Alexander Molev

Professor Alexander Molev is Professor of Pure Mathematics in the School of Mathematics and Statistics, Faculty of Science, at the University of Sydney. He received his PhD in 1986 from Lomonosov Moscow State University under the supervision of Alexandre Kirillov. His research specializations encompass representation theory, Lie theory, quantum groups including Yangians, algebraic combinatorics, vertex algebras, and mathematical physics. Molev's fields of research include algebraic structures in mathematical physics, algebra and number theory, Lie groups, harmonic and Fourier analysis, and mathematical aspects of quantum theory. He is a world-leading expert on Yangians, a class of quantum groups, which he has employed to address longstanding open problems in representation theory.

Molev has advanced the understanding of infinite-dimensional Lie algebras of vector fields and resolved the unitarizability of Enright-Varadarajan modules for the Lie algebra u(p,q), yielding a rigorous derivation of the Gelfand-Graev formulas. He constructed the theory of twisted Yangians, classifying their irreducible representations, and determined analogues of Gelfand-Tsetlin formulas for the classical Lie algebra series C. Further contributions include a simple formula for the Sklyanin determinant, Capelli-type identities for Howe's dual reductive pairs, super generalizations of Schur functions, and multiplication rules for factorial Schur functions known as the Molev-Sagan rule. His monographs Yangians and Classical Lie Algebras (American Mathematical Society, 2007) and Sugawara Operators for Classical Lie Algebras (American Mathematical Society, 2018) are recognized as definitive works. With over 3,500 citations on Google Scholar, his influence extends to recent publications on super-Yangians, quantum Sugawara operators, and generalized W-algebras. Career appointments include Lecturer and subsequent promotion to Professor at the University of Sydney. Major honors comprise the Australian Mathematical Society Medal (2001) and election as Fellow of the Australian Academy of Science (2019). He has received Australian Research Council Discovery Project grants, such as one for quantum algebras with supersymmetries.

Professional Email: alexander.molev@sydney.edu.au