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Herman Servatius

Classes: C Term 2020

Discrete Mathematics

Foundations of Computer Science

• Education
• Fields of Interest
• Books
• Selected Articles by Topic
• Structural Rigidity
• Symmetry and Duality
• Graphs and Networks
• Algebra and Geometry
• Student Projects

Education

Ph.D. Syracuse University, 1987.

Dissertation: "Graph Groups"

Advisor: Jacques Lewin

Fields of Interest

• Combinatorics
• Rigiditiy of Structures
• Algebra and Group Theory
• Symmetry and Duality

Books

• "Combinatorial Rigidity," Graudate Studies in Math., AMS Press, 1993.

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Selected Articles by Topic

Structural Rigidity 

1. "Combinatorial Rigidity,"
2. "Higher order rigidity - What is the proper definition?"
3. "Path decompositions of rigid graphs",
4. "Abstract rigidity in n-space",

Symmetry and Duality 

1. "The Symmetry of Self-Dual Periodic Tilings",
2. "Cayley graphs and connectivity",
3. "Construction and classification of planar Cayley graphs",
4. "A note on the rank of self-dual polyhedra",
5. "Self-dual graphs",
6. "The 24 symmetry pairings of self--duality maps",
7. "Self--dual maps on the sphere",

Graph and Network Theory 

1. "The Structure of Locally Finite Two-Connected Graphs",
2. "Dual Eulerian Graphs I",

Algebra and Group Theory 

1. "Automorphisms of graph groups"
2. "Surface subgroups of graph groups",
3. "An Artin Relation of Length $n$ in the Braid Group,"
4. "Tree groups and the 4-string pure braid group,"
5. "The Tits conjecture and the 5-string braid group"
6. "Permutation representations of the symmetry groups of regular hyperbolic tessellations,"
7. "Cayley graphs of Coxeter and Artin groups,"
8. "The length of elements in free solvable groups,"
9. "The finite basis extension property and graph groups",
10. "Groups assembled by free and direct products",

Student Projects

• MQP
• Some future topics