My research work concerns the study of singularities in real algebraic geometry. In particular, I am interested in the real algebraic sets equipped with the action of a real algebraic group, their invariants and, to some extent, their classifications.
Below, you will find the list of my publications :
- Distance to a constitutive tensor isotropy stratum by the Lasserre polynomial optimization method, with Perla Azzi, Rodrigue Desmorat, Boris Kolev, Mathematics and Mechanics of Complex Systems, 11 (3), 2023, 393-428 (https://doi.org/10.2140/memocs.2023.11.393).
- The distance to cubic symmetry class as a polynomial optimization problem, with Perla Azzi, Rodrigue Desmorat, Boris Kolev, Journal of Elasticity, 156 , 2024, 157-191 (https://doi.org/10.1007/s10659-023-10041-w).
- Quotients and invariants of AS-sets equipped with a finite group action, Mathematische Annalen, 377 , 2020, 1015-1055 (https://doi.org/10.1007/s00208-020-01994-7).
- Products of real equivariant weight filtrations, manuscripta mathematica, 164 , 2021, 151-192 (https://doi.org/10.1007/s00229-020-01178-2).
- On the equivariant blow-Nash classification of simple invariant Nash germs, Bulletin de la Société Mathématique de France, 148 (2), 2020, 329-382 (https://doi.org/10.24033/bsmf.2808).
- Equivariant zeta functions for invariant Nash germs, Nagoya Mathematical Journal, 222 (1), 2016, 100-136 (https://doi.org/10.1017/nmj.2016.12).
- Cohomology and products of real weight filtrations, with Thierry Limoges, Annales de l'Institut Fourier, 65 (5), 2015, 2235-2271 (https://doi.org/10.5802/aif.2987).
- Equivariant weight filtration for real algebraic varieties with action, Journal of the Mathematical Society of Japan, 68 (4), 2016, 1789-1818 (https://doi.org/10.2969/jmsj/06841789).
- Complexe de poids des variétés algébriques réelles avec action, Mathematische Zeitschrift, 277, 2014, 63-80 (https://doi.org/10.1007/s00209-013-1244-8).
Here is also a link to the manuscript (written in French) of my PhD thesis, defended at the University of Rennes 1 and advised by Goulwen Fichou :