Béla Bollobás

Béla Bollobás FRS (born 3 August 1943) is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory, and percolation. He was highly influenced by Paul Erdős since he was 14.

As a student, he took part in the first three International Mathematical Olympiads, winning two gold medals. Paul Erdős invited Bollobás to a lunch after hearing about his accomplishment and they kept in touch since then. His first publication was a joint publication with Erdős on extremal problems in graph theory that was written when he was in high school in 1962.

With Erdős’s recommendation to Harold Davenport and Bollobás’s long campaigning to get permission from the Communist authorities, Bollobás was able to spend a year in Cambridge, England, during his undergraduate studies. However, his return to Cambridge again to complete his Ph.D. upon an offer from the university was denied by the Communist authorities. A following scholarship offer from Paris was also rejected by the authorities. He wrote his first doctorate in discrete geometry under the supervision of László Fejes Tóth and Paul Erdős in Budapest University, 1967, after which he spent a year in Moscow with Israïl Moiseevich Gelfand. After spending a year at Christ Church, Oxford, where Michael Atiyah held the Savilian Chair of Geometry, and vowing never to return to Hungary due to his disillusion with the 1956 Soviet intervention and subsequent puppet communist regime, he went to Trinity College, Cambridge, where in 1972 he received a second Ph.D. in functional analysis (on Banach algebras) under the supervision of Frank Adams. In 1970, he was awarded a fellowship to the college.

By then, I said to myself, "If I ever manage to leave Hungary, I won't return."

— Béla Bollobás, Quoted in NUS Newsletter Issue 11.

His main area of research was combinatorics, particularly in graph theory. The two areas that interest him most are extremal graph theory and random graph theory. Bollobás stayed in Cambridge from 1971 to 1996.

He has been a Fellow of Trinity College, Cambridge, since 1970; in 1996 he was appointed to the Jabie Hardin Chair of Excellence at the University of Memphis, and in 2005 he was awarded a Senior Research Fellowship at Trinity College.

He has proved results on extremal graph theory, functional analysis, the theory of random graphs, graph polynomials and percolation. For example, with Paul Erdős he proved results about the structure of dense graphs; he was the first to prove detailed results about the phase transition in the evolution of random graphs; he proved that the chromatic number of the random graph on n vertices is asymptotically n/2 log n; with Imre Leader he proved basic discrete isoperimetric inequalities; with Richard Arratia and Gregory Sorkin he constructed the interlace polynomial; with Oliver Riordan he introduced the ribbon polynomial (now called the Bollobás–Riordan polynomial); with Andrew Thomason, József Balogh, Miklós Simonovits, Robert Morris and Noga Alon he studied monotone and hereditary graph properties; with József Balogh, Hugo Duminil-Copin and Robert Morris he studied bootstrap percolation; with Oliver Riordan he proved that the critical probability in random Voronoi percolation in the plane is 1/2; and with Svante Janson and Oliver Riordan he introduced a very general model of heterogeneous sparse random graphs.

In addition to over 350 research papers on mathematics, he has written several books, including the research monographs "Extremal Graph Theory" in 1978, "Random Graphs" in 1985 and "Percolation" (with Oliver Riordan) in 2006, the introductory books "Modern Graph Theory" for undergraduate courses in 1979, "Combinatorics" and "Linear Analysis" in 1990, and the collection of problems "The Art of Mathematics – Coffee Time in Memphis" in 2006, with drawings by Gabriella Bollobás. He has also edited a number of books, including "Littlewood's Miscellany".

Béla Bollobás has had a great many research students, including Andrew Thomason, Keith Carne, Timothy Gowers (who was awarded a Fields Medal in 1998 and is Rouse Ball Professor of Mathematics) and Imre Leader at the University of Cambridge, Alexander Scott and Oliver Riordan now at Oxford, Jonathan Partington and Charles Read now at Leeds, and Keith Ball and Graham Brightwell now in London at UCL and the LSE, respectively.

Béla Bollobás is an External Member of the Hungarian Academy of Sciences; in 2007 he was awarded the Senior Whitehead Prize by the London Mathematical Society. In 2011 he was elected a Fellow of the Royal Society for his major contributions to many different areas of mathematics within the broad field of combinatorics, including random graphs, percolation, extremal graphs, set systems and isoperimetric inequalities. The citation also recognizes the profound influence of his textbooks in many of these areas, and his key role in establishing Britain as one of the leading countries in probabilistic and extremal combinatorics. In 2012 he became a fellow of the American Mathematical Society.

Lee Hsien Loong, the present Prime Minister of Singapore, studied mathematics with Bollobás in Cambridge, but later decided to pursue computer science instead.

Bollobás was elected a Fellow of the Royal Society in 2011. His nomination reads

Bollobás is also a sportsman, having represented the University of Oxford at modern pentathlon and the University of Cambridge at fencing.

His father is a physician. His wife, Gabriella Bollobás, also born in Budapest, was an actress, a musician and a painter in Hungary before moving to England to become an accomplished sculptor. She made busts of mathematicians and scientists, including Bill Tutte, George Batchelor, John von Neumann, Paul Dirac, and Stephen Hawking, as well as a cast bronze of David Hilbert.

• Extremal Graph Theory. Academic Press 1978, Dover 2004.
• Graph theory- an introductory course. Springer 1979.
• Random Graphs. Academic Press 1985. Cambridge University Press 2001.
• Combinatorics - set systems, hypergraphs, families of vectors, and combinatorial probability. Cambridge University Press 1986.
• Linear Analysis – an introductory course. Cambridge University Press 1990, 1999.
• with Alan Baker, András Hajnal (ed.): A tribute to Paul Erdös. Cambridge University Press 1990.
• (ed.): Probabilistic combinatorics and its applications. American Mathematical Society 1991.
• with Andrew Thomason (ed.): Combinatorics, Geometry and Probability- a tribute to Paul Erdös. Cambridge University Press 1997.
• Modern Graph Theory. Springer 1998.
• (ed.): Contemporary Combinatorics. Springer und Janos Bolyai Mathematical Society, Budapest 2002.
• with Oliver Riordan: Percolation. Cambridge University Press 2006.
• The Art of Mathematics - Coffee Time in Memphis. Cambridge University Press 2006 (with drawings by his wife Gabrielle Bollobás)
• with Robert Kozma, Dezső Miklós: Handbook of Large-Scale Random Networks. Springer 2009.