J. Malkoun

activity

20162020

collaborators

7 papers

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…