Discrete Algebra and Geometry 1 (DAG1)

ECTS: 4
(TU/e vakcode 2E040)

Topics

• Basic properties of block designs, designs from projective spaces over a finite field, the Bruck-Ryser-Chowla theorem.
• Permutation groups: (multiple) transitivity, primitivity, permutation rank, GL(n,q)-graphs,graphs from permutation groups.
• Mathieu designs and groups.
• Group presentations, Cayley graphs and Todd Coxeter.
• Hadamard matrices and designs, extensions, designs from transitive groups, difference sets.
• Association schemes and distance regular graphs.
• Automorphism group as a permutation group on vectors of given length.
• Codes, Hamming codes, MacWilliams relations.
• Assmus-Mattson theorem and applications.
• Latttices. E8, Leech lattice, connection with codes.
• Algebraic graph theory, eigenvalue spectra of distance regular graphs.
• Distance transitive graphs with imprimitive symmetry groups.

• Prof.dr. A. Blokhuis (TU Eindhoven) - course leader.
• Prof.dr. A.M. Cohen (TU Eindhoven).
• Dr. F.G.M.T. Cuypers (TU Eindhoven).
• Dr. J. Draisma (TU Eindhoven).
• Dr.ir. W.H. Haemers (Universiteit van Tilburg).
• Prof.dr.ir. H.C.A. van Tilborg (TU Eindhoven).
• Dr. A.J. van Zanten (TU Delft).

• Elements of algebra and number theory.

• P.J. Cameron and J.H. van Lint, “Designs, graphs, codes and their links”, London Mathematical Society Student Texts 22, Cambridge University Press, Cambridge, 1991.
• A.E. Brouwer, A.M. Cohen, A. Neumaier, “Distance-regular graphs”, Springer Verlag, Berlin, 1989.
• M. Suzuki, “Group Theory I”, Springer Verlag, Berlin, 1982.

Registration
You can register by sending an e-mail to: eidma@tue.nl at least two weeks before the course starts. This e-mail should contain your full postal address. Students from the TU Eindhoven should furthermore mention their student identification number. Please note that your registration is only official after our written confirmation.