# Autobiography of Demetrios Christodoulou

I was born in Athens in 1951 to a lower middle class family. My father was born in Alexandria to Greek parents from Cyprus who had immigrated to Egypt. My mother was born in Athens to a family of Greek refugees from Asia Minor. Neither of my parents had higher education, but my father inspired me in childhood with stories from a distant past when ancient Greece had made outstanding contributions to human civilization. A problem in Euclidean geometry was the spark which initiated in me, in the summer of 1966, a burning interest in mathematics and theoretical physics. My case was brought to the attention of Achilles Papapetrou, a Greek physicist at IHP, who in turn contacted Princeton physics professor John Wheeler, on leave in Paris at that time. So, at the beginning of 1968 I came to Paris and was examined by them. This led to my admission as a graduate student in the Princeton physics department in the fall of 1968.

A decisive turn in my career came in 1977, at a time when I was a postdoctoral fellow at the Max Planck Institute for Astrophysics in Munich. There, Jurgen Ehlers, the leader of the group in which I was working, although himself a physicist, realized that I had a talent in mathematics and gave me an unlimited leave of absence with pay to study mathematics in Paris under the guidance of Yvonne Choquet-Bruhat. Thus, I finally found my true calling and in the period 1977-1981 I studied mathematical analysis in the French school.

In 1981, I returned to the U.S. and one of the first scientists I met was the famous Chinese mathematician Shing-Tung Yau. I became closely associated with him for a period of five years, an association which played a decisive role in my mathematical make-up. From Yau I learned geometry and how to effectively combine geometry with analysis in what is today called geometric analysis, a field which Yau pioneered. I can summarize my scientific contribution since, as the extension of geometric analysis from the initial field of elliptic equations to the field of hyperbolic equations.

The first work of geometric analysis of hyperbolic equations was my work with Sergiu Klainerman on the stability of the Minkowski space-time, the fruit of an intensive effort in the period 1984-1991. This work demonstrated the stability of the flat spacetime of special relativity in the framework of the general theory and gave a detailed description of the asymptotic behavior of the solutions. Basically, an initial disturbance in the fabric of space-time propagates, like the disturbance in a quiet lake caused by the throwing of a stone, in waves, the so-called gravitational waves. However, as I showed in a further 1991 paper, there is a subtle difference from the lake paradigm. For whereas spacetime becomes, again, like the lake, flat after the passage of the waves, the final flat spacetime is related in a non-trivial manner to the initial flat spacetime and this leads to an observable effect: the permanent displacement of the test masses of a gravitational wave detector.

Roger Penrose had introduced, in 1965, the concept of a trapped surface and had proved that a spacetime containing such a surface cannot be complete. A little later, it was shown that under the same assumption there is a region of spacetime which is inaccessible to observation from infinity: the black hole. However, the available mathematical methods were incapable of investigating how trapped surfaces form in evolution and of revealing the nature of the spacetime boundary. Penrose conjectured that the boundary is always contained in a black hole, a conjecture called cosmic censorship. Seeking to answer these questions in a simpler setting I studied, in a series of papers completed in the period 1984-1997, the spherically symmetric Einstein equations with a scalar field as the matter model. An unexpected result was that naked singularities, that is, singularities not contained in a black hole, can also form. Nevertheless, I proved that these are unstable, thus establishing a generic version of cosmic censorship in this framework.

As professor of mathematics at the Courant Institute 1988-1992 and at Princeton 1992-2001, I enjoyed a very stimulating scientific environment. In 2001, I returned to Europe, taking up my present position as professor of mathematics and physics at ETH in Zurich.

The period 2001-2008 was, for me, one of most intense intellectual effort. I turned to the study of the formation of shocks in compressible fluids in the physical case of 3 spatial dimensions. Here the aim was to carry out the analysis up to the singular boundary. The Eulerian equations of fluid mechanics have affinity with the Einstein equations of general relativity, both constituting nonlinear systems of hyperbolic type. At the same time, I turned to the study of the formation of trapped surfaces in general relativity, in vacuum and without any symmetry assumptions, through the focusing of incoming gravitational waves. The breakthroughs came in 2004, and the two works were completed in 2006 and 2008 respectively. In the case of the second work, the breakthrough took the form of a new method which exploits the assumption that the initial data contain somewhere an abrupt change and allows us to attack problems which had seemed unapproachable.

28 September 2011, Hong Kong