Publications

Journal articles, refereed conference papers, books, and selected preprints. Continuously updated lists live on arXiv, Google Scholar, and dblp.

Publications per year

The wonderful geometry of the Vandermonde map
with J. Acevedo, G. Blekherman, and S. Debus
Foundations of Computational Mathematics 26, 2005–2051
doi arXiv pdf
Quadrature rules with few nodes supported on algebraic curves
with E. Teixeira Turatti
Journal of Complexity 96, 102067
doi arXiv pdf
Slices of stable polynomials and connections to the Grace–Walsh–Szegő theorem
with S. Debus and R. Schabert
Journal of Symbolic Computation 133, 102488
doi
Constructively describing orbit spaces of finite groups by few inequalities
with P. Moustrou and R. Schabert
Journal of Symbolic Computation 132, 102471
doi
#P-hardness proofs of matrix immanants evaluated on restricted matrices
with I. Miklós
Theoretical Computer Science 1062, 115660
doi
Symmetric and isotypic Hilbert series for symmetric ideals
with H. Breloer
preprint
arXiv pdf
Eigenvalues of locally positive semidefinite matrices: non-convexity and geometry
with J. Acevedo, G. Blekherman, S. Debus, and S. Lee
preprint
arXiv pdf
The Lie–Størmer Center
with H. Z. Munthe-Kaas
EMS Magazine 140, 37–39
doi
Deciding connectivity in symmetric semi-algebraic sets
with R. Schabert and T. X. Vu
Journal of Symbolic Computation 138
arXiv pdf
A semidefinite programming hierarchy for covering problems in discrete geometry
with J. Rolfes and F. Vallentin
Numerical Algebra, Control and Optimization 16, 157–170
doi arXiv pdf

Return of the plane evolute
with R. Piene and B. Shapiro
Annales de l’Institut Fourier 75, 1685–1751
doi arXiv pdf
Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs
with E. Hubert, T. Metzlaff, and P. Moustrou
Mathematical Programming 213, 517–573
doi
Symmetric SAGE and SONC forms, exactness and quantitative gaps
with P. Moustrou, T. Theobald, and H. Verdure
Journal of Symbolic Computation 127, 102374
doi
On nonnegative invariant quartics in type A
with S. Debus, C. Goel, and S. Kuhlmann
Journal of Symbolic Computation 128, 102393
doi
Symbolic computation with symmetric polynomials in real algebraic geometry
with T. X. Vu
survey chapter, preprint
arXiv pdf
Symmetric nonnegative functions, the tropical Vandermonde cell and superdominance of power sums
with J. Acevedo, G. Blekherman, and S. Debus
Collectanea Mathematica
doi arXiv pdf
Equivariant algebraic and semi-algebraic geometry of infinite affine space
with M. Kummer
Journal of Algebra 666, 28–46
doi arXiv pdf

Orbit spaces of Weyl groups acting on compact tori: a unified and explicit polynomial description
with E. Hubert and T. Metzlaff
SIAM Journal on Applied Algebra and Geometry 8, 612–649
doi
Connectivity in symmetric semi-algebraic sets
with R. Schabert and T. X. Vu
Proceedings of ISSAC 2024, 162–169
doi arXiv pdf
Linear slices of hyperbolic polynomials and positivity of symmetric polynomial functions
with R. Schabert
Journal of Pure and Applied Algebra 228, 107552
arXiv pdf

Reflection groups and cones of sums of squares
with S. Debus
Journal of Symbolic Computation 119, 112–144
doi
Faster real root decision algorithm for symmetric polynomials
with G. Labahn, M. Safey El Din, É. Schost, and T. X. Vu
Proceedings of ISSAC 2023, 452–460
doi arXiv pdf
The poset of Specht ideals for hyperoctahedral groups
with S. Debus, P. Moustrou, and H. Verdure
Algebraic Combinatorics 6, 615–634
arXiv pdf
Symmetries in polynomial optimization
with P. Moustrou and H. Verdure
in: Polynomial Optimization, Moments, and Applications, Springer
doi
Polynomial Optimization, Moments, and Applications
edited with M. Kočvara and B. Mourrain
Springer Optimization and Its Applications, vol. 206
doi
Attitudes towards mathematics, achievement, and drop-out intentions among STEM and non-STEM students in Norway
with G. Óturai and S. E. Martiny
International Journal of Educational Research Open 4, 100230
doi

Vandermonde varieties, mirrored spaces, and the cohomology of symmetric semi-algebraic sets
with S. Basu
Foundations of Computational Mathematics 22, 1395–1462
doi
Symmetry reduction in AM/GM-based optimization
with P. Moustrou, H. Naumann, T. Theobald, and H. Verdure
SIAM Journal on Optimization 32, 765–785
doi

Symmetric non-negative forms and sums of squares
with G. Blekherman
Discrete & Computational Geometry 65, 764–799
doi
Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations
with P. Moustrou and H. Verdure
Journal of Symbolic Computation 107, 106–121
doi

Generalized eigenvalue methods for Gaussian quadrature rules
with G. Blekherman, M. Kummer, M. Schweighofer, and C. Vinzant
Annales Henri Lebesgue 3, 1327–1341
doi
On the isotypic decomposition of cohomology modules of symmetric semi-algebraic sets: polynomial bounds on multiplicities
with S. Basu
International Mathematics Research Notices 2020, 2054–2113
doi

On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms
with S. Basu
Selecta Mathematica 24, 3241–3281
doi
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 dimensions
with M. Schweighofer
Journal of Complexity 45, 22–54
doi
Real root finding for equivariant semi-algebraic systems
with M. Safey El Din
Proceedings of ISSAC 2018
doi
Reflection groups, reflection arrangements, and invariant real varieties
with T. Friedl and R. Sanyal
Proceedings of the American Mathematical Society 146, 1031–1045
doi

Bounding the equivariant Betti numbers of symmetric semi-algebraic sets
with S. Basu
Advances in Mathematics 305, 803–855
doi
Efficient algorithms for computing the Euler–Poincaré characteristic of symmetric semi-algebraic sets
with S. Basu
in: Ordered Algebraic Structures and Related Topics, Contemporary Mathematics 697
doi
On irreducible components of real exponential hypersurfaces
with N. Vorobjov
Arnold Mathematical Journal 3, 423–443
doi

Bounds on the individual Betti numbers of complex varieties, stability and algorithms
with S. Basu
preprint
arXiv pdf
Deciding positivity of multisymmetric polynomials
with P. Görlach and T. Weißer
Journal of Symbolic Computation 74, 603–616
doi
Symmetric semi-algebraic sets and non-negativity of symmetric polynomials
Journal of Pure and Applied Algebra 220, 2809–2815
doi

Exploiting symmetries in SDP-relaxations for polynomial optimization
with T. Theobald, L. Jansson Andrén, and J. B. Lasserre
Mathematics of Operations Research 38, 122–141
doi

On the degree and half-degree principle for symmetric polynomials
Journal of Pure and Applied Algebra 216, 850–856
doi
A note on extrema of linear combinations of elementary symmetric functions
with A. Kovačec and S. Kuhlmann
Linear and Multilinear Algebra 60, 219–224
doi

Symmetries in semidefinite and polynomial optimization: relaxations, combinatorics, and the degree principle
PhD thesis, Goethe University Frankfurt

Positive Polynome und semidefinite Optimierung
with T. Theobald
Jahresbericht der DMV 110, 3–21

On extreme forms in dimension 8
Journal de théorie des nombres de Bordeaux 18, 677–682
doi