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 …

The review is based on the authro's papers since 1985 in which a new approach to the
separation of variables (SoV) has being developed. It is argued that SoV, understood …

algebras and deformations of W-algebras Page 174 http://dx. doi. org/10.1090/conm/248/03823
Contemporary Mathematics Volume 248, 1999 The q-characters of representations of quantum …

We reformulate the Ω-deformation of four-dimensional gauge theory in a way that is valid
away from fixed points of the associated group action. We use this reformulation together …

We study macroscopically two dimensional N=(2, 2) N=(2, 2) supersymmetric gauge
theories constructed by compactifying the quiver gauge theories with eight supercharges on …

Seiberg-Witten geometry of mass deformed $\mathcal N= 2$ superconformal ADE quiver
gauge theories in four dimensions is determined. We solve the limit shape equations …

The Langlands Program has emerged in recent years as a blueprint for a Grand Unified
Theory of Mathematics. Conceived initially as a bridge between Number Theory and …

The moduli space of SL2 flat connections on a punctured Riemann surface Σ with the fixed
conjugacy classes of the monodromies around the punctures is endowed with a system of …

We conjecture, and prove for all simply-laced Lie algebras, an identification between the
spaces of $ q $-deformed conformal blocks for the deformed ${\mathcal W} $-algebra …