Problem seminar in commutative algebra (and other mathematics)

This seminar has a format very different from the usual seminar activities. Instead of listening to talks on sporadic topics, we in the first place try to brainstorm and (hopefully) solve concrete problems suggested by the seminar participants. At the moment we are actively discussing different aspects and questions around the Waring problem for polynomials. The important aspects of suggested problems should be an easy elegant formulation snd relevance to mathematics in general. We are trying to avoid complicated technical language which usually shadows the content of good problems. 

The topic for the first seminar is "On the zero set of a multivariate polynomial with coefficients from {0,1} over a field of prime order”