Related papers: Chiral differential operators: formal loop group a…

The aim of the lectures is to introduce first-year Ph.D. students and research workers to the theory of the Dirac operator, spinor techniques, and their relevance for the theory of eigenvalues in Riemannian geometry. Topics: differential…

A framework for higher gauge theory based on a 2-group is presented, by constructing a groupoid of connections on a manifold acted on by a 2-group of gauge transformations, following previous work by the authors where the general notion of…

The D1-D5 system has an orbifold point in its moduli space, at which it may be described by an ${\cal N} = (4,4)$ supersymmetric sigma model with target space $M^N/S(N)$ where $M$ is $\mathbb{T}^4$ or $K3$. In this paper we consider…

Scalar relative invariants play an important role in the theory of group actions on a manifold as their zero sets are invariant hypersurfaces. Relative invariants are central in many applications, where they often are treated locally since…

This paper develops the theory of a sheaf of normal differential operators to a submanifold Y of a complex manifold X as a generalization of the normal bundle. We show that the global sections of this sheaf play an analogous role for formal…

We approach the question of complexification of the diffeomorphism group of the circle by considering real-analytic maps from the circle into the punctured complex plane with winding number +1. Such complex deformations form an…

We study differential invariants of the third order linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles on two dimensional manifolds with respect to groups of…

The principal group of a Klein geometry has canonical left action on the homogeneous space of the geometry and this action induces action on the spaces of sections of vector bundles over the homogeneous space. This paper is about…

The space of linear differential operators on a smooth manifold $M$ has a natural one-parameter family of $Diff(M)$ (and $Vect(M)$)-module structures, defined by their action on the space of tensor-densities. It is shown that, in the case…

In this survey paper, we will collate various different ideas and thoughts regarding equivariant operations on quantum cohomology (and some in more general Floer theory) for a symplectic manifold. We will discuss a general notion of…

In this paper, we develop a manifestly geometric framework for equivariant manifold neural ordinary differential equations (NODEs) and use it to analyse their modelling capabilities for symmetric data. First, we consider the action of a Lie…

Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model, we suggest a setup for the study of CDR on manifolds with special holonomy. We show how to systematically…

In this expository article, we consider first order elliptic differential operators acting on smooth vector bundles over compact manifolds, and certain invariants derived from the analysis of these operators, namely the eta invariant} and…

We formulate the Chern-Simons action for any compact Lie group using Deligne cohomology. This action is defined as a certain function on the space of smooth maps from the underlying 3-manifold to the classifying space for principal bundles.…

For a manifold M we define a structure on the group action of Diff(M) on the smooth functions on M which reduces to the usual differential geometry upon differentiation at zero along the one-parameter groups of Diff(M). This ``integrated…

In two-dimensional conformal field theory (CFT) the building blocks are given by chiral CFTs, i.e.~CFTs on the unit circle (compactified light-ray). They are generated by quantum fields depending on one light-ray coordinate only. There are…

We construct a new equivariant cohomology theory for a certain class of differential vertex algebras, which we call the chiral equivariant cohomology. A principal example of a differential vertex algebra in this class is the chiral de Rham…

Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector fields on M. Assume that V contains a finite dimensional semisimple maximal subalgebra A, the projective or conformal subalgebra. A projective or conformal…

Fundamental solutions of Dirac type operators are introduced for a class of conformally flat manifolds. This class consists of manifolds obtained by factoring out the upper half-space of $\mathbb{R}^n$ by arithmetic subgroups of generalized…

We construct Chern-Weil classes on infinite dimensional vector bundles with structure group contained in the algebra $\cl[\leq 0](M, E)$ of non-positive order classical pseudo-differential operators acting on a finite rank vector bundle $E$…