J. Malkoun

activity

20142025

most citedA new proof of Atiyah's conjecture on configurations of four points

2 citations · 5 across the 13 of their papers we have counts for

collaborators

15 papers

math.CO2025

Finite graphs and configurations of points

Joseph Malkoun

We generalize the Atiyah problem on configurations and the related Atiyah--Sutcliffe conjectures 1 and 2 using finite graphs, configurations of points and tensors. Our conjectures…

math.CO2022★ 2 cited

A new proof of Atiyah's conjecture on configurations of four points

Joseph Malkoun

In Surveys in Differential Geometry, Volume 7, published in 2002 and Philosophical Transactions of the Royal Society A, Volume 359, published in 2001, Sir Michael Atiyah introduced…

math.MG2020★ 1 cited

Continuous Maps from Spheres Converging to Boundaries of Convex Hulls

Joseph Malkoun, Peter J. Olver

Given $n$ distinct points $x_{1}, \dots, x_{n}$ in $R^{d}$ , let $K$ denote their convex hull, which we assume to be $d$ -dimensional, and $B = \partial K$ its…

math.MG2020

Rational Maps and Boundaries of Convex Hulls

Joseph Malkoun

If $C_{n} (R^{d})$ denotes the configuration space of $n$ distinct points in $R^{d}$ , we construct a sequence of maps $(f_{m}),$ $m \geq 1$ , where \[f_m: C_n(\mathbb{R}^d)…

math.MG2019

Towards the Atiyah-Sutcliffe conjectures for coplanar hyperbolic points

Joseph Malkoun

The Atiyah-Sutcliffe normalized determinant function $D$ is a smooth complex-valued function on $C_{n} (H^{3})$ , where $C_{n} (H^{3})$ denotes the configuration space of $n$ distinct points…

math.RT2019

Weights, Weyl-equivariant maps and a rank conjecture

Joseph Malkoun

In this note, given a pair $(g, λ)$ , where $g$ is a complex semisimple Lie algebra and $λ \in h^{*}$ is a dominant integral weight of $g$ ,…

math.MG2019

The Atiyah-Sutcliffe Determinant

Joseph Malkoun

We present a general formula for the Atiyah-Sutcliffe determinant function, which holds for any integer $n \geq 2$ , as a global factor times a sum of terms, with each term similar…

math.GR2019

Root Systems and the Atiyah-Sutcliffe Problem

Joseph Malkoun

In this short note, we show that the Atiyah-Sutcliffe conjectures for $n = 2 m$ , related to the unitary groups $U (2 m)$ , imply the author's analogous conjectures, which are associate…

math.CO2018

Determinants, Choices and Combinatorics

Joseph Malkoun

We prove a formula which generalizes both Onn's colorful determinantal formula, related to Rota's basis conjecture, and Svrtan's $n!$ formula, related to the Atiyah-Sutcliffe probl…

math.GR2016

Commutators and Cartan subalgebras in Lie algebras of compact semisimple Lie groups

Joseph Malkoun, Nazih Nahlus

First we give a new proof of Goto's theorem for Lie algebras of compact semisimple Lie groups using Coxeter transformations. Namely, every $x$ in $L = Lie (G)$ can be…

math.MG2015

Configuration spaces of points, symmetric groups and polynomials of several variables

Joseph Malkoun

Denoting by $C_{n} (X)$ the configuration space of $n$ distinct points in $X$ , with $X$ being either Euclidean $3$ -space $E^{3}$ or hyperbolic $3$ -space $H^{3}$ or $\mat…

math.MG2015

Constructions of $S U (2)$ and Weyl equivariant maps for all classical groups

Joseph Malkoun

If $G$ is a compact Lie group, $T$ a maximal torus in $G$ (with Lie algebras $g$ and $t$ respectively) and $W$ the corresponding Weyl group, then the Berry-Ro…

math.MG2015

On the Atiyah problem on hyperbolic configurations of four points

Joseph Malkoun

Given a configuration $x$ of $n$ distinct points in hyperbolic $3$ -space $H^{3}$ , Michael Atiyah associated $n$ polynomials $p_{1}, \dots, p_{n}$ of a variable $t \in \mathbb{C}P…

math.DG2014

An Ansatz for Hyperkähler $8$ -Manifolds with two Commuting Rotating Killing Fields

Joseph Malkoun

We consider a hyperkähler $8$ -manifold admitting either a $U (1) \times R$ , or a $U (1) \times U (1)$ action, where the first factor preserves $g$ and $I$ , and acts on $ω_2+i…

math.MG2014★ 2 cited

Configurations of Points and the Symplectic Berry-Robbins Problem

Joseph Malkoun

We present a new problem on configurations of points, which is a new version of a similar problem by Atiyah and Sutcliffe, except it is related to the Lie group $\operatorname{Sp}(…

Finite graphs and configurations of points

A new proof of Atiyah's conjecture on configurations of four points

Continuous Maps from Spheres Converging to Boundaries of Convex Hulls

Rational Maps and Boundaries of Convex Hulls

Towards the Atiyah-Sutcliffe conjectures for coplanar hyperbolic points

Weights, Weyl-equivariant maps and a rank conjecture

The Atiyah-Sutcliffe Determinant

Root Systems and the Atiyah-Sutcliffe Problem

Determinants, Choices and Combinatorics

Commutators and Cartan subalgebras in Lie algebras of compact semisimple Lie groups

Configuration spaces of points, symmetric groups and polynomials of several variables

Constructions of SU(2) and Weyl equivariant maps for all classical groups

On the Atiyah problem on hyperbolic configurations of four points

An Ansatz for Hyperkähler 8-Manifolds with two Commuting Rotating Killing Fields

Configurations of Points and the Symplectic Berry-Robbins Problem

Constructions of $S U (2)$ and Weyl equivariant maps for all classical groups

An Ansatz for Hyperkähler $8$ -Manifolds with two Commuting Rotating Killing Fields