Values and Ideals in Combinatorial Problems

  • Date: 04/18/2007

Bernhard Schmidt (Nanyang Technological University)


University of Calgary


The absolute value of complex numbers is surprisingly useful in the
investigation of certain combinatorial problems. The connection often
arises from imbedding finite cyclic groups into the complex numbers by
sending the group elements to roots of unity. The modulus of the
resulting sums of roots of unity usually is known explicitly, which
allows the application of two powerful tools: the ideal theory of
algebraic numbers and size arguments involving the absolute value of
complex numbers. We will present some highlights of this approach
including recent progress on Circulant Hadamard Matrices, Barker
Sequences, Ryser's and Lander's Conjectures.

Other Information: 

10th Anniversary Speaker Series 2007