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 goal of this paper is to give a category theory based definition and classification of “finite
subgroups in Uq (sl 2)” where q= eπi/l is a root of unity. We propose a definition of such a …

We present a project of classification of a certain class of bihamiltonian 1+ 1 PDEs
depending on a small parameter. Our aim is to embed the theory of Gromov-Witten …

We study the triplet vertex operator algebra W (p) of central charge 1− 6 (p− 1) 2p, p⩾ 2. We
show that W (p) is C2-cofinite but irrational since it admits indecomposable and logarithmic …

To study the representation category of the triplet W-algebra W\left (p\right) that is the
symmetry of the (1, p) logarithmic conformal field theory model, we propose the equivalent …

This is a survey of the theory of complex projective (CP^ 1) structures on compact surfaces.
After some preliminary discussion and definitions, we concentrate on three main topics:(1) …

Homotopy Batalin–Vilkovisky algebras Page 1 J. Noncommut. Geom. 6 (2012), 539–602 DOI
10.4171/JNCG/99 Journal of Noncommutative Geometry © European Mathematical Society …

We study the vertex algebras associated with modular invariant representations of affine Kac–
Moody algebras at fractional levels, whose simple highest weight modules are classified by …

We introduce a class of quantum integrable systems generalizing the Gaudin model. The
corresponding algebras of quantum Hamiltonians are obtained as quotients of the center of …