We review the status and present range of applications of the “string-inspired” approach to
perturbative quantum field theory. This formalism offers the possibility of computing effective …

We discuss general properties of A∞-algebras and their applications to the theory of open
strings. The properties of cyclicity for A∞-algebras are examined in detail. We prove the …

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation
quantization. Informally, it means that the set of equivalence classes of associative algebras …

We develop techniques to compute higher loop string amplitudes for twisted N= 2 theories
with ĉ= 3 (ie the critical case). An important ingredient is the discovery of an anomaly at …

Bibliography Page 1 Bibliography In addition to the usual data each title contains one or more
code numbers indicating the particular fields the paper belongs to (eg, <K16>, knot groups; …

Operads are mathematical devices that describe algebraic structures of many varieties and
in various categories. Operads are particularly important in categories with a good notion of …

Factorization algebras are local-to-global objects that play a role in classical and quantum
field theory that is similar to the role of sheaves in geometry: they conveniently organize …

The algebraic world of associative algebras has many deep connections with the geometric
world of two-dimensional surfaces. Recently, D. Tamarkin discovered that the operad of …

If classical Lie groups preserve bilinear vector norms, what Lie groups preserve trilinear,
quadrilinear, and higher order invariants? Answering this question from a fresh and original …

We review in detail the Batalin–Vilkovisky formalism for Lagrangian field theories and its
mathematical foundations with an emphasis on higher algebraic structures and classical …