Since I was seventeen my great passion has been the solution of partial differential equations. I used an old book written by Italian mathematicians to face for the first time the technique of variable separation applied to the free Schrödinger equation. The article was written by Paolo Straneo, professor at University of Genova in the first part of the last century and Einstein’s friend, and from it I was exposed to quantum theories in a not too simpler way. At eighteen, some friends of mine, during my vacation in Camdridge, gave to me my first book of mathematics on PDEs: François Treves, Basic Linear Partial Differential Equations. You can find this book at low cost from Dover (see here).
Since then I have never given up with my passion with this fundamental part of mathematics and today I am a professional in this area of research. As a professional in this area, important references come from the work of Terry Tao (see also his blog), the Fields medalist. Terry, together with Jim Colliander at University of Toronto, manage a Wiki, Dispersive Wiki, with the aim to collect all the knowledge about differential equations that are at the foundation of dispersive effects. Most of you have been exposed at their infancy with the wave equation. Well, this represents a very good starting point. On the other side, it would be helpful to add some contributions for Einstein or Yang-Mills equations. Indeed, Dispersive Wiki is open to all people that, like me, is addicted to PDEs and all matter around them.
I have had the chance to write some contributions to Dispersive Wiki. Currently, I am putting down some lines on Yang-Mills equations (I did it before but this was recognized as self-promotion… just look at the discussion there), Dirac-Klein-Gordon equations and other articles. I think it would be important to help Jim and Terry in their endeavor as PDEs are the bread and butter of our profession and to have on-line such a bookkeeping of results would be extremely useful. Just take your time to give a look.