Related papers: Connes integration formula for the noncommutative …
Our aim in this review article is to present the applications of Connes' noncommutative geometry to elementary particle physics. Whereas the existing literature is mostly focused on a mathematical audience, in this article we introduce the…
We prove a new residue formula for integrals with singularities along affine hyperplanes. Our formula makes use of a notion for real matrices called stability which is inspired by ideas from total positivity.
Topological structure of translation-invariant noncommutative Yang-Mills theories are studied by means of a cohomology theory, so called star-cohomology, which plays an intermediate role between de Rham and cyclic (co)homology theory for…
A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…
It is proven that for any topological or analytical types of isolated singular points of plane curves, there exists a non-real irreducible plane algebraic curve of degree $d$ which goes through $d^2$ real distinct points and has imaginary…
We prove Cauchy's formula for repeated integration on time scales. The obtained relation gives rise to new notions of fractional integration and differentiation on arbitrary nonempty closed sets.
The contraction is applied to obtaining of integrable systems associated with nonsemisimple algebras. The effect of contraction is splitting off some components from initial system without loss of integrability.
In this two-part series of articles, we present a new proof comparing the trace formula for a general linear group with that of one of its inner forms. Our methodology relies on the trace formula for Lie algebras, incorporating the notion…
The Landau problem in the noncommutative plane is discussed in the context of realizations of the two-fold centrally extended planar Galilei group and the anyon theory.
We give a new, simple proof of the trace formula for Hecke operators on modular forms for finite index subgroups of the modular group. The proof uses algebraic properties of certain universal Hecke operators acting on period polynomials of…
We introduce a convex integration scheme for the continuity equation in the context of the Di Perna-Lions theory that allows to build incompressible vector fields in $C_{t}W^{1,p}_x$ and nonunique solutions in $C_{t} L^{q}_x$ for any $p,q$…
The aim of this article is twofold: give a short proof of the existence of real spectral shift function and the associated trace formula for a pair of contractions, the difference of which is trace-class and one of the two a strict…
We consider positive solutions to semilinear elliptic problems with singular nonlinearities, under zero Dirichlet boundary condition. We exploit a refined version of the moving plane method to prove symmetry and monotonicity properties of…
We introduce singular homology for non-Archimedean analytic spaces using a cosimplicial perfectoid space as a Galois representation. We define an integration along a cycle, which gives a pairing with the singular homology and the space of…
We discuss a non--commutative integration calculus arising in the mathematical description of anomalies in fermion--Yang--Mills systems. We consider the differential complex of forms $u_0\ccr{\eps}{u_1}\cdots\ccr{\eps}{u_n}$ with $\eps$ a…
We develop Conley's theory for multivalued maps on finite topological spaces. More precisely, for discrete-time dynamical systems generated by the iteration of a multivalued map which satisfies appropriate regularity conditions, we…
The mathematical apparatus of non commutative geometry and operator algebras which Connes has brought to bear to construct a rational scheme for the internal symmetries of the standard model is presented from the physicist's point of view.…
In a recent work (Int Math Res Not 24:18604-18612, 2021), Carlen-Jauslin-Lieb-Loss studied the convolution inequality $f \ge f*f$ on $\mathbb{R}^d$ and proved that the real integrable solutions of the above inequality must be non-negative…
Let $p$ be a polynomial in several non-commuting variables with coefficients in a field $K$ of arbitrary characteristic. It has been conjectured that for any $n$, for $p$ multilinear, the image of $p$ evaluated on the set $M_n(K)$ of $n$ by…
We provide a generalization of an algebraic linear combination for the trace of certain elliptic modular forms, and through specializing the expression at a suitable pair consisting of an elliptic curve over algebraic number fields and its…