Seidel Seminar

Seidel Seminar

There is a funny thing that occurs in mathematics where eigenvalues of various adjacency matrices of graphs capture information about the graph. Trivially, they give the number of vertices and edges of a graph. Less trivially, eigenvalues give bounds on the chromatic number, coclique number and other graph invariants. It is conjectured by Haemers that the eigenvalues of a graph almost always determines the isomorphism class.

This semester (Spring 2013), I am organising a learning seminar on the algebraic graph theory of J.J. Seidel. We will cover topics including two-graphs, strongly regular graphs and matrices relating to combinatorial properties of graphs. No prior background in algebraic graph theory will be assumed; during the course of the seminar, we will present a basic introduction to spectral graph theory. It will be a 2-hour per week seminar.

The seminar will follow the book Geometry and Combinatorics: Selected Works of J.J. Seidel, edited by D.G. Corneil and R. Mathon. We will present a paper each week.

Below is the schedule of talks. All talks are at 12:30 pm to 2:30 pm unless specified.

Date Title of Paper Speaker
January 25, 2013 A Survey of Two Graphs, J.J. Seidel, 1976 Krystal Guo
February 1, 2013 Equiangular Lines, P.W.H. Lemmens and J.J. Seidel, 1971 Matt DeVos
February 8, 2013 Quadratic Forms Over GF(2), P.J. Cameron and J.J. Seidel, 1972 Krystal Guo
February 15, 2013 The Regular Two-Graph on 276 Vertices, J.M. Goethals and J.J. Seidel, 1974 Tony Huynh
February 22, 2013 Bounds for Systems of Lines, and Jacobi Polynomials, P. Delsarte, P.J. Cameron and J.J. Seidel, 1976 Karen Yeats
March 1, 2013 Line Graphs, Root Systems, and Elliptic Geometry, P.J. Cameron, J.M. Goethals, J.J. Seidel and E.E. Shult, 1976 Avi Kulkarni
March 8, 2013 Strongly Regular Graphs with (-1,1,0) Adjacency Matrix Having Eigenvalue 3, Seidel, 1968. Krystal Guo
March 15, 2013 Strongly Regular Graphs Having Strongly Regular Subconsituents, P.J. Cameron, J.M. Goethals, and J.J. Seidel, 1977. Krystal Guo
March 22, 2013 Equi-isoclinic subspaces of Euclidean spaces, P.W.H. Lemmens and J.J. Seidel, 1973. Krystal Guo
March 29, 2013 Easter Weekend (no seminar)
April 5, 2013 Spherical Codes and Designs, P. Delsarte, J.M. Goethals and J.J. Seidel, 1977. Matt DeVos
April 12, 2013 Part 2 of previous week Matt DeVos
April 19, 2013 The Krein Condition, Spherical Designs, Norton Algebras and Permutation Groups, P. Delsarte, J.M. Goethals and J.J. Seidel, 1978. Krystal Guo