Cordian Riener

Schwerpunkt Reelle Geometrie und Algebra > Dr. Cordian Riener

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Preprints:

with Saugata Basu
On the equivariant Betti numbers of symmetric semi-algebraic sets: vanishing, bounds and algorithms
with Nicolai Vorobjov
On irreducible components of real exponential hypersurfaces
with Saugata Basu
Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets
with Markus Schweighofer
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 dimension
with Saugata Basu
Bounds on the individual Betti numbers of complex varieties, stability and algorithms
with Tobias Friedl and Raman Sanyal
Reflection groups, arrangements, and invariant real varieties
with Saugata Basu
On the isotypic decomposition of homology modules of symmetric semi-algebraic sets: polynomial bounds on multiplicities ( video )
with Greg Blekherman
Symmetric Nonnegative Forms and Sums of Squares

Published articles:

with Saugata Basu
Bounding the equivariant Betti numbers of symmetric semi-algebraic sets ( video )
Advances in Mathematics 305 , pp. 803-855 (2017)
Symmetric semi-algebraic sets and non-negativity of symmetric polynomials polynomials
Journal of Pure and Applied Algebra 220 No. 4, 2809-2815 (2016)
with Paul Goerlach and Tillmann Weisser
Deciding positivity of multisymmetric polynomials
Journal of Symbolic Computation 74, pp. 603-616 (2016)
with Thorsten Theobald, Lina Jansson Andrén, and Jean Bernard Lasserre
Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization
Mathematics of Operations Research 38(1), 122-141 (2013)

with Alexander Kovacec, and Salma Kuhlmann
A Note on Extrema of Linear Combinations of Elementary Symmetric Functions
Linear and Multilinear Algebra 60 No. 2, 219-224 (2012)

On the degree and half degree principle for symmetric polynomials
Journal of Pure and Applied Algebra 216 No. 4, 850-856 (2012)
with Thorsten Theobald
Positive Polynome und semidefinite Optimierung
Jber. DMV 110/2110, No. 2, 57-74 (2008)

On extreme forms in dimension 8
Journal de theorie des nombres Bordeaux, 18 No. 3, 677-682 (2006).

See also: MathSciNet

Thesis:

Symmetries in Semidefinite and Polynomial Optimization
Dissertation an der Johann Wolfgang Goethe-Universität (2011) (pdf)