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Motivic structures on quantum cohomology and pencils of Calabi-Yau motives. Final reports

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Organiser(s): 
V. Golyshev
Date: 
Sat, 2014-09-13 (All day) - Wed, 2014-09-17 (All day)
Location: 
MPIM Lecture Hall

The goal is to report on the progress made since the first  meeting in 2010 on a variety of subjects, including:

  • The arithmetic of mirror families and quantum motives.
  • Automorphicity of the classical Calabi-Yau motives.
  • Mirror objects in characteristic p and respective automorphic representations.
  • Extremal Laurent polynomials and their analogieswith modular families over rational base.
  • Congruence properties of Galois representations in mirror families andrelation to Fano topologies.
  • Motivic fibrations over G_m and generalizations of Gross-Koblitz.
  • The crystalline approach to Galois representations of the field of rational functions in finite characteristic.
  • Frobenius manifolds, almost Frobenius manifolds and F-manifolds Isomonodromic deformations.
  • Monodromies of (almost) Frobenius manifolds.
  • The geometricity conjecture.
  • Dubrovin's conjecture
  • gamma conjecture I, gamma conjecture II.
  • Linearizing Gromov--Witten calculus.
  • Tannakian formalism and
  • Gromov-Witten.
  • Quantum motives.
  • Affine Grassmannians and quantum corrections to geometric Satake.



Speakers/participants:

  • T. Coates
  • A. Corti
  • B. Dubrovin
  • N. Dummigan
  • V. Gritsenko
  • H. Iritani
  • A. Kasprzyk
  • A. Kresch
  • E. Mann
  • A. Mellit
  • F. Rodriguez-Villegas
  • J. Stienstra
  • A. Strangeway
  • P. Vanhove
  • D. van Straten
  • M. Watkins
  • R. Weissauer
  • D. Zagier
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