Departmental/CECM Colloquium

June 11, 2003 in CoLab, SFU

2:30 - 3:30
Alf van der Poorten
Macquarie, Australia

Title: "An introduction to continued fractions of quadratic irrationals."

Abstract: The continued fraction expansions (cfe s) of $\sqrt D$ with $D=59$ (the age of a friend whose 60th was recently celebrated) and with $D=41$ (the age I believe myself to be living at) display the well known symmetries in the period of the cfe of a quadratic irrational integer. I use that information to expand the square root of a generic quartic polynomial so as to obtain all pseudo-elliptic integrals involving the square root of a quartic.

3:30 - 4:30
Richard E. Crandall
Director, Center for Advanced Computation, Reed College

Title: "Digitally motivated analysis: New results in transcendency theory."

Abstract: It turns out that binary expansions of algebraic numbers are not entirely arbitrary; such expansions must obey certain constraints. Recently, new constraints have been discovered, thereby establishing new classes of provably transcendental numbers. The lecturer will indicate some open problems in regard to such "digitally motivated analysis."