# Publications

## Submitted articles:

- with Saugata Basu

On the equivariant Betti numbers of symmetric semi-algebraic sets: vanishing, bounds and algorithms - with Saugata Basu

Bounds on the individual Betti numbers of complex varieties, stability and algorithms - 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 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

to appear in Journal of Complexity (2017) - with Tobias Friedl and Raman
Sanyal

Reflection groups, arrangements, and invariant real varieties

to appear in Proceedings of the American Mathematical Society (2017) - with Nicolai Vorobjov

On irreducible components of real exponential hypersurfaces

Arnold Mathematical Journal**3**(3), pp. 423-443 (2017) - with Saugata Basu

Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets

*Ordered Algebraic Structures and Related Topics,**Contemporary Mathematics***697**, pp. 53 --81

- 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 110/2***110**, 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 and Google Scholar for more details*

*Thesis:*

*Symmetries in Semidefinite and Polynomial Optimization*

*Dissertation an der Johann Wolfgang Goethe-Universität (2011)*(pdf)