Algebraic combinatorics. I'm currently focusing on the combinatorics of Macdonald eigenoperators. This involves the following areas: parking functions, symmetric and quasi-symmetric functions, Macdonald polynomials, the space of diagonal harmonics, and others.

E. Sergel Leven. " A proof of the Square Paths Conjecture." arxiv preprint 1601.06249.

A. Garsia, E. Sergel Leven, N. Wallach, and G. Xin. " A new Plethystic Symmetric Function Operator and the Rational Shuffle Conjecture at t=1/q." To appear in JCTA. arxiv preprint 1501.00631.

F. Bergeron, A. Garsia, E. Leven and G. Xin. "Some remarkable new Plethystic Operators in the Theory of Macdonald Polynomials." To appear in JOC. arXiv preprint 1405.0316.

F. Bergeron, A. Garsia, E. Leven and G. Xin. "Compositional (km,kn)-Shuffle Conjectures." Int. Math. Res. Not. (2015) rnr272.

T. Amdeberham and E. Leven. " Multi-cores, posets, and lattice paths." Adv. Appl. Math. 71 (2015), pp. 1-13.

A. Hicks and E. Leven. "A simpler formula for the number of diagonal inversions of an (m,n)-Parking Function and a returning Fermionic formula." Discrete Math. 383.3 (2015), pp. 48-65.

E. Leven. " Two special cases of the Rational Shuffle Conjecture." DMTCS FPSAC Proceedings (2014), pp. 789-800.

E. Leven, B. Rhoades and A. Wilson. "Bijections for the Shi and Ish Arrangements." European Journal of Combinatorics 39 (2014): 1-23.

A. Hicks and E. Leven. "A refinement of the Shuffle Conjecture with cars of two sizes and t=1/q." Journal of Combinatorics 5.1 (2014): 31-50.

P. Richter, E. Leven, A. Tran, B. Ek, J. Jacob, and D. Narayan "Rank numbers for bent ladders." Discussiones Mathematicae Graph Theory 34 (2014): 309-329.

E. Sergel. "Noncommutative Biorthogonal Polynomials." Advances in Applied Mathematics 48.1 (2012): 99-105.

E. Sergel, P. Richter, A. Tran, P. Curran, J. Jacob, and D. Narayan. "Rank numbers for some trees and unicyclic graphs." Aequationes Mathematicae 82.1-2 (2011): 65-79.