> Duality in mathematics has been a profound tool for theoretical understanding. Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel algorithms?
Duality in mathematics is in general a principle that objects in one category can be mapped onto another category (and vice versa), that two objects are reflections of each other in some abstract sense.
https://en.wikipedia.org/wiki/Duality_(mathematics)
It most often appears as a principle in geometry. Looking at or working with the 'dual' of something can give additional insight or allow another way of working. For example, Fourier Transform can be considered a type of duality.
I'm not clear what computational techniques are expected here - I personally don't think it's a very well-formed problem.