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Explore an advanced lecture on quantum spectrum in algebraic geometry delivered by Maxim Kontsevich from IHES and University of Miami. Delve into the mysterious relationship between quantum spectrum and semi-orthogonal decompositions of the derived category of coherent sheaves for complex projective varieties. Discover the formulation of the quantum blow-up formula and its potential applications in mainstream algebraic geometry. Learn about new birational invariants, including their use in proving non-rationality of generic cubic 4-folds over complex numbers. Investigate the construction of exotic motivic measures and potential connections to the Minimal Program, categorification of intersection cohomology for varieties with canonical singularities, and obstacles to strong resolution of singularities in positive characteristic.
