What is the best (Numerically stable, robust, quickest, etc.) method to 
compute the resultant of two polynomials?

Implement of a good exclusion method for finding real solutions to polynomial systems.  
Interesting progress likely from using a mixture of exclusion methods and Ming Zhang's 
Bezier-subdivision.

Given a method to compute implicit equations from a parametrization, how 
(i.e. continuity, sensitivity to inputs) does the implicit equation depend upon 
the input polynomials.

Find good algorithms to approximately parametrize a curve.

How might numerical stability of, say surface creation be related to metric 
structures of algebraic objects.

Suppose that X is a rational surface.
How many different reparametrizations are needed to ensure that every real point of 
X is covered by a real parameter, in some reparametrization?

All cubic surfaces arise as the determinant of a matrix of linear forms.
Are there any special features of the cubic surface if the matrix has a 
special form, for example if the matrix is symmetric?

(Needs a clarification from Jorg)
Jorg is hoping that a mathematical analysis (?) could give different choices of basis
 functions to get more fairness in patches.   For example, how much can we expect or hope 
 to have linear precision?
 

(Clarification from Josef Schicho)
Why should we care about normal forms of real rational curves?

What can be said about linear precision for Toric Bezier patches?

What are good or desired basis functions for parametrization of (what?)

Classify M-patches

Describe the universal rational parametrization of del Pezzo surfaces

What Control structures are needed for, say Del Pezzo Surfaces of degree 4, in order to 
control their shape?   (By this we mean their features of degree 1 and 2.)

What is the multiplicity of a base point?  It equals the degree of the mase locus at a 
point only if it is a local complete intersection.