Multivariate approximation theory
with: Marco Vianello, Len Bos, Alvise Somariva, Ludovico Bruni Bruno, Stefano De Marchi, Akil Narayan
polynomial sampling inequalities (admissible meshes)
polynomial differential forms and sampling by currents
asymptotics of multivariate orthogonal polynomials
least squares fitting and optimal designs
polynomial quadrature and measure compression
polynomial optimization
Pluripotential Theory
with: Norm Levenberg, Len Bos, Tom Bloom, Frank Wielonsky, Sione Ma'u, Turgay Bayraktar
pluripotential theory on irreducible algebraic varieties
Bernstein Markov property
pluripotential theory w.r.t. a convex polytope (generalizing the Lelong class)
numerical approximation of extremal functions and equilibrium measures
L^1 optimal transport: energy formulation
L^1 optimal transport numerical approximation by FEM
Branched optimal transport: energy formulation and numerical approximation
Linear elliptic PDEs in bounded and unbounded domains
Linear parabolic PDEs for etherogeneous media
Parametric linear elliptic and parabolic problems in mild dimension: model order reduction by polynomial approximation