Abstract
The 1982, the International Congress of Mathematicians should have been held in Warsaw, but the political situation there did not allow it. On 13 December 1981, in the early hours of the morning, General Wojciech Jaruzelski declared a state of war and imposed martial law: the rights to strike and hold public protests were suspended, as were the right to call public meetings. The junta imposed judiciary procedures that allowed for summary judgements and the denial of any appeal processes, even in the case of death sentences. The main object of these repressive rules was Solidarność, the union that had made life difficult for the previous government through waves of strikes and strong political actions of dissent based on Catholic and anti-Communist ideologies. On that tragic night in 1981, its entire leadership, including Lech Walesa, were arrested, together with thousands of others. The prisoners were then held in structures that were wholly inadequate to cope with the rigors of the Polish winter.
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Notes
- 1.
An Amnesty International document reads: “Amnesty International does not know the exact number of people who have been detained. Official sources initially reported around 5000. On 25 January, General Jaruzelski spoke of 6309 people detained (the highest official number reported), of whom 1760 had already been released. The unofficial estimates, however, invariably gave much greater numbers.”—Document provided by A. Marino (Pisa, 14 February 2007).
- 2.
E. De Giorgi, “Message to General Jaruzelski,” Pisa, 12 January 1982. Published in [2].
- 3.
News reported by the newspaper Il Tirreno, 18 January 1982.
- 4.
News reported by the newspaper La Nazione, 28 July 1982.
- 5.
Proceedings of the Comité des Mathématiciens, on which most of the information in these pages is based.
- 6.
There were 22 dedications to 12 scientists, including Cieciura.
- 7.
De Giorgi’s intervention was on 16 August 1983. The text is published in [2]. No record of the presumed dedication remains in the official transcripts, but subsequently a letter emerged, signed by five people, including R. Duda, B. Gleichgewicht, and J. Waszkiewicz (Warsaw, 24 August 1983), that reads: “Dear Ennio De Giorgi, to all of you who dedicated your lectures to Polish mathematicians and who offered your sympathy and help to the Polish mathematical community at this Congress and during the last 20 months we express our sincere thanks.”
- 8.
Z. Denkowska (email, 27 October 2008). Denkowska adds: “While the ICM was being held, Poland was under martial law, and we [her and her husband, Z. Denkowski] remember clearly that De Giorgi worried that he might cause us problems as we were always together.”
- 9.
Z. Denkowska understood French and checked the text of the speech that De Giorgi had prepared for the ICM. She had met him in Pisa in the Autumn of 1982: “I met him in the canteen of the Scuola Normale, but I had no idea that the modest and pleasant person I was talking to was him. I was young and this was my first trip abroad, and the following day I asked whom I should usefully meet in Pisa, and everyone said, ‘De Giorgi, obviously’; and I replied: ‘I would not dare talk to him!’ and was told: ‘But you did, just yesterday!’ I believed that great professors like him were aloof and distant, but he was warm and accommodating, someone who was good and altruistic. Later on, it turned out that it was my husband, not I, who worked in a field much closer to his. My husband arrived in Pisa, invited by De Giorgi. I will never forget, our first evening in the canteen, that De Giorgi spoke with him in Italian and, like me, he was barely proficient in the language, but seemed to understand anyway. Initially, De Giorgi and I both spoke French, but after some toing and froing, of the sort: ‘Quand est-ce qu’elle est arrivée?’ (De Giorgi intended to use the Italian polite form, which is feminine in gender (“Lei”), to say “When did you arrive?”) and I: ‘Qui?’ (who?)—we learned Italian quickly, which is now our preferred language. For this reason, De Giorgi gave me his ICM speech to check. I was quite honored by this request and asked the daughter of Waclaw Sierpiński (one of Poland’s most notable mathematicians), who was also the conference secretary, to help me”. (Z. Denkowska, email, 27 October 2008).
- 10.
During the weekend of 20–21 August, a total of 200 Western participants petitioned for Cieciura’s freedom, which was delivered to the authorities immediately after the congress. About 30 mathematicians denounced the situation at the university, where the government had taken control of admissions and expulsions of professors and students without seeking the approval of the academic senate, and indeed with the right to dissolve the academic senate itself, hindering Solidarność sympathizers. Unfortunately, in the days following the congress, the situation in Poland did not normalize and on 10 September, 23,000 people were sentenced to forced labor on charges of being “social parasites.” The prosecution asked that Cieciura be sentenced to 3 years in prison.
- 11.
Z. Denkowski adds: “De Giorgi played a particularly important role for myself and for my young colleagues from Krakow, J. Traple, and S. Migorski. Not only did he show me a new field of mathematics and encouraged my research, but he also invited me often to the Scuola Normale. For example, when he took a sabbatical leave in the academic year 1985/1986, he invited me to take his position as a contract professor at the Scuola Normale Superiore.” Z. Denkowski, email, 29 September, 2008. During his sabbatical year, De Giorgi continued without any apparent break in his activities at the Scuola Normale Superiore. His course of analysis on Tuesday was held by Z. Denkowski (L. Ambrosio, 18 January 2008), whereas the Wednesday course on the foundations of mathematics continued without change (M. Forti, 19 January 2009).
- 12.
S. Spagnolo, email, 28 January 2008.
- 13.
Otherwise De Giorgi would not have told anyone. E. De Giorgi did not like talking about himself. “I was very surprised after his death, when looking over all the documents relating to his scientific activities, and all the awards and recognition he had been given, of how many there were and that he had never mentioned a word about them”. F. De Stefano in [3].
- 14.
L. Carbone, 17 February 2007.
- 15.
F. Murat, January 2007.
- 16.
Text taken from an article by G. Locchi in the newspaper Il Tempo (7 November 1983). Krée also mentioned De Giorgi’s humanitarian activities, recalled the words he spoke at the Warsaw conference, and added: “Prof. De Giorgi’s work in this field quickly became famous in the world (…) and contributed to the full solution of Hilbert’s nineteenth problem. He also discovered, and then developed with his students, the theory of Gamma-convergence (...) which, in many parts of the world, has encouraged numerous papers, with a multiplicity of applications in mechanics and physics.”
- 17.
P. Donato, February 2007.
- 18.
L. Carbone, Naples, October 2006.
- 19.
A. Leaci, Lecce, 18 December 2006.
- 20.
L. Ambrosio, Pisa, 13 February 2007.
- 21.
Regarding the origins of Gamma-convergence, L. Carbone notes (email, 18 February 2008): “A few years before De Giorgi, Umberto Mosco had introduced a convergence (called M-convergence, or convergence according to Mosco), which was related to Gamma-convergence. Even closer to Gamma-convergence was K-convergence or convergence according to Kuratowski, from the name of a Polish mathematician who had conceived it a few decades earlier.”
- 22.
J. Peetre, “Rectification à l’article: Une caracterisation abstraite des operateurs differentiels.” Math. Scand. Vol 7, issue 1 (1960).
- 23.
S. Spagnolo in [7].
- 24.
S. Spagnolo here refers to the coefficients of differential equations (considered as operators).
- 25.
S. Spagnolo, email, 4 February 2008.
- 26.
S. Spagnolo in [7].
- 27.
Green’s functions (from George Green) are important in the field of differential equations.
- 28.
S. Spagnolo, Pisa, 6 February 2007.
- 29.
According to L. Carbone, at that time, E. De Giorgi was particularly interested in Tullio Zolezzi’s work on energy. He said, “We must do what Tolezzi suggests: make the energies converge.” L. Carbone, telephone call, 20 December 2007.
- 30.
F. Murat, 30 January 2007.
- 31.
S. Spagnolo, Pisa, 6 February 2007.
- 32.
E. De Giorgi, “Sulla convergenza di alcune successioni d’integrali del tipo dell’area.” Collection of articles dedicated to Mauro Picone on the occasion of his 90th birthday, Rend. Mat. (6) 8 (1975).
- 33.
The link between the two aspects consists of the Euler–Lagrange equation, which transforms a problem of the calculus of variations in the resolution of a partial differential equation.
- 34.
Given a sequence {fk(x)} of functions defined on a topological space X (which satisfies some very general hypotheses) and with real or extended real values, the formal definition of Gamma-convergence is as follows. “{fk(x)} is Gamma-convergent towards f if in every point x0 of space X, the following statements are true: for every sequence of points {xk} converging to x0 one has lim in fkfk(xk) ≥ f(x0), and there also exists at least one of such sequences {xk} for which {fk(xk)} converges to f(x0)”. Ennio De Giorgi, Boll. Umi, Sez. B (8) 2 (1999). The most important property of Gamma-convergence can be summarized thus: “If a sequence of functionals is Gamma-convergent, then the solutions of the related minimum problems converge towards the solution of the corresponding minimum problem for the Gamma-limit functional,” explains G. Dal Maso (7 December 2007). The minimum of the Gamma-limit functional is the limit of the minima of the Gamma-convergent functionals, and the theory provides a method for calculating it.
- 35.
S. Spagnolo in [7].
- 36.
E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale, Atti dell’Accademia Nazionale dei Lincei Rendiconti Cl. Sci. Fis. Mat. Natur. (8) 58 (1975).
- 37.
T. Franzoni, Pisa, 7 February 2007.
- 38.
In this sense, one speaks of minimums in that variational sense, that is of curves, surfaces or hypersurfaces that minimize a specific functional.
- 39.
S. Mortola, Milan, 2007.
- 40.
“This link had been sought without success for years; it was De Giorgi who figured out that it could be established through Gamma-convergence.” L. Modica, 12 September 2008.
- 41.
This is shown, to give a single example, by the school for young researchers called “30 years from De Giorgi’s conjecture” (25–29 May 2009). This school, organized by A. Farina and E. Valdinoci, concerns a conjecture formulated by De Giorgi in 1978, specifically on the themes studied by Modica and Mortola, and still open in its more general aspects: E. De Giorgi, Convergence problems for functionals and operators, Proceedings of the International Meeting on Recent Methods in Nonlinear Analysis, (Rome, 1978), Pitagora (Bologna, 1979). The conjecture was proven by N. Ghoussoub and C. Gui, and independently by H. Berestycki, L. Caffarelli, and L. Nirenberg in the 2D case, and by L. Ambrosio and X. Cabré in the 3D case; up to 2008, however, a proof in the most general case is still lacking.
- 42.
Modica explains that the method he studied with De Giorgi is applicable, for instance, in the following case: “There are fluids, known as Van der Walls’ fluids, which are made up of two states (liquid and gas) that coexist and are separated by a minimal surface. The shape of the surface depends on the geometry of the system, and close to the borders of their containers, also by capillarity phenomena.” L. Modica, 12 September 2008.
- 43.
During the same period, another group guided by E. Fabes proved the same result using a different technique: “They used complex variables, we used variational techniques.”—S. Mortola, Milan, 2007.
- 44.
L. Modica, email, 30 January 2009. Modica adds: “I cite this episode to recall one of the ways in which Ennio approached mathematical analysis: he possessed an unsurpassed ability to connect differential equations to physical models, generally relative to classical mechanics and electromagnetism, over which he had a complete and profound mental domination; he then applied his physical-mathematical intuition on these physical models.”
- 45.
E. De Giorgi, Problemi con discontinuità libera, International Symposium “Renato Caccioppoli” (Naples, 1989).
- 46.
L. Ambrosio, Pisa, 13 February 2007. E. De Giorgi and L. Ambrosio published a general theory on the study of variational problems with volume and surface terms in E. De Giorgi and L. Ambrosio, Un nuovo tipo di funzionale del calcolo delle variazioni, Atti Acc. Naz. Lincei Rendiconti Cl. Sci. Fis. Mat. Natur. (8) 82 (1988).
- 47.
E. Virga, Pavia, 21 May 2008.
- 48.
Ibid.
- 49.
In this field, De Giorgi proposed many conjectures that are still open. E. De Giorgi, Introduzioneai problemi di discontinuità libera, Symmetry in Nature—A volume in honor of Luigi Radicati di Brozolo, Sns (Pisa, 1989).
- 50.
D. Mumford, email, 20 January 2008.
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Dossier Ennio De Giorgi. In: Guerraggio, A. (ed.) Lettera Matematica Pristem, pp. 27–28. Springer (1998)
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Parlangeli, A. (2019). Solidarity, Liquid Crystals, and Computer Vision. In: A Pure Soul. Springer, Cham. https://doi.org/10.1007/978-3-030-05303-1_19
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