Brigitte Servatius

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

Class 2021

Univerity of Puerto Rico, Talk 2022

Ryerson 2022

Contents

• Editorial Work
• Fields of Interest
• Books
• Selected Articles by Topic
  • Structural Rigidity
  • Symmetry and Duality
  • Computer Aided Design
  • Network Theory
  • Group Theory
  • Mathematics Teaching
• Meetings
• 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.
• "Planar Rigidity," PhD Disseration, Syracuse University, 1987.

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

Meetings

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

Slides from a selection of talks.

• AMS Western Section Meeting, Portland, OR. 2002
• Fifth Yugoslavian International Conference On Graph Theory, Bled, 2003.
• Modeling Protein Flexibility and Motions, Banff International Research Station, 2004.
• Technische Universität Graz, 2005.
• 15th Fall Workshop on Computational and Combinatorial Geometry (fwccg) Mount Holyoke College, 2005.
• MAA Eastern Section, Montgomery College, 2005.
• ESI-Program on Rigidity and Flexibility, 2006.
• 16th Fall Workshop on Computational and Combinatorial Geometry (fwccg) Smith College, 2006.
• Southeast International Conference on Combinatorics, Graph Theory and Computing, Florida, 2007.
• Institute for Mathematics and its Applications, Minneapolis, 2008.
• Cool Math Talk, WPI, 2008.
• Oregon State University Colloquium, 2008.
• Pi Mu Epsilon Address, Fitchburg, 2008.
• Fall Workshop on Computational Geometry, RPI, 2008.
• AMS Sectional MeetingWPI, 2009.
• Fall Workshop on Computational Geometry, Tufts, 2009.
• Rigidity of Frameworks and Applications, Lancaster UK, 2010
• Mathfest Special Session, Visualizing Combinatorics Through Tilings, Pittburgh, 2010.
• AMS Special Session on Graphs Embedded in Surfaces, and Their Symmetries, Syracuse NY, 2010
• 7th Yugoslavian International Conference on Graph Theory, Bled, 2011.
• Discrete Math Day, Vermont, 2011.
• AWM 40th Anniversary, ICERM,Brown, 2011.
• Workshop on Rigidity and Symmetry, Fields Institute, 2011.
• AMS Special Session on Discrete Geometry in Crystallography, USF, Tampa, 2012.
• Workshop on Rigidity Theory, Banff, 2012.
• Pi Mu Epsilon Induction, Westfield State, 2013.
• Summer Combo in Vermont, 2013.
• AMS Special Session on Discrete Geometry in Crystallography, University of Maryland, 2014.
• Workshop on Configuration Spaces of Linkages, AIM, 2014.
• Workshop on Advances in Combinatorial and Geometric Rigidity, Banff, 2015.
• Séminaire de Géométrie Algorithmique et Combinatoire, l'École polytechnique, Paris, 2017.
• Discrete Math Day, Dartmouth, 2017
• SIAM Session on Matroid Theory, Denver, 2018
• Bob Connelly 75th Birthday Conference, Stability of Structures, Large and Small, Cornell, 2017.
• Bond-node structures: rigidity, combinatorics and materials science, Lancaster University, UK, 2017.
• A Gathering of Worcester Mathematicians, Joyce Contemplative Center, 2018.
• Pi Mu Epsilon Golden Galla, St. Peters University, 2018.
• IMA Workshop for Women in Mathematical Biology, Minnesota, 2018.
• Workshop on Rigidity and Flexibility of Geometric Structures, Erwin Schoedinger Institute, Vienna, 2019.
• Denksport, WPI 2018.
• Discrete Mathematics Research Group, Monash University, 2018.
• 50'th Southeast International Conference on Combinatorics, Graph Theory and Computing, FAU, 2019.
• Worskshop on Soft Packings, Nested Clusters, and Condensed Matter, The Casa Matemática Oaxaca (CMO), 2019.
• AIM Workshop on Rigidity and flexibility of microstructures, 2019.
• 51'st Southeast International Conference on Combinatorics, Graph Theory and Computing, FAU, 2020.
• ICERM Workshop on Circle Packings and Geometric Rigidity, Brown University, 2010.

In the Media

• OSTA Profile: Office of Science and Technology of Austria
• Midi Libre
• Der Standard Interview

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,"