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Packing and counting arbitrary Hamilton cycles in random digraphs
RANDOM STRUCTURES & ALGORITHMS issue 3 volume 54 page 499-514 (May 2019) Full text available
Packing, counting and covering Hamilton cycles in random directed graphs
ISRAEL JOURNAL OF MATHEMATICS issue 1 volume 220 page 57-87 (June 2017) Full text available
Counting Hamilton Decompositions of Oriented Graphs
International Mathematics Research Notices (16 May 2017)
Set families with a forbidden pattern
European Journal of Combinatorics volume 62 page 183-196 (May 2017)
Extremal Combinatorics, Graph Theory, Set Systems, Probabilistic Methods in Combinatorics, High Dimensional Phenomena, Discrete Geometry.
University of Oxford:
- Constructive Mathematics
- Linear Algebra
- Number Theory
- Rings and Modules
Queen Mary, University of London:
Lectured course in Extremal Combinatorics
University of Cambridge:
Courses supervised from the Cambridge Tripos:
- Analysis II
- Complex Analysis
- Graph Theory
- Math IA revision supervisions
- Metric and Topological Spaces
- Probability IA
- Probability and Measure
Prizes, awards, and scholarships:
Smith-Knight Prize (2010): University of Cambridge
Benefactor's Scholarship (2008): St. John's College, Cambridge.
Gates Scholarship (2006): University of Cambridge.
Hamilton Prize (2005): Royal Irish Academy.
Foundation Scholarship and Toronto Prize (2004): Trinity College Dublin.
Major / recent publications:
- Hypercontractivity for global functions and sharp thresholds, P. Keevash, N. Lifshitz, E. Long, D. Minzer.
- Stability for vertex isoperimetry in the cube, P. Keevash, E. Long, Submitted.
- Cycle-complete Ramsey numbers, P. Keevash, E. Long, J. Skokan, Submitted.
- Forbidden vector-valued intersections, P. Keevash, E. Long, Submitted.
- Packing and counting arbitrary Hamilton cycles in random digraphs, A. Ferber, E. Long, Random Structures and Algorithms, to appear.
Counting Hamilton decompositions of oriented graphs, A. Ferber, E. Long, B. Sudakov, International Mathematics Research Notices, 22 (2018), 6908-6933.
A stability result for the cube edge isoperimetric inequality, P. Keevash, E. Long, Journal of Combinatorial Theory Series A, 155 (2018), 360-375.
On a Ramsey-type problem of Erdős and Pach, R.J. Kang, E. Long, V. Patel, G. Regts, Bulletin of the London Mathematical Society, 49 (2017), 991-999.
Set families with a forbidden pattern, I. Karpas, E. Long, European Journal of Combinatorics, 62 (2017), 183-196.
- Packing, counting and covering Hamilton cycles in random directed graphs, A. Ferber, G. Kronenberg, E. Long, Israel Journal of Mathematics, 220 (2017), 57–87.
- Frankl-Rödl type theorems for codes and permutations, P. Keevash, E. Long, Transactions of the American Mathematical Society, 369 (2017), 1147-1162.
- Large unavoidable subtournaments, E. Long. Combinatorics, Probability and Computing, 26 (2017), 68-77.
- On the normalized Shannon capacity of a union, P. Keevash, E. Long. Combinatorics, Probability and Computing, 25 (2016), 766-767.
- Forbidding intersection patterns between layers of the cube, E. Long. Journal of Combinatorial Theory Series A, 134 (2015), 103–120.
- Long geodesics in subgraphs of the cube, I. Leader, E. Long. Discrete Mathematics, 326 (2014), 29-33.
- Forbidding a set difference of size 1, I. Leader, E. Long. Discrete Applied Mathematics, 169 (2014), 219-224.
- Tilted Sperner families, I. Leader, E. Long. Discrete Applied Mathematics, 163 (2014), 194-198.
- Long paths and cycles in subgraphs of the cube, E. Long. Combinatorica, 33 (2013), 395-428.
- Random walks on quasirandom graphs, B. Barber, E. Long. Electronic Journal of Combinatorics, 20 (2013) P25.