## 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 |