Boris L. Feigin
- Professor, Research Team Leader:Faculty of Mathematics
- Senior Research Fellow:Faculty of Mathematics / HSE – Skoltech International Laboratory of Representation Theory and Mathematical Physics
- Tenured Professor (2013)
- Boris L. Feigin has been at HSE University since 2009.
Education, Degrees and Academic Titles
- 2022Corresponding Member of the Russian Academy of Sciences
- 1996
Doctor of Sciences* in Physical and Mathematical Sciences
Landau Institute of Theoretical Physics of the Russian Academy of Sciences - 1983
Candidate of Sciences* (PhD) in Physical and Mathematical Sciences
Steklov Mathematical Institute of the Russian Academy of Sciences, St. Petersburg Branch - 1979
Doctoral programme
P.G. Demidov Yaroslavl State University - 1974
Degree
Lomonosov Moscow State University
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.
Courses (2023/2024)
- Research Seminar "Representation Theory 1" (Optional course (faculty); 1, 2 module)Rus
- Research Seminar "Representation Theory 2" (Optional course (faculty); 3, 4 module)Rus
- Past Courses
Courses (2022/2023)
- Research Seminar "Representation Theory 1" (Optional course (faculty); 1, 2 module)Rus
- Research Seminar "Representation Theory 2" (Optional course (faculty); 3, 4 module)Rus
Courses (2020/2021)
- Research seminar "Additional chapters of algebra" (Optional course (faculty); Faculty of Mathematics; 1-3 module)Rus
- Research Seminar "Representation Theory 1" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Research Seminar "Representation Theory 2" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
Courses (2019/2020)
- Algebra (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
- Research Seminar "Representation Theory 1" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Research Seminar "Representation Theory 2" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
Editorial board membership
2000: Member of the Editorial Board, Moscow Mathematical Journal.
2000: Member of the Editorial Board, Transformation Groups.
1996: Member of the Editorial Board, Функциональный анализ и его приложения (Functional Analysis and Its Applications).
Publications147
- Article B. Feigin, L. Rybnikov, F. Uvarov. Gaudin model and Deligne’s category // Letters in Mathematical Physics. 2023. Vol. 114. Article 3. doi
- Article B. Feigin, Jimbo M., Mukhin E. Combinatorics of vertex operators and deformed W-algebra of type D(2, 1; α) // Advances in Mathematics. 2022. Vol. 403. Article 108331. doi
- Article Feigin B. L., Mukhin E., Jimbo M. Quantum Toroidal Comodule Algebra of Type An−1 and Integrals of Motion // Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2022. Vol. 18. Article 51. doi
- Article Feigin B. L., Creutzig T., Arakawa T. Urod algebras and Translation of W-algebras // Forum of Mathematics, Sigma. 2022. Vol. 10. Article 33. doi
- Article Feigin B. L., Hu Y. Shuffle algebra realization of quantum affine superalgebra U-v ((D)over-cap(2, 1; theta)) // Journal of Algebra. 2021. Vol. 573. P. 539-560. doi
- Article Alfimov M., Feigin B. L., Hoare B., Litvinov A. Dual description of eta-deformed OSP sigma models // Journal of High Energy Physics. 2020. Vol. 2020. No. 12. P. 1-45. doi
- Article Feigin B. L., Odesskii A. Flat deformations of algebras and functional equations. // Journal of Combinatorial Algebra, Швейцария. 2019. Vol. 3. No. 3. P. 215-236. doi
- Article Feigin B. L., Jimbo M., Mukhin E. The (gl(m) ,gl(n) ) duality in Quantum toroidal setting // Communications in Mathematical Physics. 2019. No. 367. P. 455-481. doi
- Article Feigin B. L., Jimbo M., Mukhin E. Towards trigonometric deformation of 𝔰𝔩ˆ2 coset VOA // Journal of Mathematical Physics. 2019. Vol. 60. No. 7. P. 073507-1-073507-16. doi
- Article Bershtein M., Feigin B. L., Merzon G. Plane partitions with a “pit”: generating functions and representation theory // Selecta Mathematica, New Series. 2018. Vol. 24. No. 1. P. 21-62. doi
- Article Feigin B. L. Extensions of vertex algebras. Constructions and applications // Russian Mathematical Surveys. 2017. Vol. 72. No. 4. P. 707-763. doi
- Article Feigin B. L., Jimbo M., Miwa T., Mukhin E. Finite Type Modules and Bethe Ansatz Equations // Annales Henri Poincare. A Journal of Theoretical and Mathematical Physics. 2017. Vol. 18. No. 8. P. 2543-2579. doi
- Article Feigin B. L., Jimbo M., Mukhin E. Integrals of motion from quantum toroidal algebras // Journal of Physics A: Mathematical and Theoretical. 2017. Vol. 50. No. 46. Article 464001. doi
- Article Feigin B. L., Makhlin I. A combinatorial formula for affine Hall–Littlewood functions via a weighted Brion theorem // Selecta Mathematica, New Series. 2016. Vol. 22. No. 3. P. 1703-1747. doi
- Article Feigin B. L., Jimbo M., Miwa T., Mukhin E. Branching rules for quantum toroidal gln // Advances in Mathematics. 2016. Vol. 300. P. 229-274. doi
- Article Bershtein M., Feigin B. L., Litvinov A. Coupling of two conformal field theories and Nakajima-Yoshioka blow-up equations // Letters in Mathematical Physics. 2016. Vol. 106. No. 1. P. 29-56. doi
- Preprint Feigin B. L., Makhlin I. A Combinatorial Formula for Affine Hall-Littlewood Functions via a Weighted Brion Theorem / Cornell University. Series math "arxiv.org". 2015.
- Article Buryak A., Feigin B. L., Nakajima H. A Simple Proof of the Formula for the Betti Numbers of the Quasihomogeneous Hilbert Schemes // International Mathematics Research Notices. 2015. No. 13 doi
- Article Buryak A., Feigin B. L., Nakajima H. A simple proof of the formula for the Betti numbers of the quasihomogeneous Hilbert schemes // International Mathematics Research Notices. 2015. Vol. 2015. No. 13. P. 4708-4715. doi
- Article Feigin B. L., Jimbo M., Miwa T., Mukhin E. Quantum toroidal gl1 and Bethe ansatz // Journal of Physics A: Mathematical and Theoretical. 2015. Vol. 48. No. 24, Article number 244001
- Article Фейгин Б. Л. Коммутативные вертексные алгебры и их вырождения // Функциональный анализ и его приложения. 2014. № 3
- Article Мутафян Г. С., Фейгин Б. Л. Характеры представлений квантовой тороидальной алгебры gl1ˆˆ: плоские разбиения «с трибуной» // Функциональный анализ и его приложения. 2014. Т. 48. № 1. С. 46-60.
- Preprint Feigin B. L., Miwa T., Jimbo M., Mukhin E. Branching rules for quantum toroidal $\mathfrak{gl}_n$ / Cornell University Library. 2013. No. 1309.2147.
- Article Feigin B. L., Jimbo M., Miwa T., Mukhin E. Representations of quantum toroidal gln // Journal of Algebra. 2013. Vol. 380. P. 78-108. doi
- Article Cherednik I., Feigin B. L. Rogers-Ramanujan type identities and Nil-DAHA // Advances in Mathematics. 2013. Vol. 248. No. 25. P. 1050-1088. doi
- Article Feigin B. L., Mytafyan G. S. The quantum toroidal algebra gl1: Calculation of characters of some representations as generating functions of plane partitions / Пер. с рус. // Functional Analysis and Its Applications. 2013. Vol. 47. No. 1. P. 50-61. doi
- Article Мутафян Г. С., Фейгин Б. Л. Квантовая тороидальная gl(1): вычисление характеров некоторых представлений как производящих функций плоских разбиений // Функциональный анализ и его приложения. 2013. Т. 47. № 1. С. 62-76.
- Article Feigin B. L., Buryak A. Homogeneous components in the moduli space of sheaves and Virasoro characters // Journal of Geometry and Physics. 2012. Vol. 62. No. 7. P. 1652-1664. doi
- Article Belavin A., Bershtein M., Feigin B. L., Litvinov A., Tarnopolsky G. Instanton Moduli Spaces and Bases in Coset Conformal Field Theory // Communications in Mathematical Physics. 2012. P. 1-33. doi
- Article Feigin B. L., Awata H., Shiraishi J. Quantum Algebraic Approach to Refined Topological Vertex // Journal of High Energy Physics. 2012. No. 3. P. 41-68. doi
- Article Feigin B. L., Jimbo M., Miwa T., Mukhin E. Quantum toroidal gl(1)-algebra: Plane partitions // Kyoto Journal of Mathematics. 2012. Vol. 52. No. 3. P. 621-659. doi
- Article Braverman A., Rybnikov L. G., Feigin B. L., Finkelberg M. V. A finite analog of the AGT relation I: finite W-algebras and quasimaps' spaces // Communications in Mathematical Physics. 2011. Vol. 308. No. 2. P. 457-478. doi
- Chapter Tipunin I. Y., Feigin B. L. Characters of coinvariants in (1,p) logarithmic models, in: http://arxiv.org/PS_cache/arxiv/pdf/0805/0805.4096v2.pdf. Singapore : , 2011. P. 35-60.
- Article Feigin B. L., Tsymbaliuk A. Equivariant K-theory of Hilbert schemes via shuffle algebra // Kyoto Journal of Mathematics. 2011. Vol. 51. No. 4. P. 831-854.
- Article Feigin B. L., Finkelberg M. V., Rybnikov L. G., Frenkel I. Gelfand-Tsetlin algebras and cohomology rings of Laumon spaces // Selecta Mathematica, New Series. 2011. Vol. 17. No. 2. P. 337-361. doi
- Article Фейгин Б. Л., Jimbo M., Miwa T. Gelfand-Zetlin Basis, Whittaker Vectors and a Bosonic Formula for the sl(n+1) Principal Subspace // Publications of the Research Institute for Mathematical Sciences. 2011. Т. 47. № 2. С. 535-551.
- Article Feigin B. L., Feigin E., Jimbo M., Miwa T., Mukhin E. Quantum continuous gl∞: Tensor products of Fock modules and Wn-characters // Kyoto Journal of Mathematics. 2011. Vol. 51. No. 2. P. 365-392.
- Article Feigin B. L., Feigin E., Jimbo M., Miwa T., Mukhin E. Quantum continuous gl∞: semiinfinite construction of representations // Kyoto Journal of Mathematics. 2011. Vol. 51. No. 2. P. 337-364.
- Article Feigin B. L. Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories // Journal of High Energy Physics. 2011. Vol. 7. No. 7(079). P. 1-18. doi
- Article Feigin B. L., Finkelberg M. V., Rybnikov L. G., Negut A. Yangians and cohomology rings of Laumon spaces // Selecta Mathematica, New Series. 2011. Vol. 17. No. 3. P. 573-607. doi
- Article Feigin B. L., Feigin E., Littelmann P. Zhu's algebras, C_2-algebras and abelian radicals // Journal of Algebra. 2011. Vol. 329. P. 130-146. doi
- Article Feigin B. L., Frenkel E., Toledano L. V. Gaudin models with irregular singularities // Advances in Mathematics. 2010. Vol. 223. No. 3. P. 873-948.
- Article Feigin B. L., Rybnikov L. G., Frenkel E. Opers with irregular singularity and spectra of the shift of argument subalgebra // Duke Mathematical Journal. 2010. Vol. 155. No. 2. P. 337-363.
- Article Lashkevich M., Feigin B. L. Form factors of descendant operators: free field construction and reflection relations // Journal of Physics A: Mathematical and Theoretical. 2009. Vol. 42. No. 304014. P. 1-32.
- Article Feigin B. L., Hashizume K., Hoshino A., Shiraishi J., Yanagida S. A commutative algebra on degenerate CP1 and Macdonald polynomials // Journal of Mathematical Physics. 2009. Vol. 50. No. 9. P. 095215-1-095215-42. doi
- Article Feigin B. L., Feigin E., Jimbo M., Miwa T., Mukhin E. Fermionic Formulas for Eigenfunctions of the Difference Toda Hamiltonian // Letters in Mathematical Physics. 2009. Vol. 88. No. 1-3. P. 39-77. doi
- Article Tipunin I., Bushlanov P., Feigin B. L., Gainutdinov A. Lusztig limit of quantum sl(2) at root of unity and fusion of (1, p) Virasoro logarithmic minimal models // Nuclear Physics B. 2009. Vol. 818. No. 3. P. 179-195.
- Article Bushlanov P., Feigin B. L., Gainutdinov A., Tipunin I. Lusztig limit of quantum sℓ(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models // Nuclear Physics B. 2009. Vol. 818. No. 3. P. 179-195. doi
- Article Frenkel E., Feigin B. L., Rybnikov L. G. On the endomorphisms of Weyl modules over affine Kac-Moody algebras at the critical level // Letters in Mathematical Physics. 2009. Vol. 88. No. 1-3. P. 163-173.
- Article Takeyama Y., Jimbo M., Feigin B. L., Miwa T., Feigin E. A $\phi_{1,3}$-filtration of the Virasoro minimal series M(p,p') with 1 // Publications of the Research Institute for Mathematical Sciences. 2008. Vol. 44. No. 2. P. 213-257.
- Article Takeyama Y., Jimbo M., Miwa T., Feigin B. L. Sets of rigid paths with Virasoro characters // The Ramanujan Journal. 2008. Vol. 15. No. 1. P. 123-145.
- Article Tipunin I., Semikhatov A., Gainutdinov A., Feigin B. L. Kazhdan-Lusztig-dual quantum group for logarithimic extensions of Virasoro minimal models. // Journal of Mathematical Physics. 2007. Vol. 48. No. 3
- Article Shoikhet B., Фейгин Б. Л. On $[A,A]/[A,[A,A]]$ and on a $W\sb n$-action on the consecutive commutators of free associative algebras. // Mathematical Research Letters. 2007. Т. 14. № 5. С. 781-795.
- Article Feigin B. L., Shoikhet B. On [A,A]/[A, [A,A]] and on a Wn-action on the consecutive commutators of free associative algebra // Mathematical Research Letters. 2007. Vol. 14. No. 5. P. 781-795.
- Article Feigin B. L., Feigin E. Two-dimensional current algebras and affine fusion product // Journal of Algebra. 2007. Vol. 313. No. 1. P. 176-198.
- Article Tipunin I., Feigin B. L., Gainutdinov A., Semikhatov A. Logarithmic extensions of minimal models: characters and modular transformations. // Nuclear Physics B. 2006. Vol. 757. No. 3. P. 303-343.
- Article Tipunin I., Feigin B. L., Gainutdinov A., Semikhatov A. Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center. // Communications in Mathematical Physics. 2006. Vol. 265. No. 1. P. 47-93.
- Article Feigin B. L., Feigin E. Principal subspace for the bosonic vertex operator $\phi\sb {\sqrt{2m}}(z)$ and Jack polynomials. // Advances in Mathematics. 2006. Vol. 206 . No. 2. P. 307-328.
- Article Типунин И. Ю., Семихатов А., Гайнутдинов А. М., Фейгин Б. Л. Соответствие Каждана-Люстига для категории представлений триплетной$W$-алгебры в логарифмических конформных теориях поля // Теоретическая и математическая физика. 2006. Т. 148. № 3. С. 398-427.
- Article Takeyama Y., Фейгин Б. Л., Miwa T., Jimbo M., Мухин Е. И. A monomial basis for the Virasoro minimal series $M(p,p')$: the case $1 // Communications in Mathematical Physics. 2005. Т. 257. № 2. С. 395-423.
- Article Feigin E., Feigin B. L. Homological realization of restricted Kostka polynomials // International Mathematics Research Notices. 2005. Vol. 33. No. 33. P. 1997-2029.
- Article Semikhatov A., Feigin B. L. $\scr W\sp {(2)}\sb n$ algebras. // Nuclear Physics B. 2004. Vol. 698. No. 3. P. 409-449.
- Article Feigin B. L., Jimbo M., Kashiwara M., Miwa T., Mukhin E., Takeyama Y. A functional model for the tensor product of level 1 highest and level $-1$ lowest modules for the quantum affine algebra $U\sb q(\widehat{\germ{sl}}\sb 2)$. // European Journal of Combinatorics. 2004. Vol. 25. No. 8. P. 1197-1229.
- Article Loktev S., Feigin B. L. Deformation of Weyl Modules and Generalized Parking Functions // International Mathematics Research Notices. 2004. Vol. 51. P. 2719-2750.
- Article Feigin B. L., Jimbo M., Miwa T., Mukhin E., Takeyama Y. Fermionic formulas for $(k,3)$-admissible configurations. // Publications of the Research Institute for Mathematical Sciences. 2004. Vol. 40 . No. 1. P. 125-162.
- Article Фейгин Б. Л., Локтев С. А. Multi-dimensional Weyl Modules and Symmetric Functions // Communications in Mathematical Physics. 2004. Т. 251. № 3. С. 427-445.
- Article Feigin E., Feigin B. L. Schubert varieties and the fusion products, // Publications of the Research Institute for Mathematical Sciences. 2004. Vol. 40. No. 3. P. 625-668.
- Article Jimbo M., Loktev S., Feigin B. L., Miwa T., Kedem R. Spaces of coinvariants and fusion product II. Affine sl2 character formulas in terms of Kostka polynomials // Journal of Algebra. 2004. Vol. 279. No. 1. P. 147-179.
- Article Loktev S., Kedem R., Jimbo M., Feigin B. L., Miwa T. Spaces of coinvariants and fusion product. I. From equivalence theorem to Kostka polynomials. // Duke Mathematical Journal. 2004. Vol. 125. No. 3. P. 549-588.
- Article Miwa T., Hong J., Feigin B. L. A construction of level 1 irreducible modules for $U\sb q(\widehat{\germ s\germ p}\sb 4)$ > using level 2 intertwiners for $U\sb q(\widehat{\germ s\germ l}\sb 2)$. // Moscow Mathematical Journal. 2003. Vol. 3. No. 4. P. 1247-1267.
- Article Feigin B. L., Jimbo M., Loktev S., Miwa T., Mukhin E. Addendum to: "Bosonic formulas for $(k,l)$-admissible partitions" // The Ramanujan Journal. 2003. Vol. 7. No. 4. P. 519-530.
- Article Feigin B. L., Jimbo M., Miwa T., Mukhin E., Takeyama Y. Symmetric polynomials vanishing on the diagonals shifted by roots of unity // International Mathematics Research Notices. 2003. No. 18. P. 999-1014.
- Article Feigin E., Feigin B. L. $Q$-characters of the tensor products in $\germ s\germ l\sb 2$-case. // Moscow Mathematical Journal. 2002. Vol. 2. No. 3. P. 567-588.
- Article Feigin B. L., Jimbo M., Miwa T., Mukhin E. A differential ideal of symmetric polynomials spanned by Jack polynomials at $\beta=-(r-1)/(k+1)$. // International Mathematics Research Notices. 2002. No. 23. P. 1223-1237.
- Article Loktev S., Tipunin I., Feigin B. L. Coinvariants for lattice VOAs and $q$-supernomial coefficients. // Communications in Mathematical Physics. 2002. Vol. 229. No. 2. P. 271-292.
- Article Feigin B. L., Kedem R., Loktev S., Miwa T., Mukhin E. Combinatorics of the $\widehat{\germ s\germ l}\sb 2$ spaces of coinvariants: loop Heisenberg modules and recursion. // Selecta Mathematica, New Series. 2002. Vol. 8. No. 3. P. 419-474.
- Article Feigin B. L., Loktev S., Miwa T., Mukhin E., Kedem R. Combinatorics of the $\widehat{\germ{sl}}\sb 2$ coinvariants: dual functional realization and recursion. // Compositio Mathematica. 2002. Vol. 134. No. 2. P. 193-241.
- Article Feigin B. L., Kedem R., Loktev S., Miwa T., Mukhin E. Combinatorics of the $\widehat{\germ{sl}}\sb 2$ spaces of coinvariants. // Transformation Groups. 2001. Vol. 6. No. 1. P. 25-52.
- Article Mukhin E., Feigin B. L., Loktev S., Miwa T., Kedem R. Combinatorics of the sl2∧ Spaces of Coinvariants // Transformation Groups. 2001. Vol. 6. No. 1. P. 25-52.
- Article Semikhatov A., Feigin B. L. The $\widehat{\rm sl}(2)\oplus\widehat{\rm sl}(2)/\widehat{\rm sl}(2)$ coset theory as a Hamiltonian reduction of $\widehat D(2\vert 1;\alpha)$. // Nuclear Physics B. 2001. Vol. 610. No. 3
- Article Feigin B. L., Belavin A., Gubanov S. Truncation of functional relations in the $XXZ$ model. // Moscow Mathematical Journal. 2001. Vol. 1. No. 2. P. 145-156.
- Article Локтев С. А., Фейгин Б. Л. О финитизации тождеств Гордона // Функциональный анализ и его приложения. 2001. Т. 35. № 1. С. 53-61.
- Article Типунин И. Ю., Семихатов А., Фейгин Б. Л. Полубесконечная реализация унитарных представлений $N=2$ алгебрыи связанные с этим конструкции. // Теоретическая и математическая физика. 2001. Т. 126. № 1. С. 3-62.
- Article Bowcock P., Semikhatov A., Feigin B. L., Taormina A. $\widehat{\rm sl}(2\vert 1)$ and $\widehat{D}(2\vert 1;\alpha)$ as vertex operator extensions of dual affine ${\rm sl}(2)$ algebras. // Communications in Mathematical Physics. 2000. Vol. 214. No. 3. P. 495-545.
- Article Ding J., Feigin B. L. Commutative quantum current operators, semi-infinite construction and functional models // Representation Theory. 2000. Vol. 4
- Article Ding J., Feigin B. L. Quantized $W$-algebra of $\germ s\germ l(2,1)$ and quantum parafermions of $U\sb q(\widehat{\germ s\germ l}(2))$. // Journal of Nonlinear Mathematical Physics. 2000. Vol. 7. No. 2. P. 170-183.
- Article Astashkevich A., Roger C., Tabachnikov S., Feigin B. L., Sossinsky A. Appendix. Personal notes. Differential topology, infinite-dimensional Lie algebras, and applications // Translations of the American Mathematical Society. 1999. Vol. 194. P. 301-313.
- Article Frenkel E., Feigin B. L. Integrable hierarchies and Wakimoto modules. Differential topology, infinite-dimensional Lie algebras, and applications // Translations of the American Mathematical Society. 1999. Vol. 194. P. 27-60.
- Article Tipunin I., Sirota V. A., Feigin B. L., Semikhatov A. Resolutions and characters of irreducible representations of the $N=2$ superconformal algebra. // Nuclear Physics B. 1999. Vol. 536. No. 3. P. 617-656.
- Article Семихатов А., Фейгин Б. Л. Резольвенты унитарных представлений $N=2$ алгебры Вирасоро в терминах свободных полей II. Резольвента бабочки // Теоретическая и математическая физика. 1999. Т. 121. № 2. С. 244-257.
- Article Pugai Y., Feigin B. L., Miwa T., Jimbo M., Odesskii A. Algebra of screening operators for the deformed $W\sb n$ algebra. // Communications in Mathematical Physics. 1998. Vol. 191. No. 3. P. 501-541.
- Article Odesskii A., Feigin B. L. Coordinate ring of the quantum Grassmannian and intertwiners for the representations of Sklyanin algebras. Topics in quantum groups and finite-type invariants // Translations of the American Mathematical Society. 1998. Vol. 185. P. 55-64.
- Article Tipunin I., Feigin B. L., Semikhatov A. Equivalence between chain categories of representations of affine ${\rm sl}(2)$ and $N=2$ superconformal algebras. // Journal of Mathematical Physics. 1998. Vol. 39. No. 7. P. 3865-3905.
- Article Rubtsov V., Enriquez B., Feigin B. L. Separation of variables for Gaudin-Calogero systems. // Compositio Mathematica. 1998. Vol. 110. No. 1. P. 1-16.
- Article Odesskii A., Feigin B. L. A family of elliptic algebras. // International Mathematics Research Notices. 1997. No. 11. P. 531-539.
- Article Antonov A., Feigin B. L. Quantum group representations and the Baxter equation. // Physics Letters B. 1997. Vol. 392. No. 1-2. P. 115-122.
- Book Фейгин Б. Л., Бурман Ю. М. Бесконечномерные алгебры Ли−1: полубесконечные формы, алгебра Вирасоро и вертексные операторы. М. : МЦНМО, 1997.
- Article Одесский А., Фейгин Б. Л. Эллиптические деформации алгебр токов и их представлений разностными операторами // Функциональный анализ и его приложения. 1997. Т. 31. № 3. С. 57-70.
- Article Frenkel E., Feigin B. L. Integrals of motion and quantum groups. // Lecture Notes in Mathematics. 1996. Vol. 1620. P. 349-418.
- Article Frenkel E., Feigin B. L. Quantum $\scr W$-algebras and elliptic algebras. // Communications in Mathematical Physics. 1996. Vol. 178. No. 3. P. 653-678.
- Article Локтев С. А., Фейгин Б. Л. Когомологии нильпотентных подалгебр алгебры sl2∧ // Функциональный анализ и его приложения. 1996. Т. 30. № 4. С. 80-83.
- Article Feigin B. L., Felder G., Shoikhet B. Hochschild cohomology of the Weyl algebra and traces in deformation quantization. // Duke Mathematical Journal. 1995. Vol. 127. No. 3. P. 487-517.
- Article Frenkel E., Feigin B. L. Kac-Moody groups and integrability of soliton equations. // Inventiones Mathematicae. 1995. Vol. 120. No. 2. P. 379-408.
- Article Varchenko A., Schechtman V., Feigin B. L. On algebraic equations satisfied by hypergeometric correlators in WZW models. II. // Communications in Mathematical Physics. 1995. Vol. 170. No. 1. P. 219-247.
- Article Andreev E., Feigin B. L. On bosonization of $2$d conformal field theories. // Nuclear Physics B. 1995. Vol. 433. No. 3. P. 685-711.
- Article Энриквес Б., Фейгин Б. Л. Интегралы движения классической системы sine-Гордон на решетке // Теоретическая и математическая физика. 1995. Т. 103. № 3. С. 507-528.
- Article Одесский А., Фейгин Б. Л. Эллиптические алгебры Склянина. Случай точки конечного порядка // Функциональный анализ и его приложения. 1995. Т. 29. № 2. С. 9-21.
- Article Malikov F., Feigin B. L. Fusion algebra at a rational level and cohomology of nilpotent subalgebras of $\widehat{{\germ s}{\germ l}}(2)$. // Letters in Mathematical Physics. 1994. Vol. 31. No. 4. P. 315-325.
- Article Frenkel E., Feigin B. L., Reshetikhin N. Gaudin model, Bethe ansatz and critical level // Communications in Mathematical Physics. 1994. Vol. 166. No. 1. P. 27-62.
- Article Varchenko A., Schechtman V., Feigin B. L. On algebraic equations satisfied by hypergeometric correlators in WZW models. I. // Communications in Mathematical Physics. 1994. Vol. 163. No. 1. P. 173-184.
- Article Стояновский А., Фейгин Б. Л. Реализация модулярного функтора в пространстве дифференциалови геометрическая аппроксимация многообразия модулей $G$-расслоений. // Функциональный анализ и его приложения. 1994. Т. 28. № 4. С. 42-65.
- Article Стояновский А., Фейгин Б. Л. Функциональные модели представлений алгебр токов и полубесконечные клетки Шуберта. // Функциональный анализ и его приложения. 1994. Т. 28. № 1. С. 68-90.
- Article Одесский А., Фейгин Б. Л. Конструкции эллиптических алгебр Склянина и квантовых $R$-матриц // Функциональный анализ и его приложения. 1993. Т. 27. № 1. С. 37-45.
- Article Frenkel E., Feigin B. L. Free field resolutions in affine Toda field theories. // Physics Letters B. 1992. Vol. 276. No. 1-2. P. 79-86.
- Article Frenkel E., Feigin B. L. Duality in $W$-algebras. // International Mathematics Research Notices. 1991. Vol. 6. P. 75-82.
- Article Frenkel E., Feigin B. L. Erratum: "Semi-infinite Weil complex and the Virasoro algebra" // Communications in Mathematical Physics. 1991. Vol. 137. No. 3. P. 617-639.
- Article Frenkel E., Feigin B. L. Affine Kac-Moody algebras and semi-infinite flag manifolds // Communications in Mathematical Physics. 1990. Vol. 128. No. 1. P. 161-189.
- Article Frenkel E., Feigin B. L. Bosonic ghost system and the Virasoro algebra. // Physics Letters B. 1990. Vol. 246. No. 1-2. P. 71-74.
- Article Varchenko A., Schechtman V., Feigin B. L. On algebraic equations satisfied by correlators in Wess-Zumino-Witten models // Letters in Mathematical Physics. 1990. Vol. 20. No. 4. P. 291-297.
- Article Frenkel E., Feigin B. L. Quantization of the Drinfeld-Sokolov reduction // Physics Letters B. 1990. Vol. 246. No. 1-2. P. 75-81.
- Article Frenkel E., Feigin B. L. Representations of affine Kac-Moody algebras, bosonization and resolutions // Letters in Mathematical Physics. 1990. Vol. 19. No. 4. P. 307-317.
- Article Fialowski A., Feigin B. L. Cohomology of the nilpotent subalgebras of current Lie algebras. // Studia Scientiarum Mathematicarum Hungarica. 1989. Vol. 24. No. 1. P. 1-9.
- Article Tsygan B., Feigin B. L. Riemann-Roch theorem and Lie algebra cohomology. I. // Rendiconti del Circolo Matematico di Palermo. 1989. Vol. 2. No. 21. P. 15-52.
- Article Schechtman V., Feigin B. L. The honour to V. Knizhnik. // Rendiconti del Circolo Matematico di Palermo. 1989. Vol. 2. No. 21. P. 9-10.
- Article Одесский А., Feigin B. L. Эллиптические алгебры Склянина // Functional Analysis and Its Applications. 1989. Vol. 23. No. 3. P. 45-54.
- Article Fuchs D. B., Feigin B. L. Cohomology of some nilpotent subalgebras of the Virasoro and Kac-Moody Lie algebras // Journal of Geometry and Physics. 1988. Vol. 5. No. 2. P. 209-235.
- Article Фейгин Б. Л. Алгебры Ли ${\rm gl}(\lambda)$ и когомологии алгебры Ли дифференциальных операторов. // Успехи математических наук. 1988. Т. 43. № 2(260). С. 157-158.
- Article Френкелем Э., Фейгин Б. Л. Семейство представлений аффинных алгебр Ли // Успехи математических наук. 1988. Т. 43. № 5(263). С. 227-228.
- Article Tsygan B., Feigin B. L. Additive $K$-theory. K$-theory, arithmetic and geometry // Lecture Notes in Mathematics. 1987. Vol. 1289. P. 67-209.
- Article Fialowski A., Feigin B. L. Cohomology of the infinite-dimensional Lie algebra $L\sb 1$ with nontrivial coefficients. // Bulletin of the American Mathematical Society( New Series). 1987. Vol. 17. No. 2. P. 333-337.
- Article Feigin B. L., Tsygan B. Cyclic homology of algebras with quadratic relations, universal enveloping algebras and group algebras. $K$-theory, arithmetic and geometry // Lecture Notes in Mathematics. 1987. Vol. 1289. P. 210-239.
- Article Фейгин Б. Л., Маликов Ф. Г., Фукс Д. Особые векторы в модулях Верма над алгебрами Каца-Муди // Функциональный анализ и его приложения. 1986. Т. 20. № 2. С. 25-37.
- Article Фейгин Б. Л. Аддитивная $K$-теория и кристалинные когомологии // Функциональный анализ и его приложения. 1985. Т. 19. № 2. С. 52-62.
- Article Фейгин Б. Л. Полубесконечные гомологии алгебр Ли. Каца-Муди и Вирасоро // Успехи математических наук. 1984. Т. 39. № 2. С. 195-196.
- Article Фейгин Б. Л., Фукс Д. Стабильные когомологии алгебры $W\sb{n}$ и соотношения в алгебре $L\sb{1}$, // Функциональный анализ и его приложения. 1984. Т. 18. № 3. С. 94-95.
- Article Фейгин Б. Л. Когомологии алгебр Ли обобщенных матриц Якоби // Функциональный анализ и его приложения. 1983. Т. 17. № 2. С. 86-87.
- Article Фейгин Б. Л., Фукс Д. Модули Верма над алгеброй Вирасоро // Функциональный анализ и его приложения. 1983. Т. 17. № 3. С. 91-92.
- Article Фейгин Б. Л. Когомологии некоторых алгебр Ли и супералгебр векторных полей // Успехи математических наук. 1982. Т. 37. № 2 (224). С. 233-234.
- Article Фейгин Б. Л., Фукс Д. Кососимметрические инварианты дифференциальных операторов на прямойи модули Верма над алгеброй Вирасоро // Функциональный анализ и его приложения. 1982. Т. 16. № 2. С. 47-63.
- Article Фукс Д., Фейгин Б. Л. Гомологии алгебры Ли векторных полей на прямой // Функциональный анализ и его приложения. 1980. Т. 14. № 3. С. 45-60.
- Article Фейгин Б. Л. Когомологии групп и алгебр токов // Успехи математических наук. 1980. Т. 35. № 2 (212). С. 225-226.
- Article Фейгин Б. Л., Фукс Д. Инвариантные дифференциальные операторы на прямой // Функциональный анализ и его приложения. 1979. Т. 13. № 4. С. 91-92.
- Article Фейгин Б. Л., Гельфанд И. М., Фукс Д. Когомологии бесконечномерных алгебр Ли и операторы Лапласа // Функциональный анализ и его приложения. 1978. Т. 12. № 4. С. 1-5.
- Article Фейгин Б. Л. Характеристические классы флагов слоений // Функциональный анализ и его приложения. 1975. Т. 9. № 4. С. 49-56.
- Article Фейгин Б. Л., Гельфанд И. М., Фукс Д. Когомологии алгебры Ли формальных векторных полей с коэффициентамив двойственном пространстве и вариации характеристиеческих классов слоений // Функциональный анализ и его приложения. 1974. Т. 8. № 2. С. 13-29.
Conferences
HSE University Staff Members Elected to the Russian Academy of Sciences
The results of the vote were announced at the General Assembly of the Russian Academy of Sciences (RAS), which took place from June 1-3. The newly elected Members and Corresponding Members of the RAS include eight scholars from HSE University.
HSE University Researchers Receive Fifteen Grants from the Russian Science Foundation
The Russian Science Foundation has announced the winners of four 2020 competitions. Some of the winners are from HSE University. They have received grants of 12 to 24 million roubles, for a term of two to four years.
International Laboratory for Mirror Symmetry and Automorphic Forms
The new International Laboratory for Mirror Symmetry and Automorphic Forms will open at HSE’s Faculty of Mathematics in 2017. This project, overseen by Ludmil Katzarkov (Professor at the University of Miami), won the Fifth Mega-Grants Competition of the Government of the Russian Federation.
‘Maths Teaches Modesty above All’
This year winner of the respected Fields medal Andrey Okounkov became the new head of HSE’s International Laboratory of Representation Theory and Mathematical Physics. In an interview for the HSE News website, he talked about what is a good mathematical education, why mathematicians are more free than other academics and what to tell people who find figures difficult.
Golden HSE -2014 Award Winners Announced
On December 1, HSE celebrated another anniversary and, according to tradition, awarded the best teachers, researchers, administrative staff, and students with the Golden HSE prize.
‘The Programme is Unique not Only for Russia, but also for the Best Universities of the World’
Sergey Lando, Dean of the HSE Faculty of Mathematics and Head of the master’s programme in Mathematics, told us about some innovations in the Faculty’s master’s courses.