My research interests include mathematical physics, algebraic geometry and noncommutative algebra. I am particularly interested in various interactions between these fields. Some of my recent work is related to the study of algebras of differential operators on singular algebraic varieties and representation theory of Cherednik algebras.
Main publications:
Automorphisms and ideals of the Weyl algebra (with G. Wilson), Math. Ann. 318 no. 1 (2000), 127–147.
Ideal classes of the Weyl algebra and noncommutative projective geometry (with G. Wilson and M. van den Bergh), Internat. Math. Res. Notices 26 (2002), 1347–1396.
Finite-dimensional representations of rational Cherednik algebras (with P. Etingof and V. Ginzburg), Internat. Math. Res. Notices 19 (2003), 1053–1088.
Cherednik algebras and differential operators on quasi-invariants (with P. Etingof and V. Ginzburg), Duke Math. J. 118 no. 2 (2003), 279–337.
Morita equivalence of Cherednik algebras (with P. Etingof and V. Ginzburg), J. Reine Angew. Math. 568 (2004), 81–99.
Yu. Yu. Berest, O. A. Chalykh, F. Eshmatov, “Recollement of deformed preprojective algebras and the Calogero–Moser correspondence”, Mosc. Math. J., 8:1 (2008), 21–37
Yu. Yu. Berest, A. P. Veselov, “On the singularities of potentials of exactly soluble Schrödinger equations and on Hadamard's problem”, Uspekhi Mat. Nauk, 53:1(319) (1998), 211–212; Russian Math. Surveys, 53:1 (1998), 208–209
Yu. Yu. Berest, A. P. Veselov, “Hadamard's Problem and Coxeter Groups: New Examples of Huygens' Equations”, Funktsional. Anal. i Prilozhen., 28:1 (1994), 3–15; Funct. Anal. Appl., 28:1 (1994), 3–12
Yu. Yu. Berest, “Group analysis of linear differential equations in generalized functions and the construction of fundamental solutions”, Differ. Uravn., 29:11 (1993), 1958–1970; Differ. Equ., 29:11 (1993), 1700–1711
Yu. Yu. Berest, “Construction of fundamental solutions for Huygens equations as
invariant solutions”, Dokl. Akad. Nauk SSSR, 317:4 (1991), 786–789; Dokl. Math., 43:2 (1991), 496–499
V. E. Adler, Yu. Yu. Berest, V. M. Buchstaber, P. G. Grinevich, B. A. Dubrovin, I. M. Krichever, S. P. Novikov, A. N. Sergeev, M. V. Feigin, J. Felder, E. V. Ferapontov, O. A. Chalykh, P. I. Etingof, “Alexander Petrovich Veselov (on his 60th birthday)”, Uspekhi Mat. Nauk, 71:6(432) (2016), 172–188; Russian Math. Surveys, 71:6 (2016), 1159–1176
Presentations in Math-Net.Ru
1.
Derived Poisson Structures Yu. Yu. Berest Algebraic Structures in Integrable Systems December 4, 2012 17:10
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