Submitted articles:

  1. with Greg Blekherman
    Symmetric Nonnegative Forms and Sums of Squares

    Published articles:

    1. 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)
    2. with Saugata Basu
      On the equivariant Betti numbers of symmetric semi-algebraic sets: vanishing, bounds and algorithms
      Selecta Mathematica (to appear)
    3. 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)
    4. 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)
    5. with Nicolai Vorobjov
      On irreducible components of real exponential hypersurfaces
      Arnold Mathematical Journal 3 (3), pp. 423-443 (2017)
    6. 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)
    7. with Saugata Basu
      Bounding the equivariant Betti numbers of symmetric semi-algebraic sets ( video )
      Advances in Mathematics 305, pp. 803-855 (2017)
    8. Symmetric semi-algebraic sets and non-negativity of symmetric polynomials polynomials
      Journal of Pure and Applied Algebra 220 No. 4, 2809-2815 (2016)
    9. with Paul Goerlach and Tillmann Weisser
      Deciding positivity of multisymmetric polynomials
      Journal of Symbolic Computation 74, pp. 603-616 (2016)
    10. 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)
    11. 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)
    12. On the degree and half degree principle for symmetric polynomials
      Journal of Pure and Applied Algebra 216 No. 4, 850-856 (2012)
    13. with Thorsten Theobald
      Positive Polynome und semidefinite Optimierung
      Jber. DMV 110/2110, No. 2, 57-74 (2008)
    14. 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)