Selected Articles by Topic
  • Structural Rigidity
  • Symmetry and Duality
  • Computer Aided Design
  • Network Theory
  • Group Theory
  • Mathematics Teaching
• Student Activities
• Student Projects
• Education

Editorial Work

• PME Journal
• College Math Journal

Fields of Interest

• Combinatorics
• Rigiditiy of Structures
• Geometric Foundations of Computer Aided Design
• Symmetry and Duality
• The History and Philosophy of Mathematics

Books

• "Combinatorial Rigidity," Graudate Studies in Math., AMS Press, 1993.
• "The Bracing of Grids," The GEOMAP Project, COMAP, 1995.
• "Matroid Theory," Contemporary Math., AMS, 1996.

Selected Articles

Structural Rigidity

1. "Combinatorial Rigidity,"
2. "The Bracing of Grids,"
3. "Birigidity in the plane,"
4. "On the two dimensional generic rigidity matroid and its dual",
5. "Path decompositions of rigid graphs",
6. "Combinatorics and the rigidity of frameworks",
7. "Abstract and generic rigidity in the plane",
8. "Abstract rigidity in n-space",
9. "Graphs, digraphs, and the rigidity of grids"
10. "On the Rigidity of Ramanujan Graphs",
11. "Planar Minimally Rigid Graphs and Pseudo-triangulations",
12. "Non-crossing frameworks with non-crossing reciprocals",
13. "Combinatorial Pseudo-Triangulations",
14. "The 2-dimensional rigidity of certain families of graphs",

Symmetry and Duality

1. "Applying Burnside's lemma to a one-dimensional Escher problem",
2. "The Symmetry of Folding Paper Dolls",
3. "Cayley graphs and connectivity",
4. "Construction and classification of planar Cayley graphs",
5. "A note on the rank of self-dual polyhedra",
6. "Self-dual graphs",
7. "The 24 symmetry pairings of self--duality maps",
8. "Self--dual maps on the sphere",
9. "Symmetry, automorphisms, and self-duality of infinite planar graphs and tilings ",

Graph and Network Theory

1. "The Structure of Locally Finite Two-Connected Graphs",
2. "Analyzing the reliability of degradable networks",
3. "2-satisfiability and the diagnosis of faulty processors in massively parallel computing systems",
4. "A note on Gaussian graphs",
5. "Dual Eulerian Graphs,",
6. "A polynomial time algorithm for determining zero euler-petrie genus of an eulerian graph,",

Computer Aided Design

1. "Constraining plane configurations in CAD: The combinatorics of direction length designs",
2. "The Geometry of Frameworks: Rigidity, Mechanisms and CAD",

Group Theory

1. "Surface subgroups of graph groups",
2. "The finite basis extension property and graph groups",
3. "Groups assembled by free and direct products",
4. "Blanuša double",

Student Activies

• Pi Mu Epsilon
• Putnam Exam
• Math Awareness Week
• Math Hour
• Mathematical Treasure Hunt
• Bulletin Board Competition

Student Projects

• IQP's Advised
• MQP's Advised
• Theses Advised

Education

PhD. Syracuse University, 1987. Jack Graver, advisor.

Mathematics Master Thesis:

\"{U}berlagerungen von Graphen (Coverings of Graphs)

Physics Masters Thesis:

Das Wasserstoffatom und seine Strahlung (The Hydrogen Atom and its Radiation)

PhD Dissertation:

"Planar Rigidity,"