Peter Keevash (born 30 November 1978) is a British mathematician, working in

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

. He is a professor of mathematics at the

University of Oxford The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...

and a Fellow of Mansfield College.

Early years

Keevash was born in

Brighton Brighton ( ) is a seaside resort in the city status in the United Kingdom, city of Brighton and Hove, East Sussex, England, south of London. Archaeological evidence of settlement in the area dates back to the Bronze Age Britain, Bronze Age, R ...

, England, but mostly grew up in

Leeds Leeds is a city in West Yorkshire, England. It is the largest settlement in Yorkshire and the administrative centre of the City of Leeds Metropolitan Borough, which is the second most populous district in the United Kingdom. It is built aro ...

. He competed in the

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is widely regarded as the most prestigious mathematical competition in the wor ...

in 1995. He entered

Trinity College Trinity College may refer to: Australia * Trinity Anglican College, an Anglican coeducational primary and secondary school in , New South Wales * Trinity Catholic College, Auburn, a coeducational school in the inner-western suburbs of Sydney, New ...

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

, in 1995 and completed his

B.A. A Bachelor of Arts (abbreviated B.A., BA, A.B. or AB; from the Latin ', ', or ') is the holder of a bachelor's degree awarded for an undergraduate program in the liberal arts, or, in some cases, other disciplines. A Bachelor of Arts degree ...

in mathematics in 1998. He earned his doctorate from

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

with Benny Sudakov as advisor. He took a postdoctoral position at the

California Institute of Technology The California Institute of Technology (branded as Caltech) is a private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small group of institutes ...

before moving to

Queen Mary, University of London Queen Mary University of London (QMUL, or informally QM, and formerly Queen Mary and Westfield College) is a public research university in Mile End, East London, England. It is a member institution of the federal University of London. Today, ...

as a lecturer, and subsequently professor, before his move to Oxford in September 2013.

Mathematics

Keevash has published many results in

, particularly in extremal graph and hypergraph theory and

Ramsey Theory Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of the mathematical field of combinatorics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in R ...

. In joint work with Tom Bohman he established the best-known lower bound for the off-diagonal

Ramsey Number In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. To demonstrate the theorem for two colours (sa ...

R(3,k)

, namely

R(3,k) \geq \left(\frac - o(1)\right)\frac.

(This result was obtained independently at the same time by Fiz Pontiveros, Griffiths and Morris.) On 15 January 2014, he released a preprint establishing the existence of

block design In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as ''blocks'', chosen such that number of occurrences of each element satisfies certain conditions making the co ...

s with arbitrary parameters, provided only that the underlying set is sufficiently large and satisfies certain obviously necessary divisibility conditions. In particular, his work provides the first examples of

Steiner system 250px, thumbnail, The Fano plane is a Steiner triple system S(2,3,7). The blocks are the 7 lines, each containing 3 points. Every pair of points belongs to a unique line. In combinatorial mathematics, a Steiner system (named after Jakob Steiner ...

s with parameter ''t'' ≥ 6 (and in fact provides such systems for all ''t''). In 2018, he was an invited speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

Rio de Janeiro Rio de Janeiro, or simply Rio, is the capital of the Rio de Janeiro (state), state of Rio de Janeiro. It is the List of cities in Brazil by population, second-most-populous city in Brazil (after São Paulo) and the Largest cities in the America ...

References

External links

Peter Keevash home page at the University of Oxford
* {{DEFAULTSORT:Keevash, Peter 1978 births Living people Alumni of Trinity College, Cambridge 20th-century English mathematicians 21st-century English mathematicians Combinatorialists International Mathematical Olympiad participants Whitehead Prize winners Academics of the University of Oxford