KASS-seminarium

Abstrakt finns enbart på engelska: The Mabuchi functional for big cohomology classes will be defined. For Kähler classes this functional is the Euler-Lagrange functional of the constant scalar curvature Kähler (cscK) equation and one of its key properties is the convexity along weak geodesics proved by Berman–Berndtsson.

For big cohomology classes, I will introduce an invariant associated to the existence of (transcendental) Fujita approximations with good properties, proving that the vanishing of such invariant gives the convexity of the Mabuchi functional along weak geodesics. I will provide examples.

Notably, the vanishing of this invariant for all integral classes will be observed to imply the resolution of the Yau-Tian-Donaldson conjecture, leading to the question if the convexity of the Mabuchi functional for all integral big classes is related to such central conjecture.

Time permitting, some pluripotential-theoretical applications will also be presented.