Benkart has made a contribution to the classification of simple modular Lie algebras. Her work with J. M. Osborn on toroidal rank-one Lie algebras became one of the building blocks of the classification. The complete description of Hamiltonian Lie algebras can stand alone, and also has applications in the theory of pro-p groups. In 2009 she published, jointly with T. Gregory and A. Premet, the first complete proof of the recognition theorem for graded Lie algebras in characteristics at least 5. In the early 90s Benkart and Efim Zelmanov started to work on classification of root-graded Lie algebras and intersection matrix algebras. The latter were introduced by P. Slodowy in his work on singularities. Berman and Moody recognized that these algebras are universal root graded Lie algebras and classified them for simply laced root systems. Benkart and Zelmanov tackled the remaining cases involving the so-called Magic Freudenthal–Tits “Square” and extended this square to exceptional Lie superalgebras. Later Benkart extended these results in two directions. In a series of papers with A. Elduque she developed the theory of root graded Lie superalgebras. In a second series of works with B. Allison, A. Pianzola, E. Neher, et al. she determined the universal central covers of these algebras. One of the pillars of the representation theory of quantum groups is Kashiwara's theory of crystal bases. These are highly invariant bases which are well suited for decompositions of tensor products. In a paper with S.-J. Kang and M. Kashiwara, Benkart extended the theory of crystal bases to quantum superalgebras. Benkart's work on noncommutative algebras related to algebraic combinatorics became a basic tool in the construction of tensor categories.
Benkart received a Woodrow Wilson Fellowship from the Woodrow Wilson National Fellowship Foundation. Her work at Wisconsin was recognized by a Romnes Fellowship in 1985, a Distinguished Teaching Award in 1987, and a WARF Mid-Career Faculty Research Award in 1996. In 2008 the University of California Lie Groups and Lie Algebras meeting was held in Benkart's honor. She has given numerous talks and series of lectures throughout the U.S., Canada, France, Germany, Hong Kong, Korea, Mexico, and Spain, including two invited lectures at the Joint Mathematics Meetings and a plenary lecture at a meeting of the Canadian Mathematical Society. In 2000–2002 Benkart was named a Polya Lecturer by the Mathematical Association of America. She was elected a Fellow of the American Mathematical Society in the inaugural class of 2013. She has served on the editorial boards of the American Mathematical Society for Surveys and Monographs and Abstracts, the Journal of Algebra, the Korean Mathematical Colloquium, the Nova Journal of Algebra and Geometry, Communications in Algebra, and Algebras, Groups, and Geometries. She served as the Associate Secretary of the American Mathematical Society for the Central Section from 2010–2016. Benkart has been active in the Association for Women in Mathematics. She was elected and served as President of the AWM from 2009–2011. In 2014 she was selected to deliver the AWM-AMS Noether Lecture. The title of her talk was Walking on Graphs the Representation Theory Way. In 2014 at the International Congress of Mathematicians held in Seoul, she delivered the ICM Emmy Noether Lecture. In 2017 she was selected as a fellow of the Association for Women in Mathematics in the inaugural class.
