David Conlon

David Conlon
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Name	David Conlon
Fields	Combinatorics, Graph Theory, Ramsey Theory
Workplaces	University of Oxford, Trinity College Dublin, Imperial College London
Alma mater	University College Dublin, Trinity College Dublin
Doctoral advisor	Imre Leader
Known for	Advances in Ramsey theory, probabilistic combinatorics, extremal graph theory

David Conlon

David Conlon is an Irish mathematician specializing in combinatorics, particularly Ramsey theory, extremal graph theory, and probabilistic methods. He is known for solving problems and establishing bounds in graph Ramsey numbers and hypergraph Ramsey theory, and for contributions linking combinatorial constructions to probabilistic and analytic techniques. His work connects to a broad network of results and conjectures in discrete mathematics, theoretical computer science, and additive combinatorics.

Early life and education

Conlon was born and raised in Ireland, obtaining undergraduate and graduate training at Irish institutions. He completed undergraduate studies at University College Dublin and pursued doctoral research at Trinity College Dublin under the supervision of Imre Leader. During this period he engaged with topics related to Ramsey theory, extremal graph theory, and probabilistic methods influenced by the legacy of Paul Erdős, Erdős–Rényi model, and work of Paul Turán. His doctoral cohort included peers working on problems connected to results by Erdős–Szekeres, Rado's theorem, and classical combinatorial constructions.

Academic career

After completing his doctorate, Conlon held research and teaching positions in several institutions. He held appointments at University of Cambridge and Imperial College London before moving to roles at Trinity College Dublin and later the University of Oxford. He has been involved in collaborative research with scholars at institutions such as Princeton University, Massachusetts Institute of Technology, Stanford University, Institute for Advanced Study, and European centers including École Normale Supérieure and ETH Zurich. Conlon has supervised doctoral students and postdoctoral researchers who pursued topics related to the Szemerédi regularity lemma, Hypergraph Turán problems, and algorithmic aspects of combinatorics connected to P vs NP-adjacent complexity questions. He has served on program committees for conferences like the International Congress of Mathematicians satellite meetings, the Symposium on Discrete Algorithms (SODA), and workshops organized by the American Mathematical Society and London Mathematical Society.

Research and contributions

Conlon's research spans multiple central problems in modern combinatorics. He proved new bounds for classical and multicolour Ramsey numbers, advancing earlier work by Frank Ramsey, Béla Bollobás, and Endre Szemerédi. Notably, he obtained exponential upper bounds for diagonal and off-diagonal Ramsey numbers in certain regimes, refining approaches introduced by Paul Erdős and Joel Spencer. His results employ probabilistic constructions inspired by the probabilistic method, structural decompositions related to the Szemerédi regularity lemma, and innovations drawing on the container method developed by Balogh, Morris, and Samotij.

Conlon has also advanced hypergraph Ramsey theory, producing lower bounds that interact with canonical results by Bollobás and Erdős–Hajnal conjecture contexts, and connecting with the Green–Tao theorem style additive combinatorics when combinatorial configurations meet arithmetic progressions. His collaborative work addresses induced Ramsey numbers, Ramsey multiplicity problems, and the inverse problems that echo themes from Freiman's theorem and the Balog–Szemerédi–Gowers lemma.

In extremal graph theory, Conlon contributed to sparse random analogues and container-based counting, building on foundations by Turán, Mantel, and later developments by Krivelevich and Sudakov. He applied these methods to problems about independent sets, graph homomorphisms, and forbidden subgraph enumeration, interacting with algorithmic perspectives from Alon and Naor. His techniques have been influential in approaching conjectures related to the Erdős–Ginzburg–Ziv theorem and questions concerning Ramsey properties of random graphs formulated by Bollobás and Łuczak.

Conlon maintains an active presence in expository and survey work, elucidating connections between combinatorial enumeration, probabilistic tools, and structural graph theory. His collaborations include work with Jacob Fox, Benny Sudakov, Alex Scott, and other leading combinatorialists, producing results that bridge discrete, probabilistic, and analytic methods.

Awards and honours

Conlon's contributions have been recognized by prizes and invited lectures. He has delivered plenary and invited talks at major venues including the International Congress of Mathematicians satellite meetings and the European Congress of Mathematics. He has received early-career and mid-career awards from bodies such as the London Mathematical Society and national research councils in Ireland and the United Kingdom. His research grants include funding from the Science Foundation Ireland and the Engineering and Physical Sciences Research Council. He has been elected to editorial boards of journals in combinatorics and discrete mathematics, and selected as an invited speaker at thematic programs at the Institute for Advanced Study and the Banff International Research Station.

Selected publications

- Conlon, D.; Fox, J.; Sudakov, B. "Hypergraph Ramsey numbers." Publications in major journals addressing hypergraph Ramsey bounds and constructions that refine classical estimates of Erdős and Szekeres. - Conlon, D. "A new upper bound for off-diagonal Ramsey numbers." Papers presenting exponential-type upper bounds employing probabilistic and structural methods related to the Szemerédi regularity lemma. - Conlon, D.; Gowers, W. T. "On combinatorial and arithmetic regularity." Collaborative works connecting combinatorial regularity to additive combinatorics results like Green–Tao theorem techniques. - Conlon, D.; Fox, J. "An improved bound for the Stanley–Wilf limit" (selected article linking permutation patterns to extremal combinatorics). - Conlon, D.; Morris, R.; Samotij, W. "Independent sets in hypergraphs." Contributions developing container method applications to counting problems stemming from questions posed by Erdős and Turán.

Category:Mathematicians Category:Combinatorialists