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| 12/11/2026 | 14h00 (salle 502) Jussieu 15-25 | ||||
| Abstract: In joint work with Matessi-Ruddat-Zharkov, we prove the existence of Lagrangian torus fibrations on Calabi-Yau hypersurfaces in toric Fano manifolds given by a reflexive polytope. The result is motivated by the Strominger-Yau-Zaslow conjecture, which predicts the existence of these fibrations on Calabi-Yau manifolds near large complex structure limits. In this talk, I will outline the main setup of the construction. The idea is to replace the ordinary algebraic equation with a new one involving "ironing coefficients" and a convex (but not strictly convex!) potential which has the effect of breaking the manifold into local models. Over these models, we apply the Liouville flow technique in the style of Evans-Mauri. | |||||
| 26/11/2026 | 14h00 (salle W, esc B 4ème étage) à l'ENS | ||||
| The theory of weight functions by Mustaţă-Nicaise on Berkovich spaces hints at an intrinsic approach to studying skeleta without the limitations of the usual tools from algebraic geometry, i.e., semistable reduction or resolution of singularities. In this talk we discuss how Mustaţă-Nicaise's construction can be generalised to define weight functions intrinsically on any quasi-smooth Berkovich space as a sort of normalised log-discrepancy of a canonical form. Next, we turn our attention to computing weight functions on the Berkovich affine line over any non-Archimedean field K. This question reduces to the entirely value-theoretic problem of describing the integral log differentials $\Omega^{\log}_{L^\circ / K^\circ}$ for a simple extension of real valued fields $L / K$ , which we describe using the data in MacLane-Vaquié chains. We find that on the affine line, weight functions are completely determined by the integral piecewise linear (Z-PL) structure the affine line and vice versa, yielding new insight into the Z-PL structure. Finally, we discuss how this can be used to define and compute the essential skeleton of certain Berkovich spaces. | |||||