Moduli Spaces of Points on the Projective Line and Other Varieties with Many Symmetries
By Yuri Tschinkel
Exponential Volumes in Geometry and Representation Theory
By Alexander Goncharov
Appears in collection : Physical Mathematics : Celebration of Albert Schwarz’s 70 Years in Science
A polynomial P in two variables defines a one-parameter family of spectral curves which are level sets of P, and the corresponding variation of Hodge structures on 1st cohomology groups of these curves. What happens if one quantizes the algebra of polynomials, i.e. deforms it to the Weyl algebra? I'll explain an approach based on second cohomology of complements to the level sets. In particular, one obtains a cohomological description of WKB series for Bohr-Sommefeld quantization rules. This is joint work with A.Soibelman.