相关论文: Non-integral geometry: additional term $f_A$ as a …
We review the noncommutative spectral geometry, a gravitational model that combines noncommutative geometry with the spectral action principle, in an attempt to unify General Relativity and the Standard Model of electroweak and strong…
The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted co-product. This allows for the definition of conformal symmetry in a non-commutative background geometry. The twisted co-product is reviewed for the…
A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step towards the construction of a consistent noncommutative gravitational theory. Historically, as well, Riemannian geometry was recognized to be the…
We consider the problem of nonlinear dimensionality reduction: given a training set of high-dimensional data whose ``intrinsic'' low dimension is assumed known, find a feature extraction map to low-dimensional space, a reconstruction map…
An integral representation result for strictly positive subharmonic functions of a one-dimensional regular diffusion is established. More precisely, any such function can be written as a linear combination of an increasing and a decreasing…
Analysis sparsity is a common prior in inverse problem or machine learning including special cases such as Total Variation regularization, Edge Lasso and Fused Lasso. We study the geometry of the solution set (a polyhedron) of the analysis…
A method for the resummation of nonalternating divergent perturbation series is described. The procedure constitutes a generalization of the Borel-Pad\'{e} method. Of crucial importance is a special integration contour in the complex plane.…
We consider parametric Feynman integrals and their dimensional regularization from the point of view of differential forms on hypersurface complements and the approach to mixed Hodge structures via oscillatory integrals. We consider…
We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (``quantum mechanical path integrals in curved space'')…
We shall describe a simple generalization of commutative rings. The category GR of such "rings", contains the ordinary commutative rings (fully faithfully), but also the "integers" and "residue field" at a real or complex place of a field ;…
We study the Lorentz and Dirac algebra, including antisymmetric $\epsilon$ tensors and the $\gamma_5$ matrix, in implicit gauge-invariant regularization/renormalization methods defined in fixed integer dimensions. They include constrained…
A perturbative non-renormalization theorem is presented that applies to general supersymmetric theories, including non-renormalizable theories in which the $\int d^2\theta$ integrand is an arbitrary gauge-invariant function $F(\Phi,W)$ of…
Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge…
Neural operators are neural network-based surrogate models for approximating solution operators of parametric partial differential equations, enabling efficient many-query computations in science and engineering. Many applications,…
In this talk we discuss a class of Feynman integrals, which can be expressed to all orders in the dimensional regularisation parameter as iterated integrals of modular forms. We review the mathematical prerequisites related to elliptic…
Robotics research has found numerous important applications of Riemannian geometry. Despite that, the concept remain challenging to many roboticists because the background material is complex and strikingly foreign. Beyond {\em Riemannian}…
We provide a functional characterization of isometries between non-reversible Finsler manifolds, in the form of a generalization of the Myers-Nakai Theorem for Riemannian manifolds. We show that, since non-reversible Finsler manifolds are a…
In the field of machine learning there is a growing interest towards more robust and generalizable algorithms. This is for example important to bridge the gap between the environment in which the training data was collected and the…
The commutative algebra of functions on a manifold is extended to a noncommutative algebra by considering its tensor product with the algebra of nxn complex matrices. Noncommutative geometry is used to formulate an extension of the…
I will summarize Noncommutative Geometry Spectral Action, an elegant geometrical model valid at unification scale, which offers a purely gravitational explanation of the Standard Model, the most successful phenomenological model of particle…