Post-doctoral Research Visit F/m Multigraded

Le descriptif de l’offre ci-dessous est en Anglais_

**Type de contrat **:CDD

**Niveau de diplôme exigé **:Thèse ou équivalent

**Fonction **:Post-Doctorant

**A propos du centre ou de la direction fonctionnelle**:
The Inria center at Université Côte d'Azur includes 42 research teams and 9 support services. The center’s staff (about 500 people) is made up of scientists of different nationalities, engineers, technicians and administrative staff. The teams are mainly located on the university campuses of Sophia Antipolis and Nice as well as Montpellier, in close collaboration with research and higher education laboratories and establishments (Université Côte d'Azur, CNRS, INRAE, INSERM...), but also with the regional economic players.

With a presence in the fields of computational neuroscience and biology, data science and modeling, software engineering and certification, as well as collaborative robotics, the Inria Centre at Université Côte d'Azur is a major player in terms of scientific excellence through its results and collaborations at both European and international levels.

**Contexte et atouts du poste**:
**References**

[BCN22] Laurent Busé, Marc Chardin and Navid Nemati. Multigraded Sylvester forms, duality and elimination matrices. Journal of Algebra, 609(1):514-546, 2022

[BFMT21] Matías R Bender, Jean-Charles Faugère, Angelos Mantzaflaris, Elias Tsigaridas. Koszul-type determinantal formulas for families of mixed multilinear systems. SIAM Journal on Applied Algebra and Geometry, 5(4):589-619, 2021

[BMT20] Laurent Busé, Angelos Mantzaflaris and Elias Tsigaridas. Matrix formulae for resultants and discriminants of bivariate tensor-product polynomials. Journal of Symbolic Computation, 98:65-83, 2020

[BN17] Laurent Busé and Ibrahim Nonkané. Discriminants of complete intersection space curves. ACM proceedings of ISSAC, p. 69-76, 2017.

**Position**: One-year post-doctoral position in the research team Aromath.

**Location**: Inria Centre at Université Côte d'Azur.

**Starting date**: flexible, but before end of May 2025.

**Contact**: Laurent Busé and Angelos Mantzaflaris.
- A curriculum vitae (CV) including a list of publications.
- A cover letter explaining their research background and interest in the position.

**Mission confiée**:
Polynomial systems, equivalently algebraic subvarieties, in a projective space have been extensively studied and there exist many tools to capture their geometry such as mínimal free resolutions, syzygies or elimination ideals and matrices. When the ambient space is a product of projective spaces the study of polynomial systems is more delicate. Nevertheless, multi-projective polynomial systems appear in many situations and are of interest for both applied and theoretical purposes. Their study is a very active research area and this research program falls in this context.

**Principales activités**:
**Responsibilities**
- Conduct high-quality research in applied algebraic geometry, elimination theory, and symbolic-numeric computation.
- Develop and analyze new algorithms for solving algebraic systems using a mix of symbolic and numerical methods.
- Collaborate with other members of Inria and participate in interdisciplinary projects.
- Prepare research papers and present results at conferences and workshops.

**Compétences**:
**Qualifications**
- A Ph.D. in Mathematics, Computer Science, or a closely related field, with a strong focus on Algebraic Geometry, Computational Algebra, or Symbolic-Numeric Computation.
- Solid knowledge of elimination theory and experience with symbolic and numerical methods for solving algebraic systems.
- Proficiency in programming and familiarity with some computational algebra software (e.g., Macaulay2, Singular, Maple, or MATLAB), experience with C++ is a plus.
- Strong analytical skills and a track record of high-quality research publications. Excellent communication and teamwork skills.

**Desirable Skills**
- Knowledge of modern algorithms in algebraic elimination, such as Gröbner bases or resultants.
- Experience working with hybrid symbolic-numeric methods, numerical algebraic geometry and software development in C++.

**Avantages**:

- Subsidized meals
- Partial reimbursement of public transport costs
- Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
- Possibility of teleworking and flexible organization of working hours
- Professional equipment available (videoconferencing, loan of computer equipment, etc.)
- Social, cultural and sports events and activities
- Access to vocational training

**Rémunération**:
Gross Salary : 2788 € per month

**Informations générales**:

- **Thème/Domaine**: Algorithmique, calcul formel et cryptologie
Calcul Scientifique (BAP E)
- **Ville**: Sophia Antipolis
- **Centre Inria**: Centre Inria d'Université Côte d'Azur
- **Date de prise de fo