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2010. május 15. –19:16

1. borito = belső 1. oldal

ANNALES Universitatis Scientiarum

Budapestinensis

de Rolando E �otv �os nominatae

SECTIO MATHEMATICA TOMUS LII.

REDIGIT

Á. CSÁSZÁR

ADIUVANTIBUS

L. BABAI, A. BENCZÚR, K. BEZDEK., M. BOGNÁR, K. BÖRÖCZKY, I. CSISZÁR, J. DEMETROVICS, GY. ELEKES , A. FRANK, E. FRIED,

J. FRITZ, V. GROLMUSZ, A. HAJNAL, G. HALÁSZ, A. IVÁNYI, A. JÁRAI, P. KACSUK, I. KÁTAI, E. KISS, P. KOMJÁTH, M. LACZKOVICH, L. LOVÁSZ,

GY. MICHALETZKY, J. MOLNÁR, P. P. PÁLFY, A. PRÉKOPA, A. RECSKI, A. SÁRKÖZY, F. SCHIPP, Z. SEBESTYÉN, L. SIMON, P. SIMON, GY. SOÓS, L. SZEIDL, T. SZŐNYI, G. STOYAN, J. SZENTHE, G. SZÉKELY, A. SZŰCS,

L. VARGA, F. WEISZ

2009

2010. május 15. –19:16

belso 2. oldal

ANNALES Universitatis Scientiarum

Budapestinensis

de Rolando E�otv�os nominatae

S E C T I O B I O L O G I C A incepit anno MCMLVII

S E C T I O C H I M I C A incepit anno MCMLIX

S E C T I O C L A S S I C A incepit anno MCMXXIV

S E C T I O C O M P U T A T O R I C A incepit anno MCMLXXVIII

S E C T I O G E O G R A P H I C A incepit anno MCMLXVI

S E C T I O G E O L O G I C A incepit anno MCMLVII

S E C T I O G E O P H Y S I C A E T M E T E O R O L O G I C A incepit anno MCMLXXV

S E C T I O H I S T O R I C A incepit anno MCMLVII

S E C T I O I U R I D I C A incepit anno MCMLIX

S E C T I O L I N G U I S T I C A incepit anno MCMLXX

S E C T I O M A T H E M A T I C A incepit anno MCMLVIII

S E C T I O P A E D A G O G I C A E T P S Y C H O L O G I C A incepit anno MCMLXX

S E C T I O P H I L O L O G I C A incepit anno MCMLVII

S E C T I O P H I L O L O G I C A H U N G A R I C A incepit anno MCMLXX

S E C T I O P H I L O L O G I C A M O D E R N A incepit anno MCMLXX

S E C T I O P H I L O S O P H I C A E T S O C I O L O G I C A incepit anno MCMLXII

2010. május 15. –19:04

We report with great sadness the passing away of György Elekes, pro- fessor of the Department of Computer Science.

The mathematical talent of Elekes showed early. Between 1963 and 1967 he was a stu- dent of Károly Kőváry, the fine mathematics teacher of the renowed Fazekas Highschool, Budapest. In 1965 and 1967, he won third, and then first prize at the International Mathematical Olimpiade. He won second prize at the József Kürschák Memorial Contest in 1966.

Between 1967 and 1972 Elekes studied mathematics at the Roland Eötvös University. After graduation, he stayed at the university, earlier at the Analysis I Department (until 1980 as a Lecturer, then as an Assistant Professor), in

1983 he became one of the founding members of newly created Department of Computer Science (until 1995 as an Assistant Professor, then till 2005 as an Associate Professor, after that as a Full Professor). He obtained the Dr. Rher. Nat. degree in 1978, the Candidate of Mathematical Sciences degree in 1994, and the Doctor of Mathematical Sciences title in 2001. He received a Szechenyi Fellowship between 1999–2002.

Elekes started doing research in set theory. He solved a problem of Erdős and Hajnal on partitions of infinite sets, which led to the development (in part with Erdős and Hajnal) of a new branch of combinatorial set theory. (Many of their results are still unpublished.)

Another important result is his theorem with György Hoffmann stating that there are almost-disjoint set systems with arbitrarily large chromatic number.

In all his life, Elekes was deeply interested in geometry, and from the 1970s, in the newly developed complexity theory. He proved a major result

2010. május 15. –19:04

4

in the theory of geometric algorithms. With the application of an elegant new inequality, he proved that the volume of a convex body in general dimension can only be estimated with very large error in polynomial time. This paper initiated several branches of important research.

His interest in geometric algorithms motivated his teaching as well: he created the curriculum of this topic at the Eötvös University. He did, however, change his research profile in the 1980s, and became interested in combina- torial geometry—another topic invented by Erdős. He discovered important connections to other branches of mathematics, in particular number theory, and his research area became what is now known as additive combinatorics. He gained significant fame in this very active topic where several Fields Medalists and other leading researchers in number theory and combinatorics work. Elekes not only proved hard theorems, but succesfully discovered the algebraic structures hidden in the background of some combinatorial phenom- ena.

György Elekes was an outstanding teacher, who considered teaching his most noble task. His students loved him as teacher and as a person. He spent a lot of time writing and rewriting teaching resources, trying to find the best presentation of thoughts, examples, details.

During his fight with his illness, almost one year long, he closely fol- lowed the issues of the Institute, of teaching, and of research, and tried to participate in them. He worked on his papers as long as his strength allowed him.

He was good friend of many, and a good colleague of us all. We will sorely miss his knowledge and his deep devotion to teaching.

Department of Computer Science, Mathematical Institute

2010. május 15. –19:04

List of papers of György Elekes

[1] G� Elekes� On a partition property of infinite subset of a set, Period� Math� Hungar�, 5 (1974), 215–218.

[2] G� Elekes� G� Hoffmann� On the chromatic number of almost disjoint families of countable sets, In�nite and �nite sets, (Colloq., Keszthely, 1973; dedi- cated to P. Erdős on his 60th birthday), Vol. I, Colloq., Math. Soc. János Bolyai, Vol. 10, North-Holland, Amsterdam, 1975, 397–402.

[3] G� Elekes� Colouring of infinite subsets of � , In�nite and �nite sets, (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. I, Colloq. Math. Soc. János Bolyai, Vol. 10, North-Holland, Amsterdam, 1975, 393–396.

[4] G� Elekes� P� Erd�os� A� Hajnal� On some partition properties of families of sets, Studia Sci� Math� Hungar�, 13 (1978), 151–155.

[5] G� Elekes� n points in the plane can determine n3�2 unit circles, Combinator� ica, 4 (1984), 131.

[6] G� Elekes� A geometric inequality and the complexity of computing volume, Discrete Comput� Geom�, 1 (1986), 289–292.

[7] G� Elekes� A� Hajnal� P� Komj�ath� Partition theorems for the power set, Sets� graphs and numbers, (Budapest, 1991), Colloq. Math. Soc. János Bolyai, 60, North-Holland, Amsterdam, 1992, 211–217.

[8] G� Elekes� Generalized breadths, circular Cantor sets, and the least area UCC, Discrete Comput� Geom�, 12 (1994), 439–449.

[9] G� Elekes� P� Erd�os� Similar configurations and pseudo grids, Intuitive geom� etry, (Szeged, 1991), Colloq. Math. Soc. János Bolyai, 63, North-Holland, Amsterdam, 1994, 85–104.

[10] G� Elekes� Circle grids and bipartite graphs of distances, Combinatorica, 15 (1995), 167–174.

[11] G� Elekes� On the number of sums and products, Acta Arith�, 81 (1997), 365–367.

[12] G� Elekes� On linear combinatorics, I., Concurrency—an algebraic approach, Combinatorica, 17 (1997), 447–458.

[13] Gy� Elekes� On some combinatorial problems, I. (Hungarian), Mat� Lapok, (N.S.) 7 (1997), 67–80.

[14] G� Elekes� A combinatorial problem on polynomials, Dedicated to the memory of Paul Erdős, Discrete Comput� Geom�, 19 (1998), 383–389.

[15] G� Elekes� On linear combinatorics, II., Structure theorems via additive number theory, Combinatorica, 18 (1998), 13–25.

[16] Gy� Elekes� On some combinatorial problems, II. Bounds on incidences, (Hungarian) Mat� Lapok, (N.S.) 8/9 (1998/99), 7–19.

2010. május 15. –19:04

6

[17] G� Elekes� On the structure of large homothetic subsets, Contemporary trends in discrete mathematics (S̆tir̆ı́n Castle, 1997), DIMACS Ser� Discrete Math� Theoret� Comput� Sci�, 49, Amer. Math. Soc., Providence, RI, 1999, 101–111.

[18] G� Elekes� On linear combinatorics, III. Few directions and distorted lattices, Combinatorica, 19 (1999), 43–53.

[19] G� Elekes� A note on the number of distinct distances, Period� Math� Hungar�, 38 (1999), 173–177.

[20] G� Elekes� L� R�onyai� A combinatorial problem on polynomials and rational functions, J� Combin� Theory, (A), 89 (2000), 1–20.

[21] G� Elekes� M� B� Nathanson� I� Z� Ruzsa� Convexity and sumsets, J� Number Theory, 83 (2000), 194–201.

[22] G� Elekes� On some combinatorial problems, III. Distances and unit circles, (Hungarian) Mat� Lapok, (N.S.), 10 (2000/01), 13–21.

[23] G� Elekes� Z� Kir�aly� On the combinatorics of projective mappings, J� Alge� braic Combin�, 14 (2001), 183–197.

[24] G� Elekes� SUMS versus PRODUCTS in number theory, algebra and Erdős geometry, Paul Erd�os and his mathematics, II (Budapest, 1999), Bolyai Soc� Math� Stud�, 11, János Bolyai Math. Soc., Budapest, 2002, 241–290.

[25] G� Elekes� On the number of distinct radii of circles determined by triplets and on parameter