55 citations · 206 across the 33 of their papers we have counts for
35 papers
A Direct Polynomial Approach to Spectral Decomposition
Simon Bossoney, Marc Troyanov
We give a direct construction of the spectral projectors of a complex square matrix, based on explicit interpolation polynomials previously introduced. This yields a spectral resol…
A Direct Approach to Hermite Interpolation
Simon Bossoney, Marc Troyanov
We introduce a family of polynomials satisfying the natural duality relations for Hermite interpolation, analogous to the classical Lagrange interpolation polynomials. They yield a…
The Isoperimetric Problem in Regular Trees
Marc Troyanov
We investigate the inner vertex-isoperimetric problem on the -regular tree . We first determine the exact value of the inner vertex-isoperimetric profile $I_d(k) = \min\{ |…
The Choreography of Geodesics in SOL
Marc Troyanov
We provide a self-contained geometric description of the geodesic flow in the three-dimensional Lie group , one of Thurston's eight model geometries. The geometry of…
Double Forms, Curvature Integrals and the Gauss-Bonnet Formula
Marc Troyanov
The Gauss-Bonnet Formula is a significant achievement in 19th century differential geometry for the case of surfaces and the 20th century cumulative work of H. Hopf, W. Fenchel, C.…
Isoperimetry in Finitely Generated Groups
Bruno Luiz Santos Correia, Marc Troyanov
We revisit the isoperimetric inequalities for finitely generated groups introduced and studied by N. Varopoulos, T. Coulhon and L. Saloff-Coste. Namely we show that a lower bound o…