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Mathematics Volume 2021 Issue 2012

Subject Areas: Computer Science (miscellaneous); ; ; ;
SJR: 43

Open Access

Journal Article

On the direct integral decomposition in branching laws for real reductive groups

Frahm, Jan

2020 Mathematics

Abstract: The restriction of an irreducible unitary representation $\pi$ of a real reductive group $G$ to a reductive subgroup $H$ decomposes into a direct integral of irreducible unitary representations $\tau$ of $H$ with multiplicities $m(\pi,\tau)\in\mathbb{N}\cup\{\infty\}$. We show that on...
Open Access

Journal Article

On the Bombieri-Lang Conjecture over finitely generated fields

Bresciani, Giulio

2020 Mathematics

Abstract: We prove that the strong Bombieri-Lang conjecture for $\mathbb{Q}$ implies it for fields finitely generated over $\mathbb{Q}$. We prove that the geometric Lang conjecture plus the weak Bombieri-Lang conjecture over $\mathbb{Q}$ imply the strong Bombieri-Lang conjecture for fields...
Open Access

Journal Article

Extensions of Tong-Yang-Ma representation

Soulié, Arthur; Takano, Akihiro

2020 Mathematics

Abstract: In 1996, Tong, Yang and Ma defined a family of representations of the braid group which have the same dimensions as the Burau representations but are not equivalent. The Burau representation was defined homologically and extended to the string links in several ways. In this paper, using...
Open Access

Journal Article

On the analytic properties of a J-Bessel integral and its applications (with an appendix by J.S. Friedman*)

Anton, George; Malathu, Jessen A.; Stinson, Shelby

2020 Mathematics

Abstract: In a recent paper the team of Cogdell, Jorgenson and Smajlović develop infinite series representations for the logarithmic Mahler measure of a complex linear form, with 4 or more variables. We establish the case of 3 variables, by bounding an integral with integrand involving the random...
Open Access

Journal Article

Comments on the holographic description of Narain theories

Dymarsky, Anatoly; Shapere, Alfred

2020 Mathematics

Abstract: We discuss the holographic description of Narain $U(1)^c\times U(1)^c$ conformal field theories, and their potential similarity to conventional weakly coupled gravity in the bulk, in the sense that the effective IR bulk description includes "$U(1)$ gravity" amended with additional light...
Open Access

Journal Article

Generalized string-net models: A thorough exposition

Lin, Chien-Hung; Levin, Michael; Burnell, Fiona J.

2020 Mathematics

doi:10.1103/PhysRevB.103.195155

Abstract: We describe how to construct generalized string-net models, a class of exactly solvable lattice models that realize a large family of 2D topologically ordered phases of matter. The ground states of these models can be thought of as superpositions of different "string-net...
Open Access

Journal Article

Roots of Garding hyperbolic polynomials

Rainer, Armin

2020 Mathematics

Abstract: We explore the regularity of the roots of Garding hyperbolic polynomials and real stable polynomials. As an application we obtain new regularity results of Sobolev type for the eigenvalues of Hermitian matrices and for the singular values of arbitrary matrices. These results are optimal...
Open Access

Journal Article

Nuclear dimension of extensions of $\mathcal{O}_\infty$-stable algebras

Evington, Samuel

2020 Mathematics

Abstract: We obtain an improved upper bound for the nuclear dimension of extensions of $\mathcal{O}_\infty$-stable $\rm{C}^*$-algebras. In particular, we prove that the nuclear dimension of a full extension of an $\mathcal{O}_\infty$-stable $\rm{C}^*$-algebra by a stable AF algebra is one.
Open Access

Journal Article

Refined bounds for randomized experimental design

Rizk, Geovani; Colin, Igor; Thomas, Albert; Draief, Moez

2020 Mathematics

Abstract: Experimental design is an approach for selecting samples among a given set so as to obtain the best estimator for a given criterion. In the context of linear regression, several optimal designs have been derived, each associated with a different criterion: mean square error, robustness,...
Open Access

Journal Article

Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk

Henheik, Joscha; Teufel, Stefan

2020 Mathematics

Abstract: We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding GNS-Hamiltonian has a spectral gap above its eigenvalue zero....

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