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Algebraic Geometry Seminar
Seminar information archive ～05/20｜Next seminar｜Future seminars 05/21～
| Date, time & place | Friday 13:30 - 15:00 118Room #118 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | GONGYO Yoshinori, KAWAKAMI Tatsuro, ENOKIZONO Makoto |
2025/05/16
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Keita Goto (University of Tokyo)
Berkovich geometry and SYZ fibration
Keita Goto (University of Tokyo)
Berkovich geometry and SYZ fibration
[ Abstract ]
The SYZ fibration refers to a special Lagrangian torus fibration on a Calabi–Yau manifold and has been extensively studied in the context of mirror symmetry.
In particular, for a degenerating family of Calabi--Yau manifolds, a family of SYZ fibrations defined on each fiber, away from a subset of sufficiently small measure, plays a central role.
However, the existence of such fibrations remains an open problem, known as the metric SYZ conjecture.
To approach this problem, formal analytic techniques are particularly effective, and Berkovich geometry lies at their foundation.
In this talk, I will explain Yang Li’s "comparison property," a sufficient condition for the conjecture, and present some related results I have been involved in. Along the way, I will also introduce some foundational ideas in Berkovich geometry.
The SYZ fibration refers to a special Lagrangian torus fibration on a Calabi–Yau manifold and has been extensively studied in the context of mirror symmetry.
In particular, for a degenerating family of Calabi--Yau manifolds, a family of SYZ fibrations defined on each fiber, away from a subset of sufficiently small measure, plays a central role.
However, the existence of such fibrations remains an open problem, known as the metric SYZ conjecture.
To approach this problem, formal analytic techniques are particularly effective, and Berkovich geometry lies at their foundation.
In this talk, I will explain Yang Li’s "comparison property," a sufficient condition for the conjecture, and present some related results I have been involved in. Along the way, I will also introduce some foundational ideas in Berkovich geometry.
