The mathematical physics research group at York is internationally recognized for its fundamental contributions to the theory of integrable systems.The researcher Boris Noyvert has worked for 8 years in conformal field theory and the theory of infinite di mensional algebras. At York he will establish a connection of his previous research to the theory of integrable systems. He will study the applications of conformal field theory to integrable models and the integrability phenomenon beyond conformal field t heory. The proposal consists of two main parts: "Classification of W-algebras" and "Pseudo root systems and vertex operator realizations of the Virasoro algebra". W-algebras is the most important for physics type of vertex algebras. W-algebras are certain extensions of the Virasoro algebra with nonlinear commutation relations between the generators. The classification of W-algebras is a long standing problem which can hopefully be solved now due to the recent breakthrough in the quantum hamiltonian reductio n of affine superalgebras. Pseudo root systems were introduced by B.Noyvert in the context of bosonization of the Virasoro algebra. They generalize the notion of root systems of simple Lie algebras. They provide new examples of rational and irrational conf ormal field theories and lead to new identities for modular functions. Both projects have applications in the integrability theory and are likely to benefit and even to get new research directions from joint work with Prof. Coriigan and the mathematical ph ysics group at York. The fellowship will allow to Boris Noyvert to broaden his expertise in mathematics and theoretical physics, to become acquainted with a related area, current trends and new problems, solution methods and structures of the theory of int egrable systems and will increase the scientific quality of the researcher. The university of York with its high scientific level will provide a perfect surrounding to achieve this goal.
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