Béla Bollobás
Encyclopedia
Béla Bollobás FRS is a Hungarian-born British mathematician
who has worked in various areas of mathematics, including functional analysis
, combinatorics
, graph theory
and percolation
. As a student, he took part in the first three International Mathematical Olympiad
s, winning two gold medals. He wrote his first doctorate in discrete geometry
under the supervision of László Fejes Tóth
and Paul Erdős
in 1967, after which he spent a year in Moscow
with Israïl Moiseevich Gelfand. After spending a year in Oxford (Christ Church
), and vowing never to return to Hungary due to his disillusion with the 1956 Soviet intervention and subsequent puppet communist regime, he went to Oxford, where in 1972 he received a Ph.D.
in functional analysis
under the supervision of Frank Adams
.
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 numerous important results on extremal graph theory, functional analysis, the theory of random graphs, graph polynomials and percolation. For example, with Paul Erdős
he proved sharp 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", "Random Graphs" and "Percolation" (with Oliver Riordan), the introductory books "Modern Graph Theory", "Combinatorics" and "Linear Analysis", and the collection of problems "The Art of Mathematics – Coffee Time in Memphis", 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 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 the LSE
.
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.
He is also a sportsman, having represented Oxford University at modern pentathlon
, and Cambridge University
at fencing. His wife, Gabriella Bollobás is an accomplished sculptor and painter.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who has worked in various areas of mathematics, including functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
, graph theory
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
and percolation
Percolation
In physics, chemistry and materials science, percolation concerns the movement and filtering of fluids through porous materials...
. As a student, he took part in the first three International Mathematical Olympiad
International Mathematical Olympiad
The International Mathematical Olympiad is an annual six-problem, 42-point mathematical olympiad for pre-collegiate students and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980...
s, winning two gold medals. He wrote his first doctorate in discrete geometry
Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles,...
under the supervision of László Fejes Tóth
László Fejes Tóth
László Fejes Tóth was a Hungarian mathematician who specialised in geometry. He proved that a honeycomb pattern is the most efficient way to pack centrally symmetric convex sets on the Euclidean plane . He also investigated packings on the sphere...
and Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
in 1967, after which he spent a year in Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
with Israïl Moiseevich Gelfand. After spending a year in Oxford (Christ Church
Christ Church, Oxford
Christ Church or house of Christ, and thus sometimes known as The House), is one of the largest constituent colleges of the University of Oxford in England...
), and vowing never to return to Hungary due to his disillusion with the 1956 Soviet intervention and subsequent puppet communist regime, he went to Oxford, where in 1972 he received a Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
under the supervision of Frank Adams
Frank Adams
John Frank Adams FRS was a British mathematician, one of the founders of homotopy theory.-Life:He was born in Woolwich, a suburb in south-east London. He began research as a student of Abram Besicovitch, but soon switched to algebraic topology. He received his Ph.D. from the University of...
.
He has been a Fellow of Trinity College, Cambridge
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
since 1970; in 1996 he was appointed to the Jabie Hardin Chair of Excellence at the University of Memphis
University of Memphis
The University of Memphis is an American public research university located in the Normal Station neighborhood of Memphis, Tennessee and is the flagship public research university of the Tennessee Board of Regents system....
, and in 2005 he was awarded a Senior Research Fellowship at Trinity College.
He has proved numerous important results on extremal graph theory, functional analysis, the theory of random graphs, graph polynomials and percolation. For example, with Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
he proved sharp 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
Imre Leader
Imre Bennett Leader is a British mathematician and Professor of Pure Mathematics, specifically combinatorics, at the University of Cambridge....
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
Bollobás–Riordan polynomial
The Bollobás–Riordan polynomial can mean a 3-variable polynomial invariant of graphs on orientable surfaces, or a more general 4-variable invariant of ribbon graphs, generalizing the Tutte polynomial...
); with Andrew Thomason, József Balogh, Miklós Simonovits, Robert Morris and Noga Alon
Noga Alon
Noga Alon is an Israeli mathematician noted for his contributions to combinatorics and theoretical computer science, having authored hundreds of papers.- Academic background :...
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
Svante Janson
Svante Janson is a Swedish mathematician. A member of the Royal Swedish Academy of Sciences since 1994, Janson has been the chaired professor of mathematics at Uppsala University since 1987....
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", "Random Graphs" and "Percolation" (with Oliver Riordan), the introductory books "Modern Graph Theory", "Combinatorics" and "Linear Analysis", and the collection of problems "The Art of Mathematics – Coffee Time in Memphis", 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
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
in 1998) and Imre Leader
Imre Leader
Imre Bennett Leader is a British mathematician and Professor of Pure Mathematics, specifically combinatorics, at the University of Cambridge....
at the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
, Alexander Scott and Oliver Riordan now at Oxford
University of Oxford
The University of Oxford is a university located in Oxford, United Kingdom. It is the second-oldest surviving university in the world and the oldest in the English-speaking world. Although its exact date of foundation is unclear, there is evidence of teaching as far back as 1096...
, Jonathan Partington
Jonathan Partington
Jonathan R. Partington is an English mathematician.-Education:Professor Partington was educated at Gresham's School, Holt, and Trinity College, University of Cambridge, where he completed his PhD thesis entitled "Numerical ranges and the Geometry of Banach Spaces" under the supervision of Béla...
and Charles Read
Charles Read (mathematician)
Charles Read is a British mathematician known for his work in functional analysis. In operator theory, Read is best known for his work in the 1980s on the invariant subspace problem, where he constructed operators with only trivial invariant subspaces on particular Banach spaces, especially on...
now at Leeds
University of Leeds
The University of Leeds is a British Redbrick university located in the city of Leeds, West Yorkshire, England...
and Keith Ball and Graham Brightwell
Graham Brightwell
Graham Brightwell is a British mathematician working in the field of discrete mathematics.His Erdős number is 2 owing to his numerous publications with Béla Bollobás....
now in London at the LSE
London School of Economics
The London School of Economics and Political Science is a public research university specialised in the social sciences located in London, United Kingdom, and a constituent college of the federal University of London...
.
Béla Bollobás is an External Member of the Hungarian Academy of Sciences
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
; in 2007 he was awarded the Senior Whitehead Prize
Senior Whitehead Prize
The Senior Whitehead Prize of the London Mathematical Society is currently awarded in odd numbered years in memory of John Henry Constantine Whitehead, president of the LMS between 1953 and 1955. The Prize is awarded to mathematicians normally resident in the United Kingdom on 1 January of the...
by the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
. 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.
He is also a sportsman, having represented Oxford University at modern pentathlon
Modern pentathlon
The modern pentathlon is a sports contest that includes five events: pistol shooting, épée fencing, 200 m freestyle swimming, show jumping, and a 3 km cross-country run...
, and Cambridge University
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
at fencing. His wife, Gabriella Bollobás is an accomplished sculptor and painter.