# Demetrios Lambrou Christodoulou

### Quick Info

Athens, Greece

**Demetrios Christodoulou**is a Greek theoretical physicist and mathematician who has made major contributions to general relativity, black holes and shocks in compressible fluids. He has won many major awards including the Shaw Prize.

### Biography

**Demetrios Christodoulou**was the son of Lambros Christodoulou (1913-1999) and Maria Georgiadis (1925-2014). His mother Maria was born in Athens on 18 February 1925. Maria's father was from Samsonta in Pontus (now called Amisos) and her mother was from Bithynia. Demetrios's

**father Lambros was born in Alexandria but Lambros's father Miltiades had come from Agios Theodoros and his mother Eleni from Choirokoitia in Cyprus. In fact, Christodoulou's grandfather's father was named Lambros Pafitis and was born in Letymbou, in the Paphos district of Cyprus. He migrated to Agios Theodoros in the province of Larnaca at the end of the 19th century, due to the very bad economic conditions of that time in the province of Paphos, and changed his surname to Christodoulou.**

Demetrios

**began his primary schooling at the Lyceum of Athens, in the Psychico district in north Athens. The school had been founded in 1936 but moved to its location in the Psychico district in 1952 when Antonis Moraitis became the headmaster. Demetrios continued his secondary education at the same school which was renamed the Moraitis School in 1976 but Demetrios had left long before then. It was when he was in the third grade at this school that he became interested in mathematics, becoming fascinated with Euclidean geometry. In 1966, during the summer between his third and fourth year of high school, Christodoulou tried to find a ruler and compass construction to trisect an angle. Of course, this had been proved impossible, but the young schoolboy was not aware of this [6]:-**

[Christodoulou] himself confesses today that it was his futile attempt to find the non-existent solution that caused him to suspect the immense depth of mathematics.During the fourth grade at the Lyceum of Athens, he studied National Technical University of Athens textbooks, while he started buying books from the Eleftheroudakis bookstore in Athens containing difficult physics and mathematics exercises and was able to solve all the exercises he found in them.

The year 1968 was a highly significant one for Christodoulou who was already achieving fame in Athens. The local papers reported on his fame with headlines like "Student-Einstein: High School Student Reads Higher Mathematics and Solves Difficult Problems." Spyros Michalopoulos, a mechanical engineer at the National Technical University, was a friend of the Christodoulou family. He was a student and acquaintance of the eminent Greek theoretical physicist Achille Papapetrou who was working at the Henri Poincaré Institute in Paris. When Michalopoulos met up with Papapetrou he told him about the remarkable way that Christodoulou was teaching himself advanced mathematics. At the beginning of 1968, Papapetrou invited Christodoulou to Paris for a week so that he might meet with the famous theoretical physicist John Archibald Wheeler (1911-2008). Wheeler, a professor at Princeton University who had studied under Niels Bohr, was spending research leave in Paris at the time. He suggested that Christodoulou should go to Princeton as a graduate student in theoretical physics. Christodoulou was quick to follow this advice and left the Lyceum of Athens without a high school diploma. From February to September 1968 he prepared for his studies at Princeton.

In September 1968 Christodoulou began studying for an M.A. at Princeton University which he received in 1970. By this time, however, he already had published his first, highly important, paper. Remo Ruffini writes [27]:-

After one year Christodoulou entered the graduate school and started collaborating with me. At the time I was working with Wheeler on the effective potential approach to geodesics co-rotating and counter-rotating in the Kerr metric. In parallel, Frank Zerilli was working on the gravitational radiation emitted by the fall of a test particle in a Schwarzschild black hole. A new approach started with the arrival of Demetrios: he was just creating mathematics following his needs. We identified the reversible and irreversible transformations of a Kerr black hole. Wheeler advanced a thermodynamic analogy. I addressed the need of identifying the concept of irreducible mass and Demetrios's contribution was to integrate, overnight, the differential equation for infinitesimal reversible transformations which led to the finite mass-energy formula of a Kerr black hole. That evening, while walking back home through the Institute for Advanced Study woods, I expressed to Wheeler the great relevance of the newly found formula by Demetrios and proposed to let Demetrios be the single author of this article, admiring his great mathematical talent. Wheeler agreed.This paper by Christodoulou was

*Reversible and irreversible transformations in black hole physics*(1970). He writes in [28]:-

When I first presented [the paper], Wheeler, seeing that a new chapter was opening, the thermodynamics of black holes, became so excited that he set off firecrackers. He had, you know, a particular love of explosions.The paper has the acknowledgement:-

I would like to thank Professor J A Wheeler and Dr R Ruffini for very helpful discussions and suggestions.Christodoulou and Ruffini continued working with the solution that Christodoulou had found and published the joint paper

*Reversible transformations of a charged black hole*(1971). It has the following Abstract:-

A formula is derived for the mass of a black hole as a function of its "irreducible mass," its angular momentum, and its charge. It is shown that 50% of the mass of an extreme charged black hole can be converted into energy as contrasted with 29% for an extreme rotating black hole.At the age of 19, just three years after entering Princeton, Christodoulou completed a doctoral thesis under the supervision of John Archibald Wheeler and Remo Ruffini. The title of his thesis was

*Investigation in gravitational collapse and the physics of black holes*. In it he shows that the area of a black hole is proportional to its entropy. The Abstract begins:-

This thesis deals with the physics of gravitational collapse and its final states, the collapsed objects called black holes. We know that a star, that is at the end point of thermonuclear evolution, will be unstable against gravitational collapse if its mass is larger than a certain critical mass. Will radiation be similarly unstable above a certain critical mass-energy and undergo gravitational collapse? This question is treated in Chapter II, in considering an imploding and re-exploding scalar pulse of radiation, and is answered in the affirmative.The thesis was examined by a committee which included Eugene Paul Wigner, John Archibald Wheeler and Remo Ruffini. Christodoulou graduated with a Ph.D. from Princeton in 1971.

Will a black hole always be stationary? Will the physics of the dynamical region inside the event horizon never come into play? No - in Chapter III it is shown that the dynamics of the interior geometry comes into play in the final stages of collapse of the Universe itself, and the Schwarzschild singularity is amalgamated into the Friedmann singularity.

In Chapter V, we show various processes that extract energy from a rotating black hole. The first such method was investigated by R Penrose. Here, the concepts of irreducible mass and of reversible and irreversible transformations in black holes are introduced. ...

Following the award of his doctorate, Christodoulou was appointed as a Research Fellow at the California Institute of Technology where he spent the academic year 1971-72. He continued to work with Remo Ruffini and published papers such as

*The electrodynamics of collapsed objects*in 1973. It has the following Abstract:-

The details of the magnetic and electric field to be expected in a collapsed object nonradioactive at infinity ("Black Hole") are here given. Also given are the formulae determining the maximum total energy extractable from a collapsed object and the definition of its angular velocity as seen from infinity. Physical meaning is given to the expression of the surface area. Typical order of magnitude of the preceding quantities for collapsed objects of different masses are here estimated.He returned to Greece in 1972 when he was appointed as a Professor of Physics at the National and Kapodistrian University of Athens. In January 1973 there was the following announcement of the engagement of Demetrios Christodoulou and Kathleen Kelly [31]:-

Mr and Mrs Frank R Kelly of South Pasadena announce the engagement of their daughter, Kathleen, to Dr Demetrios L Christodoulou of Athens, Greece. Kathleen is a graduate of South Pasadena High and Pasadena City College. She will be continuing her studies in nutrition at the University of Athens. Dr Christodoulou is the son of Mr and Mrs Lambros Christodoulou of Athens. He received his degrees from Princeton University, lectured at California Institute of Technology and returned to Athens last fall to accept the 2nd Chair of the Theoretical Physics Department, University of Athens. The wedding will be held the evening of 8 March, in historical settings in Athens. The couple will visit the Isle of Rhodes and then return to Athens to make their home.Demetrios and Kathleen Christodoulou had two children, Penelope Christodoulou and Alexandra Christodoulou. Let us note at this point that Demetrios and Kathleen Christodoulou were divorced in May 1995 and Demetrios married Nikoleta Sigala, on 12 June 1997.

Although Demetrios and Kathleen Christodoulou made their home in Athens after their honeymoon on Rhodes, they moved to Geneva in Switzerland before the end of 1973 where Christodoulou spent a year as a Visiting Scientist at CERN. It was in 1952 that CERN, the European Council for Nuclear Research, was set up and the site in Geneva was chosen. By the time Christodoulou visited CERN, they had made great steps forward with the announcement of the first colliding protons being detected. After the year at CERN, Christodoulou moved to the International Centre for Theoretical Physics in Trieste where he spent two years 1974-76. While there he published

*The chronos principle*(1975) with Abstract:-

The definition of time is established as a fundamental physical principle. From this principle, in connection with the quantum and relativity principles, the laws of quantum geometrodynamics and, in the classical limit, those of general relativity theory, are uniquely deduced.In 1976 Christodoulou became a fellow of the Humboldt Foundation and spent the following five years at the Max Planck Institute for Theoretical Astrophysics in Munich. Up to this time, although he had shown great mathematical skills, his work had been in theoretical physics. It was while he was at the Max Planck Institute, however, that his interests turned more to mathematics. Partly, this was because mathematics had always had great appeal to him, but partly it was due to Jürgen Ehlers, the director of its gravitational theory department at the Max Planck Institute, who saw the enormous potential in Christodoulou's mathematical skills. Christodoulou wrote [5]:-

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, Jürgen Ehlers, the leader of the group in which I was working, although himself a physicist, realised 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.He began a collaboration with the Italian mathematician Mauro Francaviglia (1953-2013) who was based in Turin and worked on applying methods of differential geometry to problems in mathematical physics. For example they published the joint paper

*Remarks Concerning the Solution of the Equations of Quantum Geometrodynamics by Successive Approximation*in 1977. The paper ends with the following Acknowledgement:-

This work was sponsored by the "Seminario Matematico dell'Università e Politecnico di Torino." We wish to express our gratefulness to Professor D Galletto and to Professor T Zeuli, who invited one of us (D Christodoulou) to Turin, making our collaboration easier.Another joint paper by Christodoulou and Francaviglia in 1977 was

*Remarks about the thin sandwich conjecture*. It has the following Abstract:-

The thin sandwich conjecture in the initial value problem of general relativity is investigated by means of differential geometrical methods, in connection to the definition of arc length in a Wheeler superspace. The conjecture is proved to be false by good physical reasons. Its failure on a flat space is related to the "functional dimension" of the superspace and to the behaviour in the linearised theory of quantum gravitation.Studying with Yvonne Choquet-Bruhat in Paris led to the three author paper

*Cauchy data on a manifold*(1978) by Yvonne Choquet-Bruhat, Demetrios Christodoulou and Mauro Francaviglia. The same three authors published

*On the wave equation in curved spacetime*(1979).

In 1981 Christodoulou returned to the United States when he spent two years as a visiting member of the Courant Institute in New York. The year 1981 also marks the time when he received his first major award, namely the Otto Hahn Medal awarded by the Max Planck Society in June of that year. Soon after arriving back in the United States, he met Shing-Tung Yau. In [7] he explains the importance of this meeting:-

I first met Yau in September 1981. I had arrived in New York from Germany a few days earlier for what turned out to be a 2-year visiting membership at the Courant Institute. I knew the Princeton area well because I had been a Ph.D. student in physics in the period 1968-1971, so I looked for housing there, the plan being to commute by train to New York. I sought people at the University and at the Institute and Yau was one of the first people I met. ... my working mathematical knowledge at that point was limited to the field of analysis. I had no working knowledge of geometry. Yau's directness of character and his hands on approach to mathematical problems, cutting through formalities to get to the heart of the matter, won me over from the beginning. He was giving a course on minimal surface theory and applications, in particular the application in the proof of the positive mass theorem, a course which continued for the next academic year. So I decided to stay most of each week at Princeton, follow his course, and learn as much as I could from him.For twelve years, after the award of his doctorate in 1971 until 1983, Christodoulou had postdoctoral positions, visiting positions and fellowships. His last visiting position in these years was from January to June 1983 at the School of Mathematics at the Institute for Advanced Study at Princeton. Only in September 1983 did he accept a permanent faculty appointment when he was appointed as Associate Professor of Physics at Syracuse University in Syracuse, New York State about 300 km north of New York City. Yau arranged for Christodoulou to be a member of the School of Mathematics at the Institute for Advanced Study from January to June 1984. He managed to fit this in with his lecturing duties at Syracuse University by having all his lectures in the first part of each week, flying to Newark each Wednesday evening and then bus to Princeton. He flew back to Syracuse each Sunday evening.

In the spring of 1985, Christodoulou changed departments at Syracuse when he became Professor of Mathematics there. He was given study leave from January to August 1986 which he spent at the University of California San Diego, working with Yau. Also in San Diego at this time was Richard Hamilton with whom he would later share the Shaw Prize. By 1986 Christodoulou was already working with Sergiu Klainerman on the problem of the global nonlinear stability of the Minkowski spacetime. This led to a number of papers and the jointly authored book

*The global nonlinear stability of the Minkowski space*(1993). Even before the book was published, his work with Klainerman was one of the factors leading to Christodoulou receiving the Basilis Xanthopoulos Award in 1991. It was awarded [29]:-

... for his many basic contributions to rigorous mathematical results in the general theory of relativity. They include: i) the boost theorems which establish the existence of a large class of solutions to Einstein's (and Yang-Mills) equations in a region obtained by boosting the initial Cauchy surface a finite amount; ii) a complete mathematical analysis of the spherical collapse of a scalar field including the structure of the horizons and singularities; and iii) his work with Klainermann on the global existence of solutions to Einstein's equations with weak initial data.By the time he won this award, Christodoulou had left Syracuse and returned to the Courant Institute where he was Professor of Mathematics from 1988 to 1992. Peter Lax, who worked at the Courant Institute for most of his career, was delighted to see Christodoulou back. Speaking of Christodoulou, Lax said [32]:-

Fortunately, after 2300 years, the Greeks have returned to mathematics!Christodoulou moved to Princeton in 1992 when he was appointed as Professor of Mathematics there. In 1993 he was awarded the prestigious MacArthur Fellows Award which supported his work over the following five years.

In 2001 he made his final move, going back to Europe to become Professor of Mathematics and Physics at ETH Zurich. He retired in 2017, remaining in Zurich as Professor Emeritus.

After taking up the professorship in Zurich, Christodoulou began to study the formation of shocks in compressible fluids. Although this appears at first sight to be quite a different problem to the equations of general relativity, in fact there are strong similarities, both leading to nonlinear systems of hyperbolic type. The "shocks" problem led to his book

*The Formation of Shocks in 3-Dimensional Fluids*(2007) while the related problems for general relativity are contained in his book

*The Formation of Black Holes in General Relativity*(2009).

For information about these books and other books by Christodoulou, see THIS LINK.

We have mentions some awards made to Christodoulou but let us now briefly mention some more. In 1999 the American Mathematical Society awarded Demetrios Christodoulou the Bôcher Prize:-

... for his contributions to the mathematical theory of general relativity.In January 2000 Demetrios Christodoulou was awarded the Zenon Prize by the Mathematical Society of Cyprus. He was awarded the Bodossaki Excellence Award in 2006:-

... for his considerable contribution to the theory of general relativity and gravity.The 2008 Tomalla Prize was awarded to Demetrios Christodoulou:-

... for his important contributions to general relativity, especially for his rigorous demonstration of global non-linear stability of Minkowski spacetime.The 2011 Shaw Prize was awarded jointly to Demetrios Christodoulou and Richard S Hamilton:-

... for their highly innovative works on nonlinear partial differential equations in Lorentzian and Riemannian geometry and their applications to general relativity and topology.In 2016 he was awarded the Nemitsas Foundation Prize for Mathematics. Following that, he was next awarded the Henri Poincaré Prize in Mathematical Physics 2021:-

... for pathbreaking contributions to mathematical understanding of the Einstein equations, including fundamental results on black hole formation and the discovery of a nonlinear memory effect in the theory of gravitational radiation, and for introducing a powerful geometric point of view for the problem of shock formation for compressible fluids.Christodoulou was awarded a 2021 Marcel Grossmann Award by the International Centre for Relativistic Astrophysics:-

... for his many lasting contributions to the foundation of mathematical physics including the dynamics of relativistic gravitational fields.For more information about all these awards to Christodoulou, see THIS LINK.

Finally let us mention other honours given to Christodoulou. These include: Honorary Doctorate in the Sciences, University of Athens (June 1996); Honorary Doctorate in the Sciences, National Technical University of Athens (May 2000); elected to the American Academy of Arts and Sciences (April 2001); Honorary Doctorate in the Sciences, Brown University (May 2001); Honorary Doctorate in the Sciences, University of Cyprus (May 2003); Honorary Doctorate in the Sciences, Aristotle University of Thessaloniki (May 2010); elected to the U.S. National Academy of Sciences (May 2012); elected a fellow of the American Mathematical Society (November 2012); elected to the Academia Europea (June 2016); and Honorary Professor, Department of Physics, University of Crete (October 2023).

### References (show)

- 1991 Xanthopoulos International Award for Research in Gravitational Physics,
*Department of Physics, University of Crete*.

https://www.physics.uoc.gr/Xanthopoulos/1991.html - 2011 Shaw Prize Mathematical Sciences,
*The Shaw Prize*.

https://www.shawprize.org/laureates/2011-mathematical-sciences/ - 2021 Marcel Grossmann Awards Announced,
*Institute for Advanced Study*(9 July 2021).

https://www.ias.edu/news/2021/marcel-grossmann-award - An Essay on the Prize, 2011 Shaw Prize Mathematical Sciences,
*The Shaw Prize*(28 September 2011).

https://www.shawprize.org/laureates/2011-mathematical-sciences/?type=Essay&laureate=1 - Autobiography of Demetrios Christodoulou,
*The Shaw Prize*(28 September 2011).

https://www.shawprize.org/autobiography/Demetrios-Christodoulou/ - Award Ceremony for the Nemitsas Prize in Mathematics,
*The Takis and Louki Nemitsas Foundation*(3 October 2016).

https://nemitsasfoundation.org/en/awards/omilia-tou-kathigiti-mariou-mavronikola-kata-tin-teleti-aponomis-tou-vraveiou-nemitsas-sta-mathimatika-stis-3-oktovriou-2016-sto-proedriko-megaro/ - D Christodoulou, Reminiscences of Yau,
*Notices of the American Mathematical Society***7**(1) (2019), 9-11.

https://www.intlpress.com/site/pub/files/_fulltext/journals/iccm/2019/0007/0001/ICCM-2019-0007-0001-a007.pdf - Christodoulou Demetrios: Honorary Professor,
*Department of Physics, University of Crete*(2024).

https://www.physics.uoc.gr/en/faculty/d.christodoulou - Christodoulou receives the MacArthur Award,
*Notices of the American Mathematical Society***40**(7) (1993), 850. - Christodoulou and Hamilton Awarded Shaw Prize,
*Notices of the American Mathematical Society***58**(9) (2011), 1293. - Demetrios Christodoulou CV,
*ETH Zurich*.

https://people.math.ethz.ch/~demetri/CV.pdf - Demetrios Christodoulou,
*National Academy of Sciences*.

https://www.nasonline.org/member-directory/members/20027256.html - Demetrios Christodoulou,
*Academia Europaea*(2024).

https://www.ae-info.org/ae/Member/Christodoulou_Demetrios - Demetrios Christodoulou,
*MacArthur Foundation*(1 January 2005).

https://www.macfound.org/fellows/class-of-1993/demetrios-christodoulou - Demetrios Christodoulou, Prabook.

https://prabook.com/web/demetrios.christodoulou/484245 - Demetrios Christodoulou, KOMVOS: Networks of Global Hellenism.

https://komvos-node.org/en/demetrios-christodoulou/ - Demetrios Christodoulou, American Academy of Arts & Sciences (2024).

https://www.amacad.org/person/demetrios-christodoulou - Demetrios Christodoulou: Honorary Doctorate, University of Cyprus (2003).

https://www.ucy.ac.cy/mas/people/honorary-doctorate/?lang=en - R Durrer, Laudatio for the Tomalla Prize 2008 for Demetrios Christodoulou, The Tomalla Foundation

http://www.tomalla.ch/docs/speechChris.pdf - Greek mathematicians share the Aristeio prize, ekathimerini.com (10 June 2006).

https://www.ekathimerini.com/culture/41019/greek-mathematicians-share-the-aristeio-prize/ - M Krichel, Demetrios Christodoulou: Nemitsas Prize, Department of Mathematics, ETH Zurich (20 October 2016).

https://math.ethz.ch/news-and-events/news/d-math-news/2016/10/demetrios-christodoulou-nemitsas-prize.html - Marcel Grossmann Awards, International Centre for Relativistic Astrophysics Network
- A Markris, Demetrios Christodoulou Wins "Shaw Prize in Mathematical Sciences", Greek Reporter (10 June 2011).

https://greekreporter.com/2011/06/10/demetrios-christodoulou-wins-shaw-prize-in-mathematical-sciences/ - F Meyer, ETH Zurich researcher wins "Asia's Nobel Prize", ETH Life (8 June 2011).

https://www.ethlife.ethz.ch/archive_articles/110608_Shaw_Prize_fm/index_EN.html - Nemitsas Prize 2016, The Nemitsas Foundation (2016).

https://nemitsasfoundation.org/en/awards/nemitsas-prize-2016/ - Prof em Dr Demetrios Christodoulou, ETH Zurich.

https://people.math.ethz.ch/~demetri/ - R Ruffini, Demetrios Christodoulou, Marcel Grossmann Awards, International Centre for Relativistic Astrophysics (2021).

https://www.icra.it/mg/mg16/mg16_awards.pdf - Talk by Demetrios Christodoulou during the Award of the Nemitsas Foundation Prize in Mathematics, The Takis and Louki Nemitsas Foundation (3 October 2016).

https://nemitsasfoundation.org/en/awards/omilia-tou-vravefthenta-kath-dimitriou-christodoulou-kata-tin-teleti-tis-aponomis-tou-vraveiou-nemitsas-sta-mathimatika-stis-3-oktovriou-2016/ - The Basilis Xanthopoulos International Award, The International Society on General Relativity & Gravitation (2024).

http://www.isgrg.org/xanthprize.php - F Toli, Asia's Nobel Prize for Greek Mathematician, Greek Reporter (30 September 2011).

https://greekreporter.com/2011/09/30/asias-nobel-prize-for-greek-mathematician/ - Kathleen Kelly Betrothal Told,
*South Pasadena Review*(Wednesday 24 January 1973). - G-S Smyrlis, Dimitri Christodoulou to Honorary Doctor of the School of Pure and Applied Sciences of the University of Cyprus,
*University of Cyprus*(31 May 2003).

https://www.ucy.ac.cy/mas/wp-content/uploads/sites/46/2021/06/ChristodoulouErgoKaiProswpikotita.pdf - Emeritus Professor Dimitrios Christodoulou was appointed Honorary Professor at the University of Crete,
*University of Crete*(10 October 2023).

https://en.uoc.gr/announce/christodoulouceremony.html - V Perlick, Review: The Global Nonlinear Stability of the Minkowski Space, by Demetrios Christodoulou and Sergiu Klainerman,
*General Relativity and Gravitation***32**(4) (2000), 761-763. - V Perlick, Review: The Global Nonlinear Stability of the Minkowski Space, by Demetrios Christodoulou and Sergiu Klainerman,
*General Relativity and Gravitation***32**(4) (2000), 761-763. - P T Chrusciel, Review: The action principle and partial differential equations, by Demetrios Christodoulou,
*General Relativity and Gravitation***35**(3) (2003), 499-501. - J Isenberg, Review: The action principle and partial differential equations, by Demetrios Christodoulou,
*Mathematical Reviews*MR1739321**(2003a:58001)**. - P G LeFloch, Review: The Formation of Shocks in 3-Dimensional Fluids, by Demetrios Christodoulou,
*Mathematical Reviews*MR2284927**(2008e:76104)**. - A D Rendall, Review: Mathematical problems of general relativity. I, by Demetrios Christodoulou,
*Mathematical Reviews*MR2391586**(2008m:83008)**. - P T Chrusciel, Review: The Formation of Black Holes in General Relativity, by Demetrios Christodoulou,
*Mathematical Reviews*MR2488976**(2009k:83010)**. - M Dreher, Review: Compressible flow and Euler's equations, by Demetrios Christodoulou and Shuang Miao,
*Mathematical Reviews*MR3288725.

### Additional Resources (show)

Other pages about Demetrios Christodoulou:

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### Honours (show)

Honours awarded to Demetrios Christodoulou

### Cross-references (show)

Written by J J O'Connor and E F Robertson

Last Update March 2024

Last Update March 2024