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Priority Programme 1786: Homotopy Theory and Algebraic Geometry
Termin:
05.12.2017
Fördergeber:
Deutsche Forschungsgemeinschaft (DFG)
In March 2014, the Senate of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) had established the Priority Programme Homotopy Theory and Algebraic Geometry, SPP 1786. The programme is designed to run for six years. The DFG invites with this call proposals for the second (and last) three-year funding period.
Ideas from algebraic geometry have influenced modern homotopy theory, for example, the use of the moduli stack of elliptic curves in the construction the topological modular forms spectrum. In the other direction, the introduction of motivic homotopy theory has enabled the application of methods and constructions from homotopy theory to problems in algebraic geometry. The slice spectral sequence was invented in motivic homotopy theory, but its counterpart in equivariant stable homotopy theory was a key ingredient in the solution of the Kervaire invariant one problem. The motivic Adams and Adams-Novikov spectral sequences have been used to extend computations of the classical stable homotopy groups of spheres, while comparison methods from classical stable homotopy theory have been adapted to compute the first few stable motivic stems. The central purpose of this programme is to advance research at the nexus between homotopy theory and algebraic geometry, with the goal of furthering the cross-fertilisation between these areas. We expect the individual research projects to contribute to at least one of the following research areas.
Motivic homotopy theory
Derived algebraic geometry
Differential homotopy theory and motivic aspects of classical homotopy theory
Equivariant homotopy theory
For further information please contact the Priority Programme's coordinator:
Prof. Dr. Marc Levine, phone +49 201 183-3114, marc.levine@uni-due.de
For administrative and formal inquiries please contact:
Dr. Carsten Balleier, DFG, phone: +49 228 885-2063, carsten.balleier@dfg.de
Heike Delmotte, DFG, phone: +49 228 885-2883, heike.delmotte@dfg.de
Weitere Informationen:
http://www.dfg.de/foerderung/info_wissenschaft/info_wissenschaft_17_39/index.html
Ideas from algebraic geometry have influenced modern homotopy theory, for example, the use of the moduli stack of elliptic curves in the construction the topological modular forms spectrum. In the other direction, the introduction of motivic homotopy theory has enabled the application of methods and constructions from homotopy theory to problems in algebraic geometry. The slice spectral sequence was invented in motivic homotopy theory, but its counterpart in equivariant stable homotopy theory was a key ingredient in the solution of the Kervaire invariant one problem. The motivic Adams and Adams-Novikov spectral sequences have been used to extend computations of the classical stable homotopy groups of spheres, while comparison methods from classical stable homotopy theory have been adapted to compute the first few stable motivic stems. The central purpose of this programme is to advance research at the nexus between homotopy theory and algebraic geometry, with the goal of furthering the cross-fertilisation between these areas. We expect the individual research projects to contribute to at least one of the following research areas.
Motivic homotopy theory
Derived algebraic geometry
Differential homotopy theory and motivic aspects of classical homotopy theory
Equivariant homotopy theory
For further information please contact the Priority Programme's coordinator:
Prof. Dr. Marc Levine, phone +49 201 183-3114, marc.levine@uni-due.de
For administrative and formal inquiries please contact:
Dr. Carsten Balleier, DFG, phone: +49 228 885-2063, carsten.balleier@dfg.de
Heike Delmotte, DFG, phone: +49 228 885-2883, heike.delmotte@dfg.de
Weitere Informationen:
http://www.dfg.de/foerderung/info_wissenschaft/info_wissenschaft_17_39/index.html