Journal of Mathematical Sciences, Vol. 136, No. 1, 2006 PETR PETROVICH KULISH N. M. Bogoliubov ∗ and E. V. Damaskinsky † Petr Petrovich Kulish was born in Leningrad on February 24, 1944, one month after the raise of the blockade of the city during the Great Patriotic War. In 1961, he graduated from a high school and became a student of the Faculty of Physics of Leningrad State University. In 1966, he was graduated with honors from the Chair of Mathematical Physics. The diploma thesis of P. Kulish, “The inverse scattering problem for the Schr¨ odinger equation on the line,” was supervised by Academician L. D. Faddeev; P. Kulish became a probationer at the research group of Faddeev in 1967. Since that time, the scientific and social life of Petr Petrovich is connected with the Laboratory of Mathematical Problems of Physics at Leningrad (now St. Petersburg) Branch of the V. A. Steklov Mathematical Institute. Now P. P. Kulish is the head of the Laboratory. Mostly, the field of scientific interests of P. P. Kulish was formed under the influence of ideas of Academician L. D. Faddeev; this field is closely related to the problems which are studied at the Laboratory. In 1971, P. P. Kulish defended his candidate dissertation “Asymptotic conditions and infrared divergences in the quantum field theory”; the dissertation was supervised by L. D. Faddeev. In the dissertation, the scattering matrix was defined in the presence of long-range action in the quantum field theory (electromagnetic and grav- itational fields). Coherent states were applied to define proper asymptotic in and out states. Until now, this research (see [1]) remains actual. Further, the scientific interests of Petr Petrovich were closely related to the quantum field theory, theory of integrable systems, soliton theory, nonlinear evolutionary equations, and supersymmetry. He has obtained important results in all of the listed parts of the modern mathematical physics. For example, in the joint work [5] with A. G. Reiman, the authors have established the role of the recursion operator in the construction of hierarchy for compatible Poisson brackets. An essential part of the Kulish research is devoted to the quantum method of the inverse scattering problem (QMSP); this method was developed by L. D. Faddeev’s school since the middle of the 1970s. In particular, Kulish had established the scattering factorization (factorization of the many-particle S-matrix) under the higher conservation laws (see [2]), noticed the role of representation theory in the inverse problem method, generalized the algebraic Bethe ansatz for the quantum, graded, matrix, nonlinear Schr¨ odinger equation [3] which corresponds to the Lie superalgebra sl(m/n) and to some other Lie algebras of higher ranks [4]. This research was recognized by the international commutity; part of these results formed the base of the Kulish doctor dissertation “Quantum method of the inverse problem for many-particle systems,” which was defended in 1983. One of the first reviews [6] devoted to the QMSP and written by P. P. Kulish and E. K. Sklyanin is now well known. Further development of the QMSP and the applications of this method to lattice models of the quantum field theory and quantum statistical physics motivated P. P. Kulish and N. Yu. Reshetikhin to consider a new algebraic object (see [7]); later this object was called the quantum algebra su q (2). In the work [8], the dual object (quantum group) had been introduced in the process of study of the lattice variant of the Liouville model. These works had originated the creation of a new section of the modern mathematical physics, the theory of quantum deformations of algebraic systems, or the theory of quantum groups and quantum algebras. The research of P. P. Kulish in the following fields is well known: the reflection equation, Yang–Baxter equation, properties of R-matrices, algebras of the q-oscillator [9], and the quantum Minkowski space [10]. At present, P. P. Kulish is active in the study of these fields; he investigates the problems of quantum deformations of superalgebras and of explicit construction of the twist transformation for Hopf algebras. He also studies the problem of integrability for models of the superconformal field theory. P. P. Kulish has published over 150 works in the leading Russian and international editions. P. P. Kulish puts a lot of effort into teaching. More than 10 candidate dissertations have been defended under his supervision. Later, some of his disciples defended doctor dissertations and became professors of leading ∗ St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia, e-mail: bogoliub@pdmi.ras.ru. † University of Military Constructional Engineering, St.Petersburg, Russia, e-mail: evd@pdmi.ras.ru. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 317, 2004, pp. 7–10. Original article submitted December 18, 2004. 1072-3374/06/1361-3531 c 2006 Springer Science+Business Media, Inc. 3531