Professor of Mathematics, University of Oxford.
Profile/Contact.

Tutorial Fellow, Mansfield College.
Profile/Contact.

Research interests

Extremal Combinatorics, Graph Theory, Hypergraphs / Set Systems,
Algebraic and Probabilistic Methods in Combinatorics,

Random Structures, Combinatorial Optimisation and
Combinatorial Number Theory.

- P. Keevash, E. Long and J. Skokan, Cycle-complete Ramsey numbers, submitted.
- M. Jenssen, P. Keevash and W. Perkins, Algorithms for #BIS-hard problems on expander graphs, submitted.
- P. Keevash and E. Long, Stability for vertex isoperimetry in the cube, submitted.
- M. Coulson, P. Keevash, G. Perarnau and L. Yepremyan, Rainbow factors in hypergraphs, submitted.
- P. Keevash and E. Long, Forbidden vector-valued intersections, submitted.
- P. Keevash, The existence of designs II, submitted.
- P. Keevash, The existence of designs, submitted.
- P. Keevash, Coloured and directed designs, submitted.
- T. Bohman and P. Keevash, Dynamic concentration of the triangle-free process, submitted.
- K. Clinch, B. Jackson and P. Keevash, Global rigidity of 2-dimensional direction-length frameworks, submitted.
- P. Keevash and L. Yepremyan, On the number of symbols that forces a transversal, submitted.
- P. Keevash, Hypergraph matchings and designs, to appear in the Proceedings of the 2018 International Congress of Mathematicians.
- P. Keevash and L. Yepremyan, Rainbow matchings in properly-coloured multigraphs, SIAM J. Discrete Math. 32 (2018), 1577--1584.
- P. Keevash and E. Long, A stability result for the cube edge isoperimetric inequality, J. Combin. Theory Ser. A 155 (2018), 360--375.
- I. Balla, F. Draxler, P. Keevash and B. Sudakov, Equiangular lines and spherical codes in Euclidean space, Inventiones 211 (2018), 179--212.
- P. Keevash, Counting designs, J. Eur. Math. Soc. 20 (2018), 903--927.
- P. Keevash, Counting Steiner Triple Systems, Proc. 7th European Congress of Mathematics (2016), 459--482.
- P. Keevash and W. Lochet, The structure of typical eye-free graphs and a Turan-type result for two weighted colours, Combin. Probab. Comput. 26 (2017), 886--910.
- P. Keevash and E. Long, Frankl-Rodl type theorems for codes and permutations, Trans. Amer. Math Soc. 369 (2017), 1147--1162.
- P. Keevash and E. Long, On the normalized Shannon capacity of a union, Combin. Probab. Comput. 25 (2016), 766--767.
- P. Keevash and R. Mycroft, A multipartite Hajnal-Szemeredi theorem, J. Combin. Theory Ser. B 114 (2015), 187--236.
- P. Keevash, F. Knox and R. Mycroft,
Polynomial-time perfect matchings in dense hypergraphs,
Adv. Math. 269 (2015), 265--334.

A preliminary version appeared in Proc. 45th ACM STOC (2013). - P. Keevash, J. Lenz and D. Mubayi, Spectral extremal problems for hypergraphs, SIAM J. Disc. Math. 28 (2014), 1838--1854.
- P. Allen, P. Keevash, B. Sudakov and J. Verstraete, Turan numbers of bipartite graphs plus an odd cycle, J. Combin. Theory Ser. B 106 (2014), 134--162.
- P. Keevash and R. Mycroft, A geometric theory for hypergraph matching, Mem. Amer. Math. Soc. 233 (2014), number 1098.
- P. Keevash, B. Sudakov and J. Verstraëte, On a conjecture of Erdős and Simonovits: Even cycles, Combinatorica 33 (2013), 699--732.
- D. Hefetz and P. Keevash, A hypergraph Turan theorem via lagrangians of intersecting families, J. Combin. Theory Ser. A 120 (2013), 2020--2038.
- D. Christofides, D. Ellis and P. Keevash, An approximate vertex-isoperimetric inequality for r-sets, Electronic J. Combin. 20 (2013), P13.
- P. Keevash, Z. Li, B. Mohar and B. Reed, Digraph girth via chromatic number, SIAM J. Disc. Math. 27 (2013), 693--696.
- D. Christofides, P. Keevash, D. Kühn and D. Osthus, Finding Hamilton cycles in robustly expanding digraphs, J. Graph Alg. Appl. 16 (2012), 337--360.
- P. Keevash and D. Mubayi, The Turan number of F33, Combin. Probab. Comput. 21 (2012), 451--456.
- P. Keevash, Hypergraph Turan Problems, Surveys in Combinatorics, Cambridge University Press, 2011, 83--140.
- B. Jackson and P. Keevash, Necessary conditions for the global rigidity of direction-length frameworks, Disc. Comp. Geom. 46 (2011), 72--85.
- B. Jackson and P. Keevash, Bounded direction-length frameworks, Disc. Comp. Geom. 46 (2011), 48--71.
- P. Keevash, D. Kühn, R. Mycroft and D. Osthus, Loose Hamilton cycles in hypergraphs, Disc. Math. 311 (2011), 544--559.
- P. Keevash, A hypergraph blowup lemma, Random Struct. Alg. 39 (2011), 275--376.
- T. Bohman and P. Keevash, The early evolution of the H-free process, Invent. Math. 181 (2010), 291--336.
- P. Keevash and D. Mubayi, Set systems without a simplex or a cluster, Combinatorica 30 (2010), 175--200.
- D. Christofides, P. Keevash, D. Kühn and D. Osthus, A semi-exact degree condition for Hamilton cycles in digraphs, SIAM J. Disc. Math. 24 (2010), 709--756.
- P. Keevash and B. Sudakov, Pancyclicity of Hamiltonian and highly connected graphs, J. Combin. Theory Ser. B 100 (2010), 456--467.
- J. Fox, P. Keevash and B. Sudakov, Directed graphs without short cycles, Combin. Probab. Comput. 19 (2010), 285--301.
- P. Keevash and B. Sudakov, Triangle packings and 1-factors in oriented graphs, J. Combin. Theory Ser. B 99 (2009), 709--727.
- P. Keevash,
A hypergraph regularity method for generalised Turan problems,
Random Struct. Alg. 34 (2009), 123--164.

- P. Keevash, D. Kühn and D. Osthus, An exact minimum degree condition for Hamilton cycles in oriented graphs, J. London Math. Soc. 79 (2009), 144--166.
- P. Keevash,
Shadows and intersections: stability and new proofs, Adv. Math. 218
(2008), 1685--1703. Addendum (January
2010).

- P. Keevash and Y. Zhao, Codegree problems for projective geometries, J. Combin. Theory Ser. B 97 (2007), 919--928.
- P. Keevash, D. Mubayi and R. M. Wilson, Set systems with no singleton intersection, SIAM J. Disc. Math. 20 (2007), 1031--1041.
- P. Keevash, D. Mubayi, B. Sudakov and J. Verstraete,
Rainbow Turan Problems, Combin. Probab. Comput. 16 (2007), 109--126.
Unabridged version. Erratum.

- J. Balogh, P. Keevash and B. Sudakov, On the minimal degree implying equality of the largest triangle-free and bipartite subgraphs, J. Combin. Theory Ser. B 96 (2006), 919--932.
- R. P. Anstee and P. Keevash, Pairwise intersections and forbidden configurations, European J. Combin. 27 (2006), Special Issue on Extremal and Probabilistic Combinatorics, 1235--1248.
- P. Keevash and C. Y. Ku, A random construction for permutation codes and the covering radius, Designs, Codes and Cryptography 41 (2006), 79--86.
- P. Keevash and B. Sudakov, On a restricted cross-intersection problem, J. Combin. Theory Ser. A 113 (2006), 1536--1542.
- P. Keevash, P. Loh and B. Sudakov, Bounding the number of edges in permutation graphs, Electron. J. Combin. 13 (2006), R44.
- P. Keevash and B. Sudakov, Sparse halves in triangle-free graphs, J. Combin. Theory Ser. B 96 (2006), 614--620.
- P. Keevash and B. Sudakov, On a hypergraph Turan problem of Frankl, Combinatorica 25 (2005), 673--706.
- P. Keevash and B. Sudakov, The Turan number of the Fano plane, Combinatorica 25 (2005), 561--574.
- P. Keevash, The Turan problem for projective geometries, J. Combin. Theory Ser. A, 111 (2005), 289--309. Here is a minor correction.
- J. Balogh, P. Keevash and B. Sudakov, Disjoint representability of sets and their complements, J. Combin. Theory Ser. B, 95 (2005), 12--28.
- P. Keevash, The Turan problem for hypergraphs of fixed size, Electron. J. Combin. 12 (2005), N11.
- P. Keevash and B. Sudakov, Set systems with restricted cross-intersections and the minimum rank of inclusion matrices, SIAM J. Disc. Math. 18 (2005), 713--727.
- N. Alon, J. Balogh, P. Keevash and B. Sudakov, The number of edge colorings with no monochromatic cliques, J. London Math. Soc. 70 (2004), 273--288.
- P. Keevash and D. Mubayi, Stability theorems for cancellative hypergraphs, J. Combin. Theory Ser. B 92 (2004), 163--175.
- B. Bollobas, P. Keevash and B. Sudakov, Multicoloured extremal problems, J. Combin. Theory Ser. A 107 (2004), 295--312.
- P. Keevash and B. Sudakov,
Packing triangles in a graph and its complement, J. Graph Theory 47
(2004), 203--216.

A magma program implementing an algorithm used in this paper can be downloaded here. - P. Keevash, M. Saks, B. Sudakov and J. Verstraete, Multicolour Turan problems, Adv. in Applied Math. 33 (2004), 238--262.
- P. Keevash and B. Sudakov, On the number of edges not covered by monochromatic copies of a fixed graph, J. Combin. Theory Ser. B 90 (2004), 41--53.
- P. Keevash and B. Sudakov, , Combin. Probab. Comput. 12 (2003), 139--153.
- B. M. Hambly, P. Keevash, N. O'Connell and D. Stark, The characteristic polynomial of a random permutation matrix, Stoch. Proc. Appl. 90 (2000), 335--346.