Objective Isoparametric hypersurfaces are intriguing geometric objects whose study has revealed connections with several areas of mathematics and mathematical physics, and which have typically been investigated with differential geometric, algebraic or topological techniques.The aim of this proposal is to develop an innovative approach to isoparametric hypersurfaces by combining already established tools with methods from geometric analysis and partial differential equations. Specifically, we intend to investigate the existence of isoparametric hypersurfaces in general Riemannian manifolds, the role of these objects in overdetermined problems of elliptic partial differential equations, and the isoparametricity of compact hypersurfaces with constant mean curvature in noncompact symmetric spaces.In order to develop this proposal, the Experienced Researcher will join the Geometric Analysis team at ICMAT, in Madrid, under the supervision of one of its main researchers, Alberto Enciso. The host group has extensive experience in the study of the geometric properties of solutions to differential equations, and their main researchers have recently developed powerful methods to address outstanding problems in fluid mechanics and geometric analysis. The scientific training strategy of this proposal consists in the assimilation of these techniques. On the other hand, the Researcher is experienced in the classical theory of isoparametric hypersurfaces, as evidenced by his contributions to the field. It is the combination of both backgrounds what is needed to develop this proposal.Finally, this MSC fellowship would boost the convergence of distinct research fields and collaborative networks, produce a synergy with the ERC Starting Grant hold by the Supervisor, diversify the fellow’s mathematical knowledge, and consolidate him as an independent researcher. Fields of science natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Keywords Isoparametric hypersurfaces constant mean curvature overdetermined boundary value problems Riemannian submanifolds symmetric spaces Programme(s) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Topic(s) MSCA-IF-2016 - Individual Fellowships Call for proposal H2020-MSCA-IF-2016 See other projects for this call Funding Scheme MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF) Coordinator AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS Net EU contribution € 158 121,60 Address Calle serrano 117 28006 Madrid Spain See on map Region Comunidad de Madrid Comunidad de Madrid Madrid Activity type Research Organisations Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
