V. Golyshev: “The Apery Class and the Gamma Class”

Here are my notes from Golshev’s talk at the Extremal Laurent Polynomials workshop at Imperial:

Golyshev_London_Sep_2010

Summary:

  • a historical analogy: the study of Fano varieties now versus the study of algebraic varieties in the early 1970s
  • the key idea: classifying Fanos by detecting and classifying Fano quantum motives and their realizations
  • possible approaches
  • the Tannakian picture
  • the quantum Satake correspondence (Golyshev–Manivel)
  • two steps in this direction:  Ueda’s proof of the Dubrovin Conjecture for Gr(k,n); Galkin–Golyshev–Iritani’s proof that Apery=Gamma
  • irregular monodromy data for Dubrovin’s quantum connection
  • the Extended Dubrovin Conjecture and the Apery=Gamma hypothesis
  • the Extended Dubrovin Conjecture and the Apery=Gamma hypothesis hold for Gr(k,n)

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