Keevash grew up in Leeds , took part in the International Mathematical Olympiad in 1995 (bronze medal) and studied mathematics at Cambridge University (Trinity College) from 1995 with a bachelor's degree in 1998. He was trained in Princeton in 2004 by Benny Sudakov on The Role of Approximate Structure in Extremal Combinatorics and was a post-doctoral student at Caltech . He was a lecturer and then professor at Queen Mary College, University of London, and has been a professor at Oxford University since 2013 . He is a Tutorial Fellow at Mansfield College, Oxford.
He deals with extremal combinatorics, graph theory , hypergraphs , algebraic and probabilistic methods in combinatorics, random structures in combinatorics, combinatorial optimization and combinatorial number theory.
In 2014 he proved an important problem of combinatorics that had been open for a long time, the question of the existence of combinatorial designs ( block plans ) for any values of the parameters, whereby these must meet certain natural divisibility conditions. He proved that for all k, t and such designs exist for all numbers v that meet the divisibility conditions mentioned, apart from a finite number of exceptions. For t = 2 Richard M. Wilson had already proved the existence of sufficiently large feasible v from 1972 to 1975. In 2015 Keevash also found an approximate estimate for the number of designs with certain parameters, also a long-standing problem. He proved and generalized a conjecture by Richard M. Wilson from 1974, who formulated it for Steiner-Triple systems. Keevash used the Randomized Algebraic Construction method he had developed . Examples of designs and Steiner systems with t greater than 2 were only incompletely known, and Keevash's theorem proved their existence even for any t.
- with T. Bohman: The early evolution of the H-free process , Inventiones Mathematicae 181 (2010), 291-336.
- with R. Mycroft: A geometric theory of hyper graph matching , Mem.AMS 233 (2014)
- The existence of designs , arxiv.org/abs/1401.3665
- WT Gowers: Probabilistic combinatorics and the recent work of Peter Keevash, Bulletin AMS 2016, Online
- Results from Keevash at the International Mathematical Olympiad
- The blocks of such a block plan are k-element subsets of a set P with v elements. It is required that every subset of P with t elements is contained in exactly blocks. In this case one speaks of Steiner systems.
- Keevash: The existence of designs, Preprint 2014, Arxiv
- Keevash, Counting Designs, Preprint 2015, Arxiv
- Gil Kalai : Amazing: Peter Keevash Constructed General Steiner Systems and Designs 2014
- Bohman, Keevash: Dynamic concentration of the triangle-free process, Arxiv 2013
|BRIEF DESCRIPTION||British mathematician|
|DATE OF BIRTH||November 30, 1978|
|PLACE OF BIRTH||Brighton|