Vyacheslav Futorny
Vyacheslav M. Futorny (June 3, 1961) is a Ukrainian-Brazilian mathematician who works in affine Lie algebra and its representation theory.[1] He is a professor at the University of São Paulo and a full member of the Brazilian Academy of Sciences. He was an invited speaker at the International Congress of Mathematicians in Rio de Janeiro (2018).[2]
Education
[edit]Futorny obtained a PhD in Mathematics in 1987 at Kiev University, supervised by Yuriy Drozd, with the thesis Weight Modules over Semi-Simple Lie Algebras.[3] He received his habilitation in 1995. He completed postdoctoral studies at the University of Oslo, Norway in 1991 and at Queen's University, Canada in 1993.[1]
Career
[edit]He is a docent professor at Kiev University and a full professor at the Institute of Mathematics and Statistics, University of São Paulo,[4] and has served as a visiting professor at Queen's University, Carleton, Utah, and Sydney.[1]
Scientific contributions
[edit]Futorny has made significant contributions to the representation theory of Lie algebras and related algebraic structures, with a particular focus on the classification and structure of modules, weight representations, and their connections to mathematical physics.
- One of his notable works, co-authored with Yuriy Drozd and S.A. Ovsienko, advanced the theory of Harish-Chandra subalgebras and Gelfand–Tsetlin modules. This research established a foundation for the study of a large class of modules characterized by explicit constructions and laid groundwork for further exploration of representations with rich combinatorial structures.[5]
- In collaboration with B. Cox and D. Melville, Futorny provided a systematic study of categories of nonstandard highest weight modules for affine Lie algebras. This work broadened the understanding of module categories beyond standard settings and remains influential for research on affine and Kac–Moody algebras.[6]
- Together with Yuly Billig, Futorny worked on the classification of irreducible representations of the Lie algebra of vector fields on a torus. Their results contributed new insights into the structure of infinite-dimensional Lie algebras and had ramifications for the understanding of symmetries in mathematical physics.[7]
Futorny's research has been instrumental in shaping modern approaches to Lie theory, weight module classifications, and the representation theory of both finite-dimensional and infinite-dimensional algebras.
Awards and honors
[edit]Futorny is a full member of the Brazilian Academy of Sciences since May 5, 2015.[1] He was an invited speaker at the International Congress of Mathematicians (ICM) 2018 in Rio de Janeiro. His lecture, titled Representations of Galois Algebras, focused on the study of the representation theory of Galois algebras—a class of algebras allowing an effective approach to their representations through their invariant skew group structure. Futorny provided an overview of theoretical developments in this field, with particular attention to recent advances involving Gelfand–Tsetlin representations of finite W-algebras.[8]This material was recognized as a key contribution in the Lie Theory and Generalizations section, highlighting ongoing research at the intersection of algebra, representation theory, and mathematical physics.[9]
References
[edit]- ^ a b c d "Vyacheslav Futorny – ABC – Academia Brasileira de Ciências". www.abc.org.br. Retrieved 2025-07-08.
- ^ "ICM Plenary and Invited Speakers | International Mathematical Union (IMU)". www.mathunion.org. Retrieved 2023-07-11.
- ^ Vyacheslav Futorny at the Mathematics Genealogy Project
- ^ "Vyacheslav Futorny, IME-USP". www.ime.usp.br. Retrieved 2025-07-08.
- ^ Drozd, Yuriy A.; Futorny, Vyacheslav M.; Ovsienko, Serge A. (1994). "Harish-Chandra Subalgebras and Gelfand-Zetlin Modules". Finite Dimensional Algebras and Related Topics. NATO ASI Series. 424. Springer: 79–93. doi:10.1007/978-94-017-1556-0_5. ISBN 978-90-481-4377-1.
- ^ Cox, Brian; Futorny, Vyacheslav; Melville, David (1996). "Categories of nonstandard highest weight modules for affine Lie algebras". Mathematische Zeitschrift. 221 (1). Springer: 193–209. doi:10.1007/BF02677999.
- ^ Billig, Yuly; Futorny, Vyacheslav (2016). "Classification of irreducible representations of Lie algebra of vector fields on a torus". Journal für die reine und angewandte Mathematik. 2016 (720). De Gruyter: 199–216. doi:10.1515/crelle-2014-0059.
- ^ Vyacheslav Futorny's plenary talk at ICM 2018 on YouTube
- ^ Sirakov, Boyan (August 1, 2018). ""International Congress of Mathematicians 2018, Volume II"" (PDF). International Mathematical Union / World Scientific.
