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HU Credits:
2
Degree/Cycle:
2nd degree (Master)
Responsible Department:
Mathematics
Semester:
1st Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Prof Eran Nevo
Coordinator Office Hours:
Teaching Staff:
Prof Eran Nevo,
Dr. Orit Raz
Course/Module description:
The seminar will deal with the notion of graph rigidity. Graph Rigidity is a classic notion in mechanics, regarding motions of solid bodies connected along flexible hinges. For example, the 4-cycle graph is rigid in R^1 and flexible in R^2.
Rigidity relates geometry with combinatorics and algebra.
We will define the notion of rigid graphs and present the characterizations of Laman and of Lovasz-Yemini for rigid graphs embedded in the plane. We will review recent works (Kiraly-Theran, Jordan-Tanigawa and others), dealing with the threshold for a giant rigid component to emerge in a random graph (usually under the Erdos-Renyi model).
Course/Module aims:
Learning outcomes - On successful completion of this module, students should be able to:
Students will be exposed to topics from the study of graph rigidity.
Students will learn how to present mathematical results in front of a peer group.
Attendance requirements(%):
90%
Teaching arrangement and method of instruction:
Lecture
Course/Module Content:
The seminar will deal with the notion of graph rigidity. Graph Rigidity is a classic notion in mechanics, regarding motions of solid bodies connected along flexible hinges. For example, the 4-cycle graph is rigid in R^1 and flexible in R^2.
Rigidity relates geometry with combinatorics and algebra.
We will define the notion of rigid graphs and present the characterizations of Laman and of Lovasz-Yemini for rigid graphs embedded in the plane. We will review recent works (Kiraly-Theran, Jordan-Tanigawa and others), dealing with the threshold for a giant rigid component to emerge in a random graph (usually under the Erdos-Renyi model).
Required Reading:
List of papers to be read will given at the beginning of the course. The reading material will be in English.
Additional Reading Material:
Course/Module evaluation:
End of year written/oral examination 0 %
Presentation 90 %
Participation in Tutorials 10 %
Project work 0 %
Assignments 0 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %
Additional information:
Prerequisites: linear algebra, rings, discrete math, topology.
[Other recommended courses: algebraic topology, convexity, commutative algebra, algebraic geometry.]
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