Fano Varieties and Extremal Laurent Polynomials

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 ; 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