# Publications

## Submitted articles:

- with Saugata Basu

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

- with Greg
Blekherman, Mario Kummer, Markus Schweighofer, Cynthia Vinzant

Generalized eigenvalue methods for Gaussian quadrature rules - with Greg
Blekherman

Symmetric Nonnegative Forms and Sums of Squares

*Published articles:*

- with Saugata Basu

On the isotypic decomposition of homology modules of symmetric semi-algebraic sets: polynomial bounds on multiplicities ( video )

International Mathematical Research Notices (to appear) - with Saugata Basu

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

Sel. Math. New Ser.**24**pp. 3241-3282 (2018) - with Mohab Safey El Din

Real Root Finding for Equivariant Semi-Algebraic Systems

ISSAC**2018**, pp. 335-342 (2018) - 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

Journal of Complexity**45**, pp. 22-54 (2018) - with Tobias Friedl and Raman
Sanyal

Reflection groups, arrangements, and invariant real varieties

Proceedings of the American Mathematical Society**146**(3), pp. 1031-1045 (2018) - 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)