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Information für die Wissenschaft Nr. 23 | 19. Mai 2014
Priority Programme “Homotopy Theory and Algebraic Geometry” (SPP 1786)

In March 2014 the Senate of Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) established the Priority Programme “Homotopy Theory and Algebraic Geometry” (SPP 1786). Applications are now invited for the first three-year funding period of the programme.

Ideas from algebraic geometry have influenced modern homotopy theory, for example, the use of the moduli stack of elliptic curves in the construction of 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 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, to which an application should explicitly refer.

Motivic homotopy theory:

  • chromatic homotopy theory in the motivic setting
  • slice towers and related spectral sequences
  • the introduction of aspects of classical homotopy theory in the motivic setting
  • construction and study of motivic cohomology operations and their application to problems in algebraic geometry and arithmetic
  • extensions to non-A1-invariant theories such as higher Chow groups with modulus
  • the development and application of a motivic homotopy theory of rigid analytic spaces and other adic spaces
  • computations of motivic homotopy groups of special varieties and applications of these to problems in algebraic geometry and K-theory
  • the use of homotopical invariants in arithmetical settings, such as existence of rational points and related questions

Derived algebraic geometry in relation to homotopy theory:

  • K-theory of ring spectra, logarithmic structures on ring spectra, logarithmic topological Hochschild homology
  • extensions of the construction of the topological modular forms spectrum to other formal groups and to the motivic setting
  • characteristic classes for String bundles, especially the use of the topological modular forms spectrum and motivic liftings of connective covers of MU and MO

Differential homotopy theory and motivic aspects of classical homotopy theory:

  • homotopical and motivic invariants arising from differential homotopy theory and motivic versions of Deligne cohomology
  • the development and application of differential aspects of motivic cohomology theories
  • equivariant aspects of differential homotopy theory
  • differential cobordism invariants, Deligne and Arakelov cobordism
  • cobordism categories and motivic analogs
  • motivic aspects of rational homotopy theory

Equivariant stable homotopy theory:

  • foundations of equivariant stable homotopy theory, global equivariant stable homotopy theory, equivariant formal group laws
  • equivariant motivic stable homotopy theory
  • real motivic homotopy theory, Hermitian K-theory and Chow-Witt groups
  • motivic aspects of real and tropical enumerative geometry

Further information concerning the research orientation of the programme can be found at the programme’s website. Proposals for the first three-year funding period have to be submitted starting 3 June and no later than 23 July 2014. They have to be submitted via the DFG’s portal “elan” for applications. Those applicants who do not yet have an account on “elan” (from earlier proposal submissions or from review tasks accomplished for DFG) need to register. The registration of a new account needs to be confirmed manually by DFG and should thus be requested no later than 16 July 2014. The proposals, which should indicate how they fit into this programme as a whole, have to be submitted in English, and need to be prepared using the respective forms and guidelines in English language.

General information on proposals in the framework of a Priority Programme (in particular concerning eligibility and admissible funding requests) can be found in guideline 50.05 (part B). See also guideline 54.01 for instructions how to prepare a proposal. The specific proposal has to be structured according to form 54.012. However, it is admissible to prepare the proposal as a pdf-file, e.g., using LaTeX, instead of using the rtf-file which is available online.

Please notice the rules for publication lists that have been modified recently: Beside the general bibliography every proposal should include a list of up to ten publications that relate directly to the project. Further the number of publications that may be listed in any academic CV has been increased to up to ten as well. These publications need to be classified as a) refereed publications (published articles and monographs; accepted articles with note of acceptance by the journal) or b) other publications (e.g. preprints on arXiv).

A review meeting with reviewers and applicants will be held in late 2014. The precise date and place will be communicated to the applicants after the submission of the proposals. The envisaged start of funding is mid-2015.

Further information

More information on the Priority Programme is available under:

DFG’s portal “elan”:

Forms and guidelines can be downloaded at:

For further scientific information, please contact the Priority Programme’s coordinator:

  • Prof. Dr. Marc Levine,
    Faculty of Mathematics,
    University of Duisburg-Essen,
    45127 Essen,
    Germany,
    marc.levine@uni-due.de

For administrative and formal inquiries please contact:

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