Project description DEENESFRITPL New study on the homology and homotopy of Lie groups Spaces of commuting elements in Lie groups play an important role in geometry and mathematical physics. However, until recently, there has not been much emphasis on their systematic study. Important open questions in the field concern their homology as well as the (stable) homotopy. The EU-funded HOTHSPOH project will attempt to prove a conjectural stable splitting theorem, which would establish a special relationship between spaces of commuting elements and commuting varieties in Lie algebras. Another part of research will be geared towards investigating homology stability for spaces of commuting elements in the unitary and orthogonal group. Project results will increase knowledge of the homology stability and the homotopy theory of Lie group actions. Show the project objective Hide the project objective Objective In this project we propose to study homotopy theoretic properties of spaces of commuting elements in compact Lie groups. These spaces play an essential role in mathematical physics and geometry, but only in the last decade a systematic study by homotopy theoretic methods has been initiated. Important open questions in the field concern the homology as well as the (stable) homotopy type. In the first part of the project, we attempt to prove a conjectural stable splitting theorem, which would establish an intriguing relationship between spaces of commuting elements and commuting varieties in Lie algebras, an object of classical interest in algebraic geometry. In the second part, we propose to investigate the phenomenon of homology stability for spaces of commuting elements in the unitary and orthogonal groups. Building on recent work of the experienced researcher, an approach to calculate the stable homology is presented. This is expected to uncover a wealth of previously unknown homology groups of these interesting spaces.The research conducted to achieve the project goals, together with the training in teaching and management received during the fellowship, will have a major positive impact on the career development of the experienced researcher. On the research level, this impact is through the acquisition of knowledge in new research areas, in particular in homology stability and the homotopy theory of Lie group actions.The project will be carried out in an exceptionally active and successful scientific community at the University of Copenhagen, supervised by a world expert in the homotopy theory of Lie groups. Completion of the project will serve as a springboard to build new collaborations and to enter further advanced projects in a range of areas. It is thus a perfect preparation for a high-level research career in mathematics. Fields of science natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry 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-2018 - Individual Fellowships Call for proposal H2020-MSCA-IF-2018 See other projects for this call Funding Scheme MSCA-IF-EF-ST - Standard EF Coordinator KOBENHAVNS UNIVERSITET Net EU contribution € 207 312,00 Address Norregade 10 1165 Kobenhavn Denmark See on map Region Danmark Hovedstaden Byen København Activity type Higher or Secondary Education Establishments 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
