Speaker: Oluwagbenga Joshua Windare

Abstract: Recently, D. Angella, S. Calamai, F. Pediconi and C. Spotti extended the Donaldson-Fujiki interpretation of the scalar curvature as a momentum map in Kahler Geometry to the wider framework of locally conformally Kahler (LCK) Geometry. In this case, the momentum map u involves both the Chern scalar curvature and the Lee form of the LCK metric. Motivated by this result, I will introduce and discuss the notion of a constant momentum metric on a complex Hermitian manifold. In the special case where the manifold is Kahler, this problem reduces to the classical problem of finding Kahler metrics with constant scalar curvature.
This is a joint work with D. Angella, F. Pediconi, C. Scarpa and C. Spotti.

Title: Prime Fano 4-folds with semi-free torus actions.

Speaker: Nicholas Lindsay

Abstract. I will present a recent preprint (arxiv 2510.17230). In it I classify smooth, complex, prime Fano 4-folds with a semi-free algebraic torus actions into four deformation families, and six cases up to a natural notion of equivalence of the torus action. The proof relies on the theory of Hamiltonian torus actions.