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Visitors at the Institute
A part of the Institute’s activity which has been receiving increasing importance during recent years is the hosting of visitors from Hungary and abroad.
Each year, the Institute offers visiting positions for mathematicians working at Hungarian universities, usually for a duration of 6 or 12 months, providing them ideal conditions for conducting undisturbed research. In such a way, the Institute has had a part in the achievement of several breakthroughs: for instance, Miklós Laczkovich of Eötvös University proved Tarski’s conjecture on the ‘squaring of the circle’ while a visiting researcher at the Institute.
The Institute has been receiving foreign scientists for short stays for decades now, many of them regular visitors and close collaborators of our researchers. During recent years, the number of foreign visitors plummeted and the Institute can now host visitors for longer stays as well. Instrumental in this change was the Centre of Excellence grant of the European Union, allotted to the Institute between 2001 and 2003, which made possible the invitation of 33 scholars and postdocs for visits ranging from one month to a whole year. This grant also contributed to the funding of 13 international conferences organized during this period.
Another institution enabling the invitation of visitors and the organization of workshops is the Paul Erdős Mathematical Summer Institute, founded, jointly with the János Bolyai Mathematical Society and several universities, in 1997. It is cofinanced by the Hungarian Ministry of Education, the Hungarian Academy of Sciences, Rutgers University (US), Microsoft Research (US), and Lucent Technologies (US).
During the coming years, the Institute wishes to develop its international contacts further, with the aim of becoming not only an important European centre but also a wellknown meeting place for mathematical research.
Scientific and postgraduate education in the Institute
During the first decades of the Institute’s existence, most of its researchers held parttime positions at various Hungarian universities and vice versa, a number of distinguished university professors were also parttime members of the Institute. This resulted in a close collaboration with the educational system and enabled to draw many talented young students towards mathematical research.
Nowadays our relation with undergraduate education is less tight. We do not offer parttime positions any more for university teachers, but we regularly host them as visiting researchers. Similarly, only a few members of the Institute hold parttime university positions, though many of them still teach undergraduate and graduate courses at various universities – mostly at Eötvös University and at the Technical University of Budapest, but also in Debrecen.
On the other hand, the Institute takes a more and more active part in graduate and postgraduate education. Our researchers usually serve as advisors to 1012 graduate students from universities in Budapest. From the academic year 2001/2002, a joint international graduate program has been launched together with Central European University, open to all countries of the world. The teaching language is English and the educational system is the one currently adopted in the US; correspondingly, the PhD titles awarded will be accepted in the US as well. Our researchers serve both as supervisors and instructors in the program.
Within the framework of a program coordinated by the Hungarian Academy of Sciences, the Institute hosts each year 1015 young researchers with a oneyear contract, which is renewable twice. These are recent PhD’s or graduate students about to finish their thesis, whose scientific work is supervised by a researcher at the Institute. After the end of their contract, several young researchers have received offers for a position at the Institute, some even tenured ones.
The Institute also regularly hosts postdoctoral students from abroad whose number is steadily increasing thanks to the availability of various intraEuropean and international fellowships. We have joined or are planning to join various European research training networks which will help to develop further the international training activities of the Institute.
Researchers currently working at the Institute
This section gives a brief presentation of our current members; it is followed by lists of our honorary members and some prominent former members. All researchers below have a PhD or equivalent title. The ‘Doctor of Science’ title is awarded by the Academy to researchers with a substantial research experience and achievement; it roughly corresponds to that of a full professor. Among the prizes mentioned, the Széchenyi Prize (formerly State Award, or Kossuth Prize) is the highest distinction of the Hungarian Republic awarded to scientists; the Academy Award and the Mathematical Award are awarded by the Academy for outstanding research achievements. Several of our researchers are members or corresponding members of the Hungarian Academy of Sciences.
Hajnal Andréka (b. 1947, at the Institute since 1977) Doctor of Science (1993).
Her main areas of interest include logic, algebraic logic, theoretical computer science, and relativity theory. She proved (jointly with Hodkinson and Németi) that every finite relativized relation algebra is representable over a finite base. She is a member of the Council of the Association of Symbolic Logic.



Pham Ngoc Ánh (b. 1956, at the Institute since 1988) Doctor of Science (1988).
His main area of interest is ring and module theory. Probably his most famous result states that a commutative rings admits Morita duality if and only if it is linearly compact.

András Ádám (b. 1934, at the Institute since 1957) Doctor of Science (1986)
He is interested in Boolean functions, graph theory and algebraic automata theory. He has written two books.



László Babai (b. 1950, at the Institute since 1997) Member of the Academy, Mathematical Award (1983)
Plenary lecturer of the 1992 European Congress of Mathematics. He contributed to the theory of graph automorphisms and of permutation groups, in particular concerning the number of elements in primitive permutation groups. His other important field is complexity theory, where his theorem about transparent proofs is of basic importance. Currently on leave from the Institute, he is a professor at the University of Chicago.

Antal Balog (b. 1956, at the Institute since 1983) Doctor of Science (2000), Mathematical Award (1992), Academy Award (1995)
His field is number theory, especially the distribution of prime numbers. A wellknown expert in sieve methods and exponential sums, his most striking result is that there are infinitely many "magic" triangles, tetrahedrons, etc. in primes.



Imre Bárány (b. 1947, at the Institute since 1978) Doctor of Science (1993), Erdős Prize (1995), Academy Award (1998)
Invited speaker at the International Congress of Mathematicians, Beijing, 2002. His main areas of interest are discrete and convex geometry, with applications in operation research and computer science. He has obtained fundamental results about the asymptotic shape of certain random objects.

István Berkes (b. 1947, at the Institute since 1971) Doctor of Science (1996), Academy Award (2003).
His main field of interest is probability theory and its applications in analysis, in particular for orthogonal and lacunary series.


András Bezdek (b. 1956, at the Institute since 1983)
His fields of interest are discrete and combinatorial geometry and convexity. Many of his results concern packing and covering problems in 2 and 3dimensional Euclidean space.

András Biró (b. 1971, at the Institute since 1997)
He works in various areas on number theory, including the analytic theory of automorphic functions, Turán’s theory of power sums and diophantine approximation. He recently solved problems of Yokoi and Chowla concerning quadratic fields of class number one.


Péter Bod (b. 1924, at the Institute since 1959; deputy director, 1985–1995; retired in 2003). Doctor of Science (1973).
His main fields of interest are operation research and actuarial problems in social security. He has achieved results in multiobjective linear programming, in the characterization of convex sets having a least element, in the nonlinear generalization of inputoutput models and in the mathematical modeling of largescale systems. He currently serves as Advisor to the Director.

János Bognár (b. 1932, at the Institute from 1960, retired in 1995)
A specialist in functional analysis, he has written a monograph on Indefinite inner product spaces (volume 78 of the prestigious Ergebnisse series of SpringerVerlag).


Károly Böröczky, Jr. (b. 1964, at the Institute since 1992; scientific secretary, 1996–2000)
His main fields of interest are discrete and combinatorial geometry as well as the theory of toric varieties. His monograph on Finite packing and covering will be published soon by Cambridge University Press. Organizer of several important international meetings in algebraic geometry and topology.

Endre Csáki (b. 1935, at the Institute since 1959) Doctor of Science (1989).
He is interested in limit theorems of probability and statistics and in combinatorial methods for random walk problems. He gave rates of convergence in Strassen’s theorem, thereby establishing a connection between Chung’s and Strassen’s laws of the iterated logarithm.



Imre Csiszár (b. 1938, at the Institute since 1961) Member of the Academy, IEEE Shannon Award (1997), Academy Award (1988).
He is the leader of the Hungarian school in information theory. His main work is the book “Information Theory” written jointly with János Körner. The book was the first overview of multiuser information theory.

Ervin Deák (b. 1929, at the Institute from 1964; retired in 1995)
At first his area of research was general topology, regarding in particular various notions of dimension, later his interest switched to questions of mathematical education.


Mátyás Domokos (b. 1968, at the Institute since 1995)
A specialist in ring theory, he first worked on polynomial identities, then his research shifted to invariant theory and its connections with representations and quantum groups.

Gábor Elek (b. 1963, at the Institute since 1996)
His work concentrates on the interface between functional analysis on manifolds, algebra and combinatorics; his main interest is in amenable groups, topological entropy and l_pcohomologies.

Miklós Erdélyi Szabó (b. 1962, at the Institute since 2002)
He is interested in set theory, topological models as well as in artificial intelligence; he is also the head of our Computer Department.

Péter L. Erdős (b. 1956, at the Institute since 19??)
He works in extremal graph theory and the application of graphs to problems in mathematical biology.


Gábor Fejes Tóth (b. 1947, at the Institute since 1974), Doctor of Science (1996).
Working in discrete geometry, he is a worldwide recognized authority on packing and covering problems. His survey papers are the standard references about the field. Organizer of prestigious international meetings in discrete geometry (including Oberwolfach seminars).

Zoltán Füredi (b. 1954, at the Institute since 1978) Doctor of Science (1989), Academy Award (1989).
Invited lecturer at the 1994 International Congress of Mathematicians. He has achieved ourstanding results in extremal set theory, graph theory and discrete geometry, including the solution (together with P. Frankl) of a famous problem of Littlewood and Offord.


János Gerlits (b. 1945, at the Institute since 1968)
His field of research is general and settheoretic topology. In particular, he has important results on function spaces and on cardinal functions of dyadic spaces.

Ervin Győri (b. 1954, at the Institute since 1977; deputy director since 1997) Doctor of Science (1994).
His main fields of interest are combinatorics and graph theory. His major results are a minimax theorem on intervals, a partition characterization of kconnected graphs (proved independently by L. Lovász as well) and solutions to several problems of Erdős in extremal graph theory.



István Juhász (b. 1943, at the Institute since 1975) Doctor of Science (1977), Mathematical Award (1977), Academy Award (1997)
His main areas of interest are set theory and general topology. Together with A. Hajnal he has created an internationally recognized school in settheoretic topology. He is the author of two monographs: Cardinal functions in topology and Cardinal functions  ten years later.

Gyula Katona (b. 1941, at the Institute since 1966; Director since 1996) Member of the Academy, Academy Award (1989).
An internationally recognized expert in combinatorics, he has achieved important results in extremal set theory and concerning the combinatorial structure of databases. He also pays great attention to educating future scientists: several of his students are leading mathematicians today. His organizing work is also of great importance.



András Kroó (b. 1954, at the Institute since 1976) Doctor of Science (1988), Academy Award (2002).
His main area of interest is Approximation Theory. His best known result concerns the differentiability of the operator of best approximation in the space of continuous functions.

Antónia L. Földes (b. 1945, at the Institute since 1969)
An expert in probability theory, she is mainly interested in questions of local time, random walks and Wiener processes. Currently on leave from the Institute.


Anna Lee (b. 1928, at the Institute from 1971; retired since 1993)
A researcher in algebra, her field of interest is matrix theory. She has investigated involutions of the complete matrix ring over the complex numbers.

Judit Madarász (b. 19??, at the Institute since 2001)
She works in algebraic logic and the logical foundations of relativity theory.


Zoltán Magyar (b. 1959, at the Institute since 1987)
His main field of research is the analytic theory of Lie groups and their representations. Author of two monographs: one on Continuous Linear Representations, the other on The Lebesgue Integral.

Péter Major (b. 1947, at the Institute since 1971) Doctor of Science (1989), Academy Award (1984)
He is interested in probability theory and statistical physics. His best known result is a joint work with János Komlós and Gábor Tusnády about the approximation of identically distributed random variables by a Wiener process. This construction is often called the KMT theory or the Hungarian method in the literature.



Endre Makai, Jr. (b. 1947, at the Institute since 1970) Doctor of Science (1996), Academy Award (1998).
He has a double research interest: he works in convex and discrete geometry and also in general topology. He has obtained important results by combining geometrical and purely topological methods.

László Márki (b. 1947, at the Institute since 1970) Doctor of Science (1996)
His main area of interest is algebra: semigroups, rings, universal algebra, categories. He has recently introduced the notion of semiabelian categories (with Janelidze and Tholen) which answers an old question of MacLane. He served as VicePresident of the European Mathematical Society from 19931996.


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