Blow Up Formulae and Invariants II - Dimension Theory

Explore advanced mathematical concepts in this 58-minute lecture on dimension theory and its applications. Delve into the introduction of a numerical invariant called "dimension" for meromorphic connections over formal discs with second-order pole singularities. Discover how this invariant relates to Landau-Ginzburg models associated with isolated singularities, drawing connections to V. Arnold's work. Examine the conjectured semi-continuity of this invariant and its analogy to singularity theory. Learn how combining semi-continuity with blow-up formulae leads to a powerful new criterion for determining the non-rationality of higher-dimensional Fano varieties. Presented by Maxim Kontsevich from IHES, University of Miami, and IMSA, this talk offers valuable insights for researchers and advanced students in mathematics and related fields.