DiscMathMeeting: News from Banff

This is the first of three independent short talks on what I learned on my last trip.

This one concerns the workshop on ``Coarsely Quantized Redundant Representations of Signals'' in the ``Canadian Oberwolfach'' in Banff.
There the following surprising result emerged:

Any matrix with entries in [0,1] can be quasi-rounded to one with entries in {-1,0,1,2) such that the rounding error in each rectangular submatrix (consecutive rows and columns) is less than two. This is surprising since rounding to {0,1} can only be done with at least logarithmic error (hence allowing -1 and 2 really helps). From this recent progress, a banff of new open questions arise. Many of them might be suitable also for people usually working in different areas.

I should note that the new result also has a much simpler proof than earlier ones. In fact, I can recommend to any-one thinking about the problem him/herself for half an hour. It is quite likely that you find the answer yourself.