Submitted articles:

  1. with Saugata Basu
    Vandermonde varieties, mirror spaces, and the cohomology of symmetric semi-algebraic sets

    Published articles:

    1. with Greg Blekherman, Mario Kummer, Markus Schweighofer, Cynthia Vinzant
      Generalized eigenvalue methods for Gaussian quadrature rules
      Annales Henri Lebesgue (to appear)
    2. with Greg Blekherman
      Symmetric Nonnegative Forms and Sums of Squares
      Discrete & Computational Geometry (to appear)
    3. 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)
    4. with Saugata Basu
      On the equivariant Betti numbers of symmetric semi-algebraic sets: vanishing, bounds and algorithms
      Sel. Math. New Ser. 24pp. 3241-3282 (2018)
    5. with Mohab Safey El Din
      Real Root Finding for Equivariant Semi-Algebraic Systems
      ISSAC 2018, pp. 335-342 (2018)
    6. 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)
    7. 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)
    8. with Nicolai Vorobjov
      On irreducible components of real exponential hypersurfaces
      Arnold Mathematical Journal 3 (3), pp. 423-443 (2017)
    9. 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 (2017)
    10. with Saugata Basu
      Bounding the equivariant Betti numbers of symmetric semi-algebraic sets ( video )
      Advances in Mathematics 305, pp. 803-855 (2017)
    11. Symmetric semi-algebraic sets and non-negativity of symmetric polynomials polynomials
      Journal of Pure and Applied Algebra 220 No. 4, 2809-2815 (2016)
    12. with Paul Goerlach and Tillmann Weisser
      Deciding positivity of multisymmetric polynomials
      Journal of Symbolic Computation 74, pp. 603-616 (2016)
    13. 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)
    14. with Alexander Kovacec, and Salma Kuhlmann
      A Note on Extrema of Linear Combinations of Elementary Symmetric Functions
      Linear and Multilinear Algebra 60 No. 2, 219-224 (2012)
    15. On the degree and half degree principle for symmetric polynomials
      Journal of Pure and Applied Algebra 216 No. 4, 850-856 (2012)
    16. with Thorsten Theobald
      Positive Polynome und semidefinite Optimierung
      Jber. DMV 110/2110, No. 2, 57-74 (2008)
    17. 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


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