The Priority Programme 1786 in Homotopy Theory and Algebraic Geometry builds upon recent developments in two central pillars of modern mathematics, algebraic geometry and homotopy theory, bringing together mathematicians working in these areas to encourage interactions among researchers and break down the classical boundaries between homotopy theory and algebraic geometry. Algebraic geometry studies the solution sets of algebraic equations, applying methods from algebra, analysis and topology, and has wide-ranging applications to other branches of mathematics as well as to physics and engineering. Homotopy theory is an important branch of topology, dealing with properties of spaces that are preserved in continuous families and studying them through algebraic invariants. This Priority Programme is based on several areas of interaction between these two fields:Motivic homotopy theory. Derived algebraic geometry. Differential homotopy theory and Arakelov Theory. Equivariant homotopy theory and its links to motivic homotopy theory.
DFG Programme
Priority Programmes
International Connection
France, Ireland, Norway, Switzerland, United Kingdom, USA
Projects
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Applying motivic filtrations
(Applicants
Levine, Marc
;
Röndigs, Oliver
;
Spitzweck, Markus
)
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Beyond Spin bordism
(Applicant
Noel, Justin
)
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C_2-equivariant Schubert Calculus for homogeneous spaces
(Applicants
Hudson, Thomas
;
Tilson, Ph.D., Sean
)
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Characterizations and Uniqueness of the stable motivic homotopy theory
(Applicant
Hornbostel, Jens
)
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Chern classes of automorphic bundles
(Applicant
Esnault, Hélène
)
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Chromatic Derived Algebraic Geometry and Equivariant Homotopy Theory
(Applicant
Meier, Lennart
)
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Classification of vector bundles over affine varieties
(Applicant
Rosenschon, Ph.D., Andreas
)
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Computations of Chow-Witt groups for split quadrics and other smooth varieties
(Applicants
Hornbostel, Jens
;
Zibrowius, Ph.D., Marcus
)
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Coordination Funds
(Applicant
Levine, Marc
)
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Enumerative geometry with quadratic forms
(Applicant
Levine, Marc
)
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Expansion principles of topological automorphic forms
(Applicant
Laures, Gerd
)
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Exponential motivic homotopy theory, foliations and applications
(Applicant
Pepin Lehalleur, Simon
)
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Global equivariant homotopy theory II
(Applicant
Schwede, Stefan
)
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Mixed Hodge structures in homotopy theory
(Applicants
Cirici, Joana
;
Levine, Marc
)
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Motives with modulus
(Applicants
Esnault, Hélène
;
Kerz, Moritz
;
Levine, Marc
)
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Motivic and homotopical methods in classical and p-adic Hodge theory
(Applicant
Huber-Klawitter, Annette
)
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Motivic homotopy theory for local quotient stacks
(Applicant
Heinloth, Jochen
)
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Motivic invariants of moduli spaces
(Applicants
Hoskins, Victoria
;
Schmitt, Alexander
)
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Motivic iterated integrals and integral points
(Applicant
Dan-Cohen, Ishai
)
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Motivic Stack Inertia of Moduli Spaces of Curves, Variation of Periods and Multiple Zeta Values in Genus 0 and 1
(Applicant
Collas, Ph.D., Benjamin
)
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New examples for logarithmic ring spectra
(Applicant
Richter, Birgit
)
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Odd primary equivariant rigidity and equivariant derivators
(Applicant
Schwede, Stefan
)
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Operads in algebraic geometry and their realizations
(Applicants
Hornbostel, Jens
;
Röndigs, Oliver
;
Spitzweck, Markus
;
Stelzer, Manfred
)
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Oriented cohomology theories and equivariant motives
(Applicant
Geldhauser, Nikita
)
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Quadratic forms, quadrics, sums of squares and Kato's cohomology in positive characteristic
(Applicant
Hoffmann, Detlev
)
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Ramified extensions of commutative ring spectra
(Applicant
Richter, Birgit
)
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The summand BtmfP of MU<6>
(Applicant
Laures, Gerd
)
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Topological dihedral homology of group rings
(Applicant
Reich, Holger
)
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Trace maps for real algebraic K-theory
(Applicant
Dotto, Ph.D., Emanuele
)