Related papers: Invariant Manifolds for Non-differentiable Operato…
We introduce Manifold tensor categories, which make precise the notion of a tensor category with a manifold of simple objects. A basic example is the category of vector spaces graded by a Lie group. Unlike classic tensor category theory,…
Chern-Weil and Chern-Simons theory extend to certain infinite-rank bundles that appear in mathematical physics. We discuss what is known of the invariant theory of the corresponding infinite-dimensional Lie groups. We use these techniques…
We conclude the construction of the algebraic complex, consisting of spaces of differentials of Euclidean metric values, for four-dimensional piecewise-linear manifolds. Assuming that the complex is acyclic, we investigate how its torsion…
We study the existence and regularity of invariant graphs for bundle maps (or bundle correspondences with generating bundle maps motivated by ill-posed differential equations) having some relative partial hyperbolicity on non-trivial and…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…
We take the fundamental group of the complement of the branch curve of a generic projection induced from canonical embedding of a surface. This group is stable on connected components of moduli spaces of surfaces. Since for many classes of…
We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical…
In this paper, we apply the theory of Chern-Cheeger-Simons to construct canonical invariants associated to a $r$-simplex whose points parametrize flat connections on a smooth manifold $X$. These invariants lie in degrees…
Stochastic invariant manifolds are crucial in modelling the dynamical behavior of dynamical systems under uncertainty. Under the assumption of exponential trichotomy, existence and smoothness of center manifolds for a class of stochastic…
In the first part of this series of papers we developed the invariant differentiation with respect to a Cartan connection, we described this procedure in the terms of the underlying principal connections, and we discussed applications of…
Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…
We construct invariants of four-dimensional piecewise-linear manifolds, represented as simplicial complexes, with respect to rebuildings that transform a cluster of three 4-simplices having a common two-dimensional face in a different…
We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold $M$. We give several applications of this theory, concerning: 1) differentiability and geometrical properties of the…
Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…
We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles over smooth manifolds with respect to groups of authomorphisms.
In low dimensional topology, we have some invariants defined by using solutions of some nonlinear elliptic operators. The invariants could be understood as Euler class or degree in the ordinary cohomology, in infinite dimensional setting.…
We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of…
Using a derivative decomposition of the Hochschild differential complex we define a generalized inverse of the Hochschild coboundary operator. It can be applied for systematic computations of star products on Poisson manifolds.
A Stein covering of a complex manifold may be used to realise its analytic cohomology in accordance with the Cech theory. If, however, the Stein covering is parameterised by a smooth manifold rather than just a discrete set, then we…
A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The quantization map is moreover required to be a linear bijection. It is known that there is in general no natural…