Boca, Florin P.
Published in
Communications in Mathematical Physics

Abstract:For each α∈ (0,1), Aα denotes the universal C*-algebra generated by two unitaries u and v, which satisfy the commutation relation uv=e2 π i αvu. We consider the order four automorphism σ of Aα defined by σ (u)=v, σ (v)=u−1 and describe a method for constructing projections in the fixed point algebra Aασ, using Rieffel's imprimitivity bimod...

Hintz, Peter Zworski, Maciej
Published in
Communications in Mathematical Physics

We consider scattering by star-shaped obstacles in hyperbolic space and show that resonances satisfy a universal bound Imλ≤-12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docum...

Esposito, R. Guo, Y. Marra, R.
Published in
Communications in Mathematical Physics

Given an obstacle in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^3}$$\end{document} and a non-zero velocity with small amplitude at the infinity, we c...

Jing, Naihuan Liu, Ming Molev, Alexander
Published in
Communications in Mathematical Physics

It is well-known that the Gauss decomposition of the generator matrix in the R-matrix presentation of the Yangian in type A yields generators of its Drinfeld presentation. Defining relations between these generators are known in an explicit form, thus providing an isomorphism between the presentations. It has been an open problem since the pioneeri...

McSwiggen, Colin
Published in
Communications in Mathematical Physics

We present a new proof of Harish-Chandra’s formula (Harish-Chandra in Am J Math 79:87–120, 1957) Π(h1)Π(h2)∫Ge⟨Adgh1,h2⟩dg=[[Π,Π]]|W|∑w∈Wϵ(w)e⟨w(h1),h2⟩,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddside...

Buryak, Alexandr Tessler, Ran J.
Published in
Communications in Mathematical Physics

In a recent work, R. Pandharipande, J. P. Solomon and the second author have initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. They conjectured that the generating series of the intersection numbers satisfies the open KdV equations. In this paper we prove this conjecture. Our proof goes through a ma...

Colombo, Maria De Lellis, Camillo De Rosa, Luigi
Published in
Communications in Mathematical Physics

We prove the ill-posedness of Leray solutions to the Cauchy problem for the hypodissipative Navier–Stokes equations, when the dissipative term is a fractional Laplacian (-Δ)α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek...

Klinker, Frank
Published in
Communications in Mathematical Physics

In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo-) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the one hand and spinor fields on the other hand as equivalent geometric objects. This is the starting point of our...

Rembado, Gabriele
Published in
Communications in Mathematical Physics

We construct a new family of flat connections generalising the KZ connection, the Casimir connection and the dynamical connection. These new connections are attached to simply-laced graphs, and are obtained via quantisation of time-dependent Hamiltonian systems controlling the isomonodromic deformations of meromorphic connections on the sphere.

Zheng, Fan
Published in
Communications in Mathematical Physics

We study a basic plasma physics model—the one-fluid Euler–Poisson system on the square torus, in which a compressible electron fluid flows under its own electrostatic field. In this paper we prove long-term regularity of periodic solutions of this system in 2 spatial dimensions with small data. Our main conclusion is that on a square torus of side ...