Dmitry Sustretov "Gromov-Hausdorff limits of maximally degenerate families of Calabi-Yau manifolds via model theory"

Dmitry Sustretov (Einstein Institute of Mathematics)
Gromov-Hausdorff limits of maximally degenerate families of Calabi-Yau manifolds via model theory

In their 2001 paper "Homological mirror symmetry and torus actions" Kontsevich and Soibelman made a series of conjectures about properties of Gromov-Hausdorff limits of certain families of Calabi-Yau manifolds with the view of applying these to the SYZ conjecture. The limits are conjectured to be of half real dimension of the family and to possess a canonical affine structure. In this talk I will make an overview of a model-theretic approach to computation of Gromov-Hausdorff limits which uses a certain tame geometric setting called o-minimality and explain its relation to the conjectures of Kontsevich and Soibelman. No prior exposure to model theory will be assumed.