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."