Institut Élie Cartan de Lorraine

Quantum roots for Kac–Moody root systems and finiteness properties of the Kac–Moody affinized Bruhat order

The notion of quantum root comes up in the study of the quantum cohomology of generalized flag varieties, quantum Bruhat graphs or in the study of the affinized Bruhat order on an affinized Weyl semi-group. In this paper, we provide a complete classification of quantum roots asso...

Boundary regularity for the polyharmonic Dirichlet problem

In this paper we prove that any solution of the m -polyharmonic Poisson equation in a Reifenberg-flat domain with homogeneous Dirichlet boundary condition, is 𝒞 m - 1 , α regular up to the boundary. To achieve this result we extend the Nirenberg method of translations to operator...

Renormalization of a 1d quadratic Schrödinger model with additive noise

The study is devoted to the interpretation and well-posedness of the stochastic NLS model (ı∂t−Δ)u=|u|2+B˙,u0=0,t∈R,x∈T, where B˙ stands for a space-time fractional noise with index H=(H0,H1) in a subset of (0,1)2. We first establish that in the situation where 0<2H0+H1≤2, the eq...