Speaker: Gorapada Bera
Affiliation: Stony Brook University, U.S.A.
Title of Talk: Uniqueness in the local Donaldson-Scaduto conjecture
Date: December 16, 2025
Time: 16:00:00 Hours
Venue: AG-77

Abstract: Donaldson’s program on the adiabatic limit of $K3$-fibered $G_2$-manifolds relates associative submanifolds to certain weighted trivalent graphs on the base called gradient cycles. A key ingredient in this relation, near a trivalent vertex, is the existence and uniqueness of a special Lagrangian pair of pants in the Calabi--Yau $3$-fold formed as a product of a $K3$ surface and the complex plane. This is known as the Donaldson--Scaduto conjecture. Although this conjecture remains open, a local version replacing the $K3$ surface with an ALE hyperkähler $4$-manifold of type $A_2$ has been shown to exist by Esfahani and Li. In this talk, I will discuss our joint work on proving the uniqueness, showing that no other special Lagrangian pair of pants satisfies this local version of the conjecture.