On Thursday 13th of July, Pierre Colmez will give a colloquium talk on the following subject:

The congruent number problem.

An integer is said to be congruent if it is the area of a rectangle triangle with sides of rational length.  Deciding whether a given number is congruent or not is a very old problem (the first written mention dates from more than 1000 years ago) and usually quite difficult.  I will explain a (conjectural) solution to this problem.