Professor of Mathematics, University of Oxford. Profile/Contact.
Tutorial Fellow, Mansfield College. Profile/Contact.

Research interests

Extremal & Probabilistic Combinatorics, Graph Theory, Hypergraphs / Set Systems, Random Structures, Phase Transitions, Combinatorial Optimisation, Algorithms, Combinatorial Geometry, Isoperimetry, Additive Combinatorics, Algebraic Methods, Expansion & Growth in Groups.

Grant funding

PI of ERC Advanced Grant 883810, Combinatorial Applications of Random Processes and Expansion (CARPE), 2021-2027.
PI of ERC Consolidator Grant 647678, Combinatorial Construction (CC), 2016-2021.
PI of ERC Starting Grant 239696 Extremal Combinatorics (EC), 2010-2016.
PI of EPSRC grant EP/G056730/1, 2009-2012.
PI of NSF grant DMS-0555755, 2006-2009.

• A. Ghosal, R. Goenka, A. Grebennikov, P. Keevash, M. Kwan and H. T. Pham, No-(k+1)-in-line problem for k ≥ 3, arXiv:2607.05255.
• P. Keevash and J. Lim, On the largest sum-free subset of the lattice cube, arXiv:2605.00816.
• P. Keevash and P. Michaeli, A very robust Ramsey theorem for matchings, arXiv:2603.03139.
• R. Goenka, P. Keevash and T. Przybyłowski, Source localisation in simple random walks, arXiv:2601.10624.
• P. Keevash and P. Michaeli, A generalised Ramsey-Turan problem for matchings, arXiv:2509.10679.
• A. Ghosal, R. Goenka and P. Keevash, On subsets of lattice cubes avoiding affine and spherical degeneracies, arXiv:2509.06935.
• N. Draganic, P. Keevash and A. Muyesser, Cyclic subsets in regular Dirac graphs, arXiv:2503.01826, Int. Math. Res. Not. 2025(14):rnaf215.
• N. Draganic and P. Keevash, Posa rotation through a random permutation, arXiv:2502.00489.
• P. Keevash, A short proof of the existence of designs, arXiv:2411.18291.
• T. Karam and P. Keevash, The structure of sets with cube-avoiding sumsets, arXiv:2411.14145, Mathematika 71(4):e70041 (2025).
• J. Haslegrave and P. Keevash, Balanced two-type annihilation: mean-field asymptotics, arXiv:2404.04128, Electron. Commun. Probab. 31:1--11 (2026).
• P. Keevash and N. Lifshitz, Sharp hypercontractivity for symmetric groups and its applications, arXiv:2307.15030.
• P. van Hintum and P. Keevash, Locality in Sumsets, arXiv:2304.01189, Advances Math. 485:110727 (2026).
• P. Keevash, The optimal edge-colouring threshold, arXiv:2212.04397.
• C. Bowtell and P. Keevash, The n-queens problem, arXiv:2109.08083.
• P. Keevash, The existence of designs II, arXiv:1802.05900.
• P. Keevash, The existence of designs, arXiv:1401.3665.
• P. Keevash, A. Sah and M. Sawhney, The existence of subspace designs, arXiv:2212.00870, Proc. London Math. Soc. 131(1):e70071 (2025).
• B. Bukh, P. van Hintum and P. Keevash, Additive Bases: Change of Domain, arXiv:2409.07442, Acta Arithmetica 221:239--252 (2025).
• P. Keevash and J. Long, The Brown-Erdos-Sos conjecture for hypergraphs of large uniformity, arXiv:2007.14824, to appear in Proc. Amer. Math. Soc.
• P. Keevash, I. Leader, J. Long and A.Z. Wagner, The extremal number of Venn diagrams, arXiv:1911.00487, Proc. Amer. Math. Soc. 154:3281--3293 (2026).
• P. Keevash and K. Staden, Ringel's tree packing conjecture in quasirandom graphs, J. Europ. Math. Soc. 27:1769--1826 (2025).
• J. Haslegrave and P. Keevash, Dissipative particle systems on expanders, Probab. Theory Related Fields 194:1287--1326 (2026).
• P. van Hintum, P. Keevash and M. Tiba, On Ruzsa's discrete Brunn-Minkowski conjecture, Proc. Amer. Math. Soc. 153:459--466 (2025).
• P. Keevash, N. Lifshitz, E. Long and D. Minzer, Turan problems for expanded hypergraphs, Combinatorica 45:27 (2025).
• P. Keevash, N. Lifshitz and D. Minzer, On the Largest Product-free Subsets of the Alternating Groups, Invent. Math. 237:1329--1375 (2024).
• P. Keevash, N. Lifshitz, E. Long and D. Minzer, Hypercontractivity for global functions and sharp thresholds, J. Amer. Math. Soc. 37:245--279 (2024).
• P. van Hintum and P. Keevash, The sharp doubling threshold for approximate convexity, Bull. London. Math. Soc. 56 (2024).
• N. Draganic and P. Keevash, Long induced paths in expanders, Combin. Probab. Comput. 34:276--282 (2025).
• P. van Hintum and P. Keevash, Sharp bounds for a Discrete John's Theorem, Combin. Probab. Comput. 33:484--486 (2024).
• Y. Cheng and P. Keevash, On the length of directed paths in digraphs, SIAM J. Disc. Math. 38:3134--3139 (2024).
• C. Chen, P. Keevash, S. Kennedy, E. Panafieu and A. Vetta, Robot positioning using torus packing for multisets, Proc. 51st ICALP 43:1--18 (2024).
• P. Keevash, N. Lifshitz, E. Long and D. Minzer, Forbidden intersections for codes, J. London Math. Soc. 108 (2023).
• M. Jenssen and P. Keevash, Homomorphisms from the torus, Advances Math. 430:109212 (2023).
• B. Barber, J. Erde, P. Keevash and A. Roberts, Isoperimetric stability in lattices, Proc. Amer. Math. Soc. 151:5021--5029 (2023).
• P. Keevash, A. Pokrovskiy, B. Sudakov and L. Yepremyan, New bounds for Ryser's conjecture and related problems, Trans. Amer. Math. Soc. Ser. B 9:288--321 (2022).
• P. Keevash and K. Staden, The generalised Oberwolfach problem, J. Combin. Theory Ser. B 152:281--318 (2022).
• P. Keevash, J. Long, B. Narayanan and A. Scott, A universal exponent for homeomorphs, Israel J. Math. 243:141--154 (2021).
• T. Bohman and P. Keevash, Dynamic concentration of the triangle-free process, Random Struct. Alg. 58:221--293 (2021).
• P. Keevash, E. Long and J. Skokan, Cycle-complete Ramsey numbers, Int. Math. Res. Not. 2021:275--300 (2021).
• M. Jenssen, P. Keevash, E. Long and L. Yepremyan, Distinct degrees in induced subgraphs, Proc. Amer. Math. Soc. 148:3835--3846 (2020).
• P. Keevash and E. Long, Forbidden vector-valued intersections, Proc. London Math. Soc. 121:702--742 (2020).
• P. Keevash and E. Long, Stability for vertex isoperimetry in the cube, J. Combin. Theory Ser. B. 145:113--114 (2020).
• K. Clinch, B. Jackson and P. Keevash, Global rigidity of direction-length frameworks, J. Combin. Theory Ser. B. 145:145--168 (2020).
• M. Coulson, P. Keevash, G. Perarnau and L. Yepremyan, Rainbow factors in hypergraphs, J. Combin. Theory Ser. A. 172:1--14 (2020).
• P. Keevash and L. Yepremyan, On the number of symbols that forces a transversal, Combin. Probab. Comput. 29:234--240 (2020).
• J. Han and P. Keevash, Finding matchings in dense hypergraphs, arXiv:2210.12643, ACM Trans. Algorithms 22(2), Article 14, 21 pp. (2026). Preliminary version in Proc. 31st SODA 2366--2377 (2020).
• P. Keevash, Coloured and directed designs, Building Bridges II: Mathematics of Laszlo Lovasz, Bolyai Society Mathematical Studies 28, 2019.
• M. Jenssen, P. Keevash and W. Perkins, Algorithms for #BIS-hard problems on expander graphs, SIAM J. Computing 49:681--710 (2020). Preliminary version in Proc. 30th SODA 2235--2247 (2019).
• P. Keevash, Hypergraph matchings and designs, 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. Preliminary version 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. Verstraëte, 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. Verstraëte, 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. Verstraëte, 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, Local density in graphs with forbidden subgraphs, 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.