## Section: New Results

### Symmetry Preserving Interpolation

Participants : Erick David Rodriguez Bazan, Evelyne Hubert.

In [22], we address multivariate interpolation in the presence of symmetry. Interpolation is a prime tool in algebraic computation while symmetry is a qualitative feature that can be more relevant to a mathematical model than the numerical accuracy of the parameters. The article shows how to exactly preserve symmetry in multivariate interpolation while exploiting it to alleviate the computational cost. We revisit minimal degree and least interpolation with symmetry adapted bases, rather than monomial bases.This allows to construct bases of invariant interpolation spaces in blocks, capturing the inherent redundancy in the computations.We show that the so constructed symmetry adapted interpolation bases alleviate the computational cost of any interpolation problem and automatically preserve any equivariance of their interpolation problem might have.