Richard Montgomery (mathematician)

Richard Montgomery
Born1990 (age 35–36)
EducationUniversity of Cambridge
Scientific career
FieldsCombinatorics
WorkplacesUniversity of Warwick
University of Birmingham
Trinity College, Cambridge
Thesis Minors and Spanning Trees in Graphs  (2015)
Andrew Thomason

Richard Montgomery (born 1990) is a British mathematician and professor at the University of Warwick. His research is principally in extremal and probabilistic combinatorics.[1][2]

Education and career

Montgomery studied at the University of Cambridge, receiving a BA and MMath in 2011 and completing his PhD in 2015 under the supervision of Andrew Thomason. His thesis was titled Minors and Spanning Trees in Graphs.[1][3]

He was a postdoctoral fellow at the University of Birmingham in 2015 and a Junior Research Fellow at Trinity College, Cambridge, from 2015 to 2019.[4] At Birmingham, he was a Birmingham Fellow from 2018 to 2020, a Senior Birmingham Fellow from 2020 to 2021 and a reader in combinatorics from 2021 to 2022. In 2022 he joined the University of Warwick as an associate professor. He became a reader there in 2024 and a full professor in 2025.[1]

Research

Montgomery works on extremal and probabilistic combinatorics, particularly problems concerning subgraphs, graph decompositions and random graphs.[5]

He resolved a conjecture of Jeff Kahn about spanning trees in random graphs. Montgomery proved that, for every fixed , there is a constant such that the binomial random graph contains a copy of every tree on vertices with maximum degree at most , with high probability.[6]

With Alexey Pokrovskiy and Benny Sudakov, Montgomery studied decompositions of edge-coloured complete bipartite graphs into rainbow perfect matchings, which correspond to decompositions of Latin squares into transversals. They also proved that every properly edge-coloured complete graph can be nearly decomposed into rainbow spanning trees.[7]

The same authors proved Ringel's conjecture for all sufficiently large . The conjecture, posed by Gerhard Ringel in 1963, states that, for every tree with edges, the edges of the complete graph can be decomposed into copies of .[8][9]

With Hong Liu, Montgomery solved a problem posed by Paul Erdős and András Hajnal in 1981 concerning the odd cycle lengths of graphs with infinite chromatic number. They proved an asymptotically sharp lower bound on the sum of the reciprocals of the odd cycle lengths in a graph in terms of its chromatic number.[10]

In 2023, Montgomery proved the Ryser–Brualdi–Stein conjecture for all sufficiently large even . This conjecture states that every Latin square of even order has a transversal containing cells.[11]

Awards and honours

Together with Alexey Pokrovskiy, Montgomery received the 2019 European Prize in Combinatorics. The prize recognised their "deep contributions to extremal and probabilistic combinatorics".[12]

In 2020, Montgomery received a Philip Leverhulme Prize.[13]

The European Mathematical Society awarded him an EMS Prize in 2024, citing his work on Ringel's conjecture, distributive absorption and sublinear expanders.[14]

In 2025, he received a Whitehead Prize from the London Mathematical Society for his work on the absorption method and sublinear expanders in extremal and probabilistic combinatorics.[15]

In 2026, Montgomery and Julian Sahasrabudhe jointly received the Adams Prize for work in discrete mathematics.[16]

Selected publications

  • Montgomery, Richard; Pokrovskiy, Alexey; Sudakov, Benny (2019). "Decompositions into spanning rainbow structures". Proceedings of the London Mathematical Society. 119 (4): 899–959. arXiv:1805.07564. doi:10.1112/plms.12245.
  • Montgomery, Richard (2023). "A proof of the Ryser–Brualdi–Stein conjecture for large even n". arXiv:2310.19779 [math.CO].

References

  1. 1 2 3 Montgomery, Richard (June 2026). "Curriculum vitae" (PDF). Retrieved 12 August 2026.
  2. ↑ "Professor Richard Montgomery". University of Warwick. Retrieved 12 August 2026.
  3. ↑ "Richard Montgomery". Mathematics Genealogy Project. North Dakota State University. Retrieved 12 August 2026.
  4. ↑ "Elected into Junior Research Fellowships under Title A" (PDF). Cambridge University Reporter. 146 (9): 168. 18 November 2015. Retrieved 12 August 2026.
  5. ↑ "Richard Montgomery". Retrieved 12 August 2026.
  6. ↑ Montgomery, Richard (2019). "Spanning trees in random graphs". Advances in Mathematics. 356 106793. arXiv:1810.03299. doi:10.1016/j.aim.2019.106793.
  7. ↑ Montgomery, Richard; Pokrovskiy, Alexey; Sudakov, Benny (2019). "Decompositions into spanning rainbow structures". Proceedings of the London Mathematical Society. 119 (4): 899–959. arXiv:1805.07564. doi:10.1112/plms.12245.
  8. ↑ Montgomery, Richard; Pokrovskiy, Alexey; Sudakov, Benny (2021). "A proof of Ringel's conjecture". Geometric and Functional Analysis. 31 (3): 663–720. arXiv:2001.02665. doi:10.1007/s00039-021-00576-2.
  9. ↑ Hartnett, Kevin (19 February 2020). "Rainbow Proof Shows Graphs Have Uniform Parts". Quanta Magazine. Retrieved 12 August 2026.
  10. ↑ Liu, Hong; Montgomery, Richard (2023). "A solution to Erdős and Hajnal's odd cycle problem". Journal of the American Mathematical Society. 36 (4): 1191–1234. arXiv:2010.15802. doi:10.1090/jams/1018.
  11. ↑ Montgomery, Richard (2023). "A proof of the Ryser–Brualdi–Stein conjecture for large even n". arXiv:2310.19779 [math.CO].
  12. ↑ "Birmingham Researcher Receives European Prize in Combinatorics". University of Birmingham. 8 October 2019. Retrieved 12 August 2026.
  13. ↑ "Philip Leverhulme Prize – Richard Montgomery". University of Birmingham. Retrieved 12 August 2026.
  14. ↑ "Fourteen prizes awarded to European mathematicians at the 9th ECM". European Mathematical Society. 15 July 2024. Retrieved 12 August 2026.
  15. ↑ "LMS Prize Winners 2025". London Mathematical Society. 4 July 2025. Retrieved 12 August 2026.
  16. ↑ "Adams Prize Winner 2025–26". University of Cambridge. 2026. Retrieved 12 August 2026.
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