The following lists the publications that are part of the research project. You can find more interesting research results on the individual web pages of the project members.

# 2020

- Generalized eigenvalue methods for Gaussian quadrature rules

G Blekherman, M Kummer, C Riener, M Schweighofer, C Vinzant,*Annales Henri Lebesgue* - Symmetric ideals, Specht polynomials, and solutions to symmetric systems of equations

P. Moustrou, C. Riener, H. Verdure (under submission)

# 2019

- Vandermonde varieties, mirrored spaces, and the cohomology of symmetric semi-algebraic sets

S. Basu, C. Riener (Revision) - Symmetric nonnegative forms and sums of squares

*G. Blekherman, C. Riener, Discrete & Computational Geometry*

# 2018

- Optimization approaches to quadrature

C. Riener, M. Schweighofer,*Journal of Complexity* - Reflection groups, reflection arrangements, and invariant real varieties

T. Friedl, C. Riener, S. Sanyal,*Proceedings of AMS* - On the isotypic decomposition of cohomology modules of symmetric semi-algebraic sets: polynomial bounds on multiplicities

S. Basu, C. Riener,*International Mathematics Research Notices* - On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms

S. Basu, C. Riener,*Selecta Mathematica*