Vertex operator algebra theory is a new area of mathematics. It has been an exciting and
ever-growing subject from the beginning, starting even before R. Borcherds introduced the …

Vertex algebras are algebraic objects that encapsulate the concept of operator product
expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming …

We examine two types of half-BPS surface defects $-$ regular monodromy surface defect
and canonical surface defect $-$ in four-dimensional gauge theory with $\mathcal {N}= 2 …

The Hamiltonian theory of zero-curvature equations with spectral parameter on an arbitrary
compact Riemann surface is constructed. It is shown that the equations can be seen as …

In this paper we study a proposal of Nekrasov, Rosly and Shatashvili that describes the
effective twisted superpotential obtained from a class S theory geometrically as a generating …

We consider the problem of quantization of classical soliton integrable systems, such as the
KdV hierarchy, in the framework of a general formalism of Gaudin models associated to …

These notes are based on lectures given at the Third International School on Geometry and
Physics at the Centre de Recerca Matemàtica in Barcelona, March 26–30, 2012. The aim of …

We consider non-twisted meromorphic connections in sl2 (C) and the associated symplectic
Hamiltonian structure. In particular, we provide explicit expressions of the Lax pair in the …

We consider the problem of diagonalization of the hamiltonians of the Gaudin model, which
is a quantum chain model associated to a simple Lie algebra. The hamiltonians of this …

We conjecture that quantum Gaudin models in affine types admit families of higher
Hamiltonians, labelled by the (countably infinite set of) exponents, whose eigenvalues are …