# 格尔德 · 法尔廷斯教授自传 (只提供英文版)

I was born July 28, 1954 in Gelsenkirchen, an industrial town in the then coal mining region of Germany called “Ruhrgebiet”. My parents originate from the Hamburg region and had PhD’s in Physics and in Chemistry. After primary school I attended the Max-Planck-Gymnasium, a high school, in Gelsenkirchen which I finished in 1972 with my Abitur. During my last years in high school I participitated twice successfully in the “Bundeswettbewerb Mathematik”, a competion for high school students interested in mathematics. As a result I became a member of the “Studienstiftung des deutschen Volkes”, a foundation dedicated to the support of talented students.

In the fall of 1972 I started to study mathematics at the University of Münster near Gelsenkirchen. Interrupted by 15 months of obligatory military service I finished my studies in 1978 with a diploma (in local cohomology) and a PhD (in Macaulayfication). My advisor was Professor H J Nastold who was specialising in commutative algebra, and so the topics are from that field. He co-organised a regular Oberwolfach meeting (together with Berger, Kunz, Szpiro) on commutative algebra.

The PhD enabled me to obtain a stipend from the Deutsche Forschungsgemeinschaft (a German NSF) to spend one year at Harvard University. My host was Professor Hironaka, to whom I was recommended by Professor Matsumura, an old friend of Professor Nastold. At Harvard I first learned about toroidal embeddings, a subject which became important to me later. Returning to Münster I became assistant to Professor Nastold and got my Habilitation in 1981. This allowed me to apply for professorships and to my surprise, the first application was successful. From 1982–84 I was a full professor at the University of Wuppertal. There I managed to prove the Mordell conjecture over numberfields, and this success changed my personal circumstances considerably. For example, I received my first prize, the Dannie-Heinemann award from the Academy in Göttingen. It involved a considerable amount of cash. Usually, such prizes are only given to established researchers who do not need the money anymore, so this was a pleasant exception. Also, in Wuppertal I met my future wife Angelika, and we got married in December 1984.

The Mordell conjecture was an old open problem and had been solved for function fields by (among others) Parshin and Arakelov. Szpiro had extended their theory to positive characteristics and tried to use Arakelov theory (another invention by Arakelov) to extend this to number fields. Unfortunately, one ingredient (the Kodaira-Spencer class) was missing. I was very fortunate to find that it could be replaced by a tool from the theory of Galois representations. Also, I profited very much from an Oberwolfach meeting (Arbeitsgemeinschaft) on the paper by Harris-Mumford proving that the moduli space of curves is usually of general type. So far, my knowledge of the theory of moduli spaces covered only the construction, after which everybody seemed to be exhausted. That they could be used for something was new to me.

From 1985–1994 I was full professor at Princeton University. In 1986 I was awarded a Fields Medal at the ICM in Berkeley, and especially recently this has been followed by quite a number of awards. Also, during my stay at Princeton my two daughters Christina and Ulrike were born (1985 and 1988). My mathematics at Princeton centred around two topics where an ad hoc solution was sufficient for the Mordell, but the full picture required more work. These were toroidal compactifications of the Siegel moduli space, and *p*-adic Hodge theory. On the first topic I wrote a book jointly with C L Chai, and on the second I extended ideas of J Tate to define “almost étale coverings”. In addition, I learned about a new idea of Vojta leading to a new proof of Mordell via diophantine approximation. Everybody talked highly about it but nobody seemed to be ready to declare it correct. Out of a sense of duty I studied it, found it to be correct, and as a reward also realised that the method allowed a vast generalisation (via the “product theorem”). At Princeton I also heard lectures from E Witten about string theory. As a result, I concluded firstly that physics is not a branch of mathematics, and secondly, was inspired to study moduli spaces of vector bundles on curves where I could show some new results. At Princeton I also was awarded a fellowship from the Guggenheim Foundation (1988).

In 1994 I accepted an offer from the Max Planck Society to become one of the directors of the Max Planck Institute for Mathematics in Bonn, and I am stll there. Shortly after resettling I was awarded a Leibniz-Preis (1996). I continued my work and watched my daughters grow up. Unfortunately, my wife died in 2011 so I am a widower. In recent years I have been honoured with a number of awards: von Staudt Preis 2008, Heinz Gumin Preis 2010, honorary degree from Münster 2012, King Faisal prize 2014, and finally the Shaw Prize 2015.

24 September 2015 Hong Kong