Post-Doctoral Research Visit F - M Topological Combinatorics And Intersection Patterns H/F - INRIA

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Inria est l'institut national de recherche dédié aux sciences et technologies du numérique. Il emploie 2600 personnes. Ses 215 équipes-projets agiles, en général communes avec des partenaires académiques, impliquent plus de 3900 scientifiques pour relever les défis du numérique, souvent à l'interface d'autres disciplines. L'institut fait appel à de nombreux talents dans plus d'une quarantaine de métiers différents. 900 personnels d'appui à la recherche et à l'innovation contribuent à faire émerger et grandir des projets scientifiques ou entrepreneuriaux qui impactent le monde. Inria travaille avec de nombreuses entreprises et a accompagné la création de plus de 200 start-up. L'institut s'eorce ainsi de répondre aux enjeux de la transformation numérique de la science, de la société et de l'économie.
Post-Doctoral Research Visit F/M Topological combinatorics and intersection patterns
Le descriptif de l'offre ci-dessous est en Anglais
Type de contrat : CDD

Niveau de diplôme exigé : Thèse ou équivalent

Fonction : Post-Doctorant

Niveau d'expérience souhaité : Jusqu'à 3 ans

Contexte et atouts du poste

Every year Inria International Relations Department has a few postdoctoral positions in order to support Inria international collaborations.

The postdoctoral contract will have a duration of 12 to 24 months. The default start date is November 1st, 2026 and not later than January, 1st 2027. The postdoctoral fellow will be recruited by one of the in France but it is recommended that the time is shared between France and the partner's country (please note that the postdoctoral fellow has to start his/her contract being in France and that the visits have to respect Inria rules for missions)

Mission confiée

Candidates for postdoctoral positions are recruited after the completion of their Ph.D. or a first postdoctoral period. To be eligible, candidates must have defended their Ph.D. no more than 3 years before the start date of the contract. As the start date will be between November 1, 2026 and January 1, 2027, the latest eligible Ph.D. defense date will vary accordingly (approximately between November 1, 2023 and January 1, 2024).

In order to encourage mobility, the postdoctoral position must take place in a scientific environment that is truly different from the one of the Ph.D. (and, if applicable, from the position held since the Ph.D.); particular attention is thus paid to French or international candidates who obtained their doctorate abroad.

Principales activités

The postdoc would join the associate team DIPPS, which works in discrete and computational geometry, more precisely on Discrete models for Intersection Patterns and Point Sets. This project tackles two established topics of discrete and computational geometry: convexity spaces and order types.

The candidate will develop research in the above directions. Here we give some examples of problems that can be investigated but this list is not exhaustive.

- Topological combinatorics. Waist theorems give lower bounds on the minimum «size» of the largest fiber in certain projections. The model statement, proven by Almgren in the 1960's, is about continuous maps from Sd to Rk (the min-max fiber has volume at least that of a (d-k)-dimensional equator), but analogous statements can be found in combinatorial settings. For instance, a theorem of Kalai and Meshulam asserts that if f:X Y is a simplicial map between simplicial complexes such that f preserves dimensions and such that every fiber has contractible connected components, then there exists a fiber with at least (L(Y)+1)/(L(X)+1) cc, where L() is the «Leray number». It would be interesting to extend this theorem to simplicial maps whose fibers have (limited) 1-dimensional homology.
- Nerve complexes and their f-vectors. Let r>0 be some integer and consider a finite family F of convex sets in Rd where no r have a point in common. The maximum proportion of (d+1)-tuples of F that intersect is given by the fractional Helly theorem. It would be interesting to understand the maximum proportion of k-tuples of F that intersect for k > d+1 (still under the condition that no r members of F intersect). This question is related to some recent property testing algorithms in LP-type problems.
- Helly-type theorems and geometric transversals. Generalizing the notion of nerve complexes and their f-vectors, we may consider the k-th nerve complex Nk of a family of convex sets in Rd, consisting of those subfamilies that can be pierced by a k-dimensional affine flat. (The case k = 0 corresponds to the usual nerve complex.) A fundamental problem of geometric transversal theory is to understand nontrivial dependencies between the f-vector of Nk and the f-vector of Nk' for 0 k

Compétences

We are seeking candidates in the fields of mathematics (discrete geometry or probabilistic/extremal combinatorics) or computer science (computational geometry/topology) with an interest in discrete geometric structures.

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 (after 6 months of employment) 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
- Social security coverage

Rémunération

From 2788 € gross/month