진학프로석·박사 채용 접수 플랫폼

The research activity will be part of the project funded by ERC Starting Grant 101165368 MAGNETIC "Minimal submanifolds in Arbitrary Geometries as Nodal sEts: Towards hIgher Codimension". The project will then revolve around questions of variational flavor in the context of geometric measure theory, calculus of variations, elliptic partial differential equations, and geometric analysis in general. 

Specifically, the project will focus on the construction and regularity of minimal submanifolds in codimension higher than one, through the calculus of variations for approximations of the area functional, obtaining critical points which are either parametrized or limiting nodal sets of critical points of energies inspired by physical models. The project will also investigate relationships between minimal submanifolds and curvature, their construction in non-smooth spaces, and other related questions in geometric analysis.

The candidate is expected to publish research papers, to contribute their own research activity to the project and to collaborate with the scientific director of the project. In particular, they will contribute to the study of stable critical points and gradient flow for the abelian Yang-Mills-Higgs model, which approximates the area functional in codimension two (see projects and methodologies detailed in section 2 of form B2). Alternatively, they will contribute to the investigation of functionals approximating the area functional in codimension greater than two (see projects and methodologies detailed in section 3 of form B2). Moreover, the candidate is expected to present their research work in conferences and seminars, to attend the department research seminars on a regular basis and to collaborate with the scientific director of the project in the organization initiatives.