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.

Blow Up Formulae and Invariants II - Dimension Theory