The Mathematics department at the University of Luxembourg currently has openings for up to 8 PhD positions in the following areas: - Modelling and computational experiments in geometry, - Algebraic geometry, representations and logic. All positions are fully funded for up to 4 years. Candidates should have (at the beginning of the contract but not necessarily at the time of application) a Master's degree in Mathematics or in mathematical aspects of Computer science, with excellent results. Possible start in the fall or winter 2024, the remaining positions will be advertised in the spring 2025 for a start in or around September 2025. PhD candidates have access to funding for travel to workshops, conferences or summer/winter schools. They will be intergrated into the "Doctoral Training Unit Geometry, Representations, and Algebra via Computation and Experimentation", which profits from generous funding by FNR. They are also expected to contribute in a limited way to the teaching and outreach activities of the department (typically approximately 45 hours of teaching/year). The following topics are indications of possible research directions. - Post-quantum cryptography and fully-homomorphic encryption (Jean-Sébastien Coron): construction and analysis of fully-homomorphic encryption schemes based on lattice problems. - Abelian varieties and their applications to cryptography (Antonella Perucca): explicit and algorithmic study of elliptic curves and, more generally, abelian varieties, defined over number fields and finite fields. - Exploration of modular forms and Galois representations (Gabor Wiese): computational and theoretical methods in number theory with possible focus on Galois representations, modular forms, number fields and potential relations to cryptography. - Local and global symmetries of geometric manifolds through computation and experimentation (Karin Melnick): group actions on manifolds, including conformal transformations of Lorentzian or other pseudo-Riemannian manifolds, as well as parabolic geometries with locally submaximal symmetry. - Computational experiments with 3-dimensional hyperbolic volume (Jean-Marc Schlenker): exploring conjectural statements on the renormalized volume of hyperbolic 3-manifolds. - Representation-theoretic methods in algebraic geometry (Pieter Belmans): algebraic geometry and representation theory. - Explicit calculations of elliptic cohomology for toric varieties and beyond (Sarah Scherotzke): on the elliptic cohomology and elliptic genus of toric varieties. - Expressivity of modal languages for spatial model checking (Bruno Teheux): connections between topology, geometry and logic. How to apply...Applications should be submitted online and include:
Early application is highly encouraged, as the applications will be processed upon reception. For full consideration, please apply by July 31, 2024. Please apply ONLINE formally through the HR system. Applications by email will not be considered. The University of Luxembourg embraces inclusion and diversity as key values. We are fully committed to removing any discriminatory barrier related to gender, and not only, in recruitment and career progression of our staff. General information:
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