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.

János Komlós, Emily Sergel, and Gábor Tusnády. " The asymptotic normality of (s,s+1)-cores with distinct parts." arXiv preprint 1809.00412.

Emily Sergel. " A combinatorial model for ∇ m_μ." arXiv preprint 1804.06037. Extended abstract to appear in Sém. Lothar. Combin. FPSAC 2018 Proceedings.

Dun Qiu, Jeffery B. Remmel, Emily Sergel, and Guoce Xin. " On the Schur positivity of Δ_e2 e_n[X]." arXiv preprint 1710.03340. Accepted for publication in Electron. J. Combin.

James Haglund and Emily Sergel. " A generalized major index statistic on tableaux." Sém. Lothar. Combin. 78 (2017) B78b.

Emily Sergel. " A proof of the Square Paths Conjecture." J. Combin. Theory, Ser. A 152C (2017) 363-379.

Adriano Garsia, Emily Sergel Leven, Nolan Wallach, and Guoce Xin. " A new plethystic symmetric function operator and the rational shuffle conjecture at t=1/q." J. Combin. Theory, Ser. A 145 (2017) 57-100.

Emily Sergel. " The Combinatorics of nabla pn and connections to the Rational Shuffle Conjecture." PhD thesis, University of California, San Diego (2016).

François Bergeron, Adriano Garsia, Emily Sergel Leven and Guoce Xin. "Some remarkable new plethystic operators in the theory of Macdonald polynomials." J. Comb. 7.4 (2016), 671-714.

François Bergeron, Adriano Garsia, Emily Leven and Guoce Xin. "Compositional (km,kn)-Shuffle Conjectures." Int. Math. Res. Not. (2015) rnr272.

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

Angela Hicks and Emily 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.

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

Emily Leven, Brendon Rhoades and Andrew T. Wilson. "Bijections for the Shi and Ish Arrangements." Euro. J. Comb. 39 (2014): 1-23.

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

Peter Richter, Emily Leven, Ahn Tran, Jobby Jacob, and Darren A. Narayan "Rank numbers for bent ladders." Discuss. Math. Graph Theory 34 (2014): 309-329.

Emily Sergel. "Noncommutative Biorthogonal Polynomials." Adv. Appl. Math. 48.1 (2012): 99-105.

Emily Sergel, Peter Richter, Ahn Tran, Patrick Curran, Jobby Jacob, and Darren A. Narayan. "Rank numbers for some trees and unicyclic graphs." Aequationes Math. 82.1-2 (2011): 65-79.