Time： Every Monday &Wednesday (9:00-11:00), From 2016-04-11 to 2016-07-01 

Considering a diophantine equation with integral coefficients, there are algorithms to get solutions over the real numbers or modulo an integer. The question is how the rational solutions are distributed relatively to these real or modulo N solutions. More precisely, by putting a bound on the size of the solution we get a finite set of solutions. The reduction modulo an integer gives a map from this finite set to the finite set of solutions modulo that integer. Do all the fibres of this map have approximately the same cardinal ? If not, can we find an invariant explaining the differences?