相关论文: On the obstruction to linearizability of 2-order o…
We determine the splitting (isomorphism) type of the normal bundle of a generic genus-0 curve with 1 or 2 components in any projective space, as well as the (sometimes nontrivial) way the bundle deforms locally with a general deformation of…
We explore the connection between the global symmetry quantum numbers of line defects and 't Hooft anomalies. Relative to local (point) operators, line defects may transform projectively under both internal and spacetime symmetries. This…
Starting from a general analysis of obstruction classes, we develop the investigation of obstructions associated with the bundle structure of the hyperbolic Clifford algebra. By taking into account particularities arising from the Whitney…
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…
We develop a geometric framework for Weyl quantization on pseudo-Riemannian manifolds, in which pseudodifferential operators act on sections of vector bundles equipped with arbitrary connections. We construct the associated star product and…
The moduli space $M$ of semi-stable rank 2 bundles with trivial determinant over a complex curve carries involutions naturally associated to 2-torsion points on the Jacobian of the curve. For every lift of a 2-torsion point to a 4-torsion…
In this paper we study gauge theory on SL(2,C)-equivariant bundles over XxP^1, where X is a compact Kahler manifold, P^1 is the complex projective line, and the action of SL(2,C) is trivial on X and standard on P^1. We first classify these…
We generalize the notion of an anomaly for a symmetry to a noninvertible symmetry enacted by surface operators using the framework of condensation in 2-categories. Given a multifusion 2-category, potentially with some additional levels of…
We present in this paper the construction of a pseudodifferential calculus on smooth non-compact manifolds associated to a globally defined and coordinate independant complete symbol calculus, that generalizes the standard…
We study the geometry and topology of (filtered) algebra-bundles ${\bf\Psi}^{\mathbb Z}$ over a smooth manifold $X$ with typical fibre $\Psi^{\mathbb Z}(Z; V)$, the algebra of classical pseudodifferential operators of integral order on the…
We investigate a class of current-current, Gross-Neveu like, perturbations of WZW models in which the full left-right affine symmetry is broken to the diagonal global algebra only. Our analysis focuses on those supergroups for which such a…
We extend our previous result on the behavior of the quadratic part of a complex points of a small $\mathcal{C}^{2}$-perturbation of a real $4$-manifold embedded in a complex $3$-manifold. We describe the change of the structure of a normal…
We consider the bifurcation problem u'' + \lambda u = N(u) with two point boundary conditions where N(u) is a general nonlinear term which may also depend on the eigenvalue \lambda. A new derivation of a variational principle for the lowest…
We construct a mathematical framework for twisted N=2 supersymmetric topological quantum field theory on a 4-manifold. Supersymmetry in flat space is defined and the twist homomorphism is constructed, giving us a supermanifold that is the…
In this dissertation the notion of deformation quantization of principal fibre bundles is established and investigated in order to find a geometric formulation of classical gauge theories on noncommutative space-times. As a generalization,…
We show that for n>2 the following equivalence problems are essentially the same: the equivalence problem for Lagrangians of order n with one dependent and one independent variable considered up to a contact transformation, a multiplication…
In a recent paper arXiv:1602.02300v2, Cook II, Harbourne, Migliore and Nagel related the splitting type of a line arrangement in the projective plane to the number of conditions imposed by a general fat point of multiplicity $j$ to the…
We give detailed descriptions of gluing pseudoholomorphic maps in symplectic geometry, especially in the presence of an obstruction bundle. The main motivation is to try to compare the symplectic and enumerative invariants of algebraic…
Linearization of coupled second order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper we describe a simple and straightforward method to…
We compute the quotient of the self-duality equation for conformal metrics by the action of the diffeomorphism group. We also determine Hilbert polynomial, counting the number of independent scalar differential invariants depending on the…