Eoin Long

MeI am a postdoctoral researcher at the Mathematical Institute, University of Oxford working with Peter Keevash. I also hold a stipendiary lecturership in mathematics at Mansfield College. I am interested in extremal combinatorics, graph theory, set systems, probabilistic methods in combinatorics, high dimensional phenomena and discrete geometry. Before coming to Oxford, I held a postdoctoral position at the School of Mathematical Sciences, Tel Aviv University hosted by Noga Alon, Michael Krivelevich, Wojciech Samotij and Asaf Shapira and at Queen Mary, University of London. I completed my PhD in mathematics in 2012 under the supervision of Imre Leader at the University of Cambridge. I was an undergraduate at Trinity College Dublin.

E-mail: long(at)maths.ox.ac.uk

Research

18. Cycle-complete Ramsey numbers
Peter Keevash, Eoin Long, Jozef Skokan
Submitted. 19p. pdf
17. Stability for vertex isoperimetry in the cube
Peter Keevash, Eoin Long
Submitted. 24p. pdf
16. Forbidden vector-valued intersections
Peter Keevash, Eoin Long
Submitted. 40p. pdf
15. Packing and counting arbitrary Hamilton cycles in random digraphs
Asaf Ferber, Eoin Long
Random Structures and Algorithms, to appear. 16p. pdf
14. Counting Hamilton decompositions of oriented graphs
Asaf Ferber, Eoin Long, Benny Sudakov
International Mathematics Research Notices, 22 (2018), 6908-6933. pdf
13. A stability result for the cube edge isoperimetric inequality
Peter Keevash, Eoin Long
Journal of Combinatorial Theory Series A, 155 (2018), 360-375. pdf
12. On a Ramsey-type problem of Erdős and Pach
Ross Kang, Eoin Long, Viresh Patel, Guus Regts
Bulletin of the London Mathematical Society, 49 (2017), 991-999. pdf
11. Frankl-Rödl type theorems for codes and permutations
Peter Keevash, Eoin Long
Transactions of the American Mathematical Society, 369 (2017), 1147-1162. pdf
10. Set families with a forbidden pattern
Ilan Karpas, Eoin Long
European Journal of Combinatorics, 62 (2017), 183-196. pdf
9. Packing, counting and covering Hamilton cycles in random directed graphs
Asaf Ferber, Gal Kronenberg, Eoin Long
Israel Journal of Mathematics, 220 (2017), 57-87. pdf
8. Large unavoidable subtournaments
Eoin Long
Combinatorics, Probability and Computing, 26 (2017), 68-77. pdf
7. On the normalized Shannon capacity of a union
Peter Keevash, Eoin Long
Combinatorics, Probability and Computing, 25 (2016), 766-767. pdf
6. Forbidding intersection patterns between layers of the cube
Eoin Long
Journal of Combinatorial Theory Series A, 134 (2015), 103-120. pdf
5. Long geodesics in subgraphs of the cube
Imre Leader, Eoin Long
Discrete Mathematics, 326 (2014), 29-33. pdf
4. Forbidding a set difference of size 1
Imre Leader, Eoin Long
Discrete Applied Mathematics, 169 (2014), 219-224. pdf
3. Tilted Sperner families
Imre Leader, Eoin Long
Discrete Applied Mathematics, 163 (2014), 194-198. pdf
2. Long paths and cycles in subgraphs of the cube
Eoin Long
Combinatorica, 33 (2013), 395-428. pdf
1. Random walks on quasirandom graphs
Ben Barber, Eoin Long
Electronic Journal of Combinatorics, 20 (2013) P25. pdf

Teaching

Courses lectured at University of Oxford:

Combinatorics
Graph Theory (short option)
Courses tutored at University of Oxford:

Combinatorics
Constructive Mathematics
Geometry
Integration
Linear Algebra
Number Theory
Rings and Modules
Courses lectured at Queen Mary, University of London:

Extremal Combinatorics
Courses supervised at University of Cambridge:

Analysis
Analysis II
Complex Analysis
Graph Theory
Math IA revision supervisions
Metric and Topological Spaces
Probability IA
Probability and Measure