Abstract: The finite Steinhaus problem asks whether for every set A in the plane with n>1 elements there could exist a Steinhaus set
S in the plane for A, that is, S meets every isometric copy of A in exactly one point. The conjecture is that this never happens.
The conjecture is easily true for n=2,3 and Xuan showed it for n=4. We make some connection between this problem and certain algebraic objects, and use this to prove the conjecture for n=5,7.

The talk(s) will start from scratch, and everyone is welcome.