82 citations · 169 across the 34 of their papers we have counts for
6 papers · 1 filter
On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms
Saugata Basu, Cordian Riener
Let be a real closed field. We prove that for any fixed , the equivariant rational cohomology groups of closed symmetric semi-algebraic subsets of de…
On irreducible components of real exponential hypersurfaces
Cordian Riener, Nicolai Vorobjov
Fix any algebraic extension of the field of rationals. In this article we study exponential sets . Such sets are described by the vani…
Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets
Saugata Basu, Cordian Riener
Let be a real closed field and an ordered domain. We consider the algorithmic problem of computing the generalized Euler-Poincaré chara…
Bounds on the individual Betti numbers of complex varieties, stability and algorithms
Saugata Basu, Cordian Riener
We prove graded bounds on the individual Betti numbers of affine and projective complex varieties. In particular, we give for each , explicit bounds on the -th Betti numb…
Optimization approaches to quadrature: new characterizations of Gaussian quadrature on the line and quadrature with few nodes on plane algebraic curves, on the plane and in higher dimensions
Cordian Riener, Markus Schweighofer
Let and be positive integers. Let be a positive Borel measure on possessing finite moments up to degree . If the support of is contained in an…
Reflection groups, reflection arrangements, and invariant real varieties
Tobias Friedl, Cordian Riener, Raman Sanyal
Let be a nonempty real variety that is invariant under the action of a reflection group . We conjecture that if is defined in terms of the first basic invariants of…