Quantum Periods for Complements

Explore a lecture on quantum periods for complements delivered by Maxim Kontsevich at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the intricacies of how a polynomial P in two variables defines a one-parameter family of spectral curves and the corresponding variation of Hodge structures on 1st cohomology groups of these curves. Discover the implications of quantizing the algebra of polynomials by deforming it to the Weyl algebra. Gain insights into an approach based on second cohomology of complements to the level sets, including a cohomological description of WKB series for Bohr-Sommefeld quantization rules. Learn about this joint work with A. Soibelman in this hour-long presentation that bridges advanced concepts in mathematics and quantum mechanics.