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Pavel Etingof studies representation theory, quantum groups and noncommutative algebra. His MIT research profile places this work at the intersection of algebra and mathematical physics.^[ref]

His Lie Groups and Lie Algebras by Pavel Etingof (2024) develops the bridge from continuous groups to their infinitesimal algebraic structures. A Lie algebra representation replaces a nonlinear group action with linear operators satisfying bracket identities; the theory then recovers structural information about Lie groups. His work on tensor categories broadens the study of representations by treating their tensor products and compatibility maps as part of the mathematical object.^[ref][ref]

In the algebraic convention used here, a tensor category over a field $k$ is a locally finite $k$-linear abelian category with a bilinear monoidal tensor product, left and right duals for every object, and a simple monoidal unit object whose endomorphisms are $k$. A locally finite category has finite-dimensional morphism spaces and objects of finite length. In broader usage, “tensor category” may mean merely a monoidal category; the extra hypotheses should therefore be stated.^[ref]

Finite-dimensional representations of a group over $k$ give a model example: the tensor product has diagonal group action, the unit is the one-dimensional trivial representation, and the dual is the dual vector space with the contragredient action. A tensor category need not have a braiding; swapping two tensor factors compatibly is additional structure.