Related papers: Critical values of moment maps on quantizable mani…

Machine learning interatomic potentials (MLIPs) have substantially advanced atomistic simulations in materials science and chemistry by balancing accuracy and computational efficiency. While leading MLIPs rely on representing atomic…

For an infinitely renormalizable negative Schwarzian unimodal map $f$ with non-flat critical point, we analyze statistical properties of periodic points as the periods tend to infinity. Introducing a weight function $\varphi$ which is a…

In this article we discuss the geometric quantization on a certain type of infinite dimensional super-disc. Such systems are quite natural when we analyze coupled bosons and fermions. The large-N limit of a system like that corresponds to a…

A moment body is a linear projection of the spectraplex, the convex set of trace-one positive semidefinite matrices. Determining whether a given point lies within a given moment body is a problem with numerous applications in quantum state…

We consider a Hamiltonian torus action on a compact connected symplectic manifold M. For a certain class of Lagrangian submanifolds Q of M we show that the image of Q under the momentum map is convex. As an application we complete the…

The space of symplectic connections on a symplectic manifold is a symplectic affine space. M. Cahen and S. Gutt showed that the action of the group of Hamiltonian diffeomorphisms on this space is Hamiltonian and calculated the moment map.…

A generalized moment map is proposed for arbitrary symplectic actions of compact connected Lie groups on closed symplectic manifolds, in the spirit of the circle -valued maps introduced by D. McDuff in the case of non-Hamiltonian circle…

The goal of this article is to study the space of smooth Riemannian structures on compact manifolds with boundary that satisfies a critical point equation associated with a boundary value problem. We provide an integral formula which…

Let G be a subgroup of finite index in SL(n,Z) for N > 4. Suppose G acts continuously on a manifold M, with fundamental group Z^n, preserving a measure that is positive on open sets. Further assume that the induced G action on H^1(M) is…

We give locally finite Markov trees in $L^p$-compact$,$ separable Hilbert$,$ supersymmetric process$:$ $[0,\infty)\!\times\!\mathbb{R}^{\lvert\mathcal{A}^{\otimes m}\rvert}/\mathcal{A}^{\otimes m}$ on quantum ${\rm…

We describe $\omega$-limit sets of completely positive (CP) maps over finite-dimensional spaces. In such sets and in its corresponding convex hulls, CP maps present isometric behavior and the states contained in it commute with each other.…

This is a review of [Michor, Peter W.: The moment mapping for a unitary representation, Ann. Global Anal. Geometry, 8, No 3(1990), 299--313] including a careful description of calculus in infinite dimensions. For any unitary representation…

Let $M$ be a graph manifold such that each piece of its JSJ decomposition has the $\Bbb H^2 \times \Bbb R$ geometry. Assume that the pieces are glued by isometries. Then, there exists a complete Riemannian metric on $\Bbb R \times M$ which…

In this paper we show the existence of non minimal critical points of the Yang-Mills functional over a certain family of 4-manifolds with generic SU(2)-invariant metrics using Morse and homotopy theoretic methods. These manifolds are acted…

Let $\varphi:\mathbb{R}\rightarrow \mathbb{R}$ be a continuously differentiable function on an interval $J\subset\mathbb{R}$ and let $\boldsymbol{\alpha}=(\alpha_1,\alpha_2)$ be a point with algebraically conjugate coordinates such that the…

Let $f:M\to \mathbb{R}$ be a Morse function on a smooth closed surface, $V$ be a connected component of some critical level of $f$, and $\mathcal{E}_V$ be its atom. Let also $\mathcal{S}(f)$ be a stabilizer of the function $f$ under the…

The contribution of this work is twofold. The first part deals with a Hilbert-space version of McCann's celebrated result on the existence and uniqueness of monotone measure-preserving maps: given two probability measures $\rm P$ and $\rm…

We consider three dimensional gravity with a positive cosmological constant and non- zero gravitational Chern-Simons term. This theory has inflating de Sitter solutions and local metric degrees of freedom. The Euclidean signature partition…

In this paper, we study the prescribed $Q$-curvature problem on closed four-dimensional Riemannian manifolds when the total integral of the $Q$-curvature is a positive integer multiple of the one of the four-dimensional round sphere. This…

Let $M$ be a smooth compact manifold and $P$ be either $R^1$ or $S^1$. There is a natural action of the groups $Diff(M)$ and $Diff(M) \times Diff(P)$ on the space of smooth mappings $C^{\infty}(M,P)$. For $f\in C^{\infty}(M,P)$ let $S_f$,…