## 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.

10th Anniversary Speaker Series 2007