Post-Doctoral Research Visit F/M Multigraded elimination, resultants and discriminants

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.

We are seeking applications for a Postdoctoral Researcher position in the areas of applied algebraic geometry, elimination theory, and symbolic-numeric computation. This position offers an exciting opportunity to engage in cutting-edge research at the intersection of pure and applied mathematics, with potential applications in geometric modeling [BC21], in polynomial system solving [BFMT21,BCN22], or in arithmetic [BMT20, BN17].

References

[BC21] Laurent Busé and Marc Chardin. Fibers of rational maps and elimination matrices: an application oriented approach. Commutative Algebra - Expository papers dedicated to David Eisenbud on the occasion of his 75th birthday, Springer, p. 189–217, 2021.

[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.

Application: Interested candidates should submit the following two documents:

- A curriculum vitae (CV) including a list of publications.
- A cover letter explaining their research background and interest in the position.

Review of applications will begin immediately and continue until the position is filled.
Inria Centre at Universtié Côte d'Azur offers a dynamic research environment with opportunities for collaboration and growth, and we encourage applications from candidates in the full spectrum of algebraic geometry and symbolic computation.

Polynomial systems, equivalently algebraic subvarieties, in a projective space have been extensively studied and there exist many tools to capture their geometry such as minimal 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.

The successful candidate, depending on his/her background and interests, will work on topics related to the study of algebro-geometric properties of elimination ideals (e.g. equations of Rees algebra, estimation of Castenuovo-Mumfprd regularity, etc), to the extension of the theory of mutli-projective resultants and discriminants, with an eye on algorithmic aspects that bridge symbolic and numerical approaches as well as their software implementation.

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.

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

- Experience in applying algebraic geometry and its computational aspects, with a view in numerical computations.
- 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++.

• 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
• Contribution to mutual insurance (subject to conditions)

Gross Salary : 2788 € per month