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 an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

. He is Professor of Mathematics at the

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

and a Fellow of Mansfield College.

Early years

Keevash was born in

Brighton Brighton () is a seaside resort and one of the two main areas of the City of Brighton and Hove in the county of East Sussex, England. It is located south of London. Archaeological evidence of settlement in the area dates back to the Bronze A ...

England England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest and the Celtic Sea to the southwest. It is separated from continental Europe b ...

, but mostly grew up in

Leeds Leeds () is a city and the administrative centre of the City of Leeds district in West Yorkshire, England. It is built around the River Aire and is in the eastern foothills of the Pennines. It is also the third-largest settlement (by populati ...

. 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. The first IMO was held in Romania in 1959. It has since been held annually, except i ...

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 , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

, in 1995 and completed his

B.A. Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four yea ...

in mathematics in 1998. He earned his doctorate from

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

with

Benny Sudakov Benny Sudakov (born October 1969) is an Israeli mathematician, who works mainly on Hungarian-style combinatorics. He was born in Tbilissi, Georgia, and completed his undergraduate studies at Tbilisi State University in 1990. After emigrating to ...

as advisor. He took a postdoctoral position at the

California Institute of Technology The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

before moving to

Queen Mary, University of London , mottoeng = With united powers , established = 1785 – The London Hospital Medical College1843 – St Bartholomew's Hospital Medical College1882 – Westfield College1887 – East London College/Queen Mary College , type = Public researc ...

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 mathematics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask a ...

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

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 frequency of the elements satisfies certain conditions making the collection of bl ...

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 Nevanlinna Prize (to be rename ...

Rio de Janeiro Rio de Janeiro ( , , ; literally 'River of January'), or simply Rio, is the capital of the state of the same name, Brazil's third-most populous state, and the second-most populous city in Brazil, after São Paulo. Listed by the GaWC as a b ...

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