Speaker: Chris Godsil. MW 1:30 - 2:30 pm, starting September 20

News

Notes are updated yet again, with changes to Chapters 7 and 8, in particular. [24-11-21]

Outline

We will work through some of the connections between linear algebra and combinatorics. Most of the lectures will be supported by the course notes (link below) but, be warned, these notes may change as the course continues. Rough outline:

  1. Incidence matrices and rank arguments.
  2. Primary decomposition and Frobenius normal form.
  3. Spectral decomposition.
  4. Tensor products.
  5. Cospectral graphs, cospectral vertices.
  6. Perturbation theory.
  7. Eigenvalue bounds on cliques and cocliques.
  8. Type-II matrices, quantum permutations.
  9. Matrices over PIDs.
  10. Quantum channels.
  11. Orthogonal and unitary groups.

Resources: pdfs

  1. Course notes.
  2. Old survey on linear algebra and combinatorics. (Relevant to the first two lectures only.)
  3. Some exercises.
  4. Linear Algebra and Combinatorics. A famous textbook by Babai and Frankl.

Recordings of Lectures

Slides:

  1. Rank arguments
  2. Modules
  3. Frobenius normal form
  4. Eigenvalues, eigenvectors
  5. Constructing cospectral graphs
  6. Local switching
  7. Cospectral vertices
  8. Controllable graphs
  9. Commutative algebras
  10. Equitable partitions
  11. Continuous quantum walks
  12. Perturbation
  13. Inertia
  14. Type-II matrices
  15. Nomura algebras
  16. Coherent algebras
  17. Smith normal form
  18. Resolvents
  19. Burnside
  20. Gates
  21. Number theory
  22. Tree eigenvalues
  23. Periodic vertices

Videos

Contact

For further information, contact Chris Godsil.