Speaker
Rosa Sena-Dias, Instituto Superior Tecnico, University of Lisbon
Abstract
Around 2000, Leung, Yau, and Zaslow introduced the deformed Hermitian Yang–Mills equation for (1,1)-forms on Kähler manifolds as the mirror of the special Lagrangian equation. The equation has since become an important object in the study of nonlinear geometric PDEs and stability. In this talk, I will introduce dHYM and its higher-rank analogue, emphasising the role of the phase in existence conjectures.
I will then discuss recent joint work with Benoit Charbonneau and Gonçalo Oliveira on the manifold of full flags in C^3. We construct explicit solutions, particularly in rank 2, where very few examples are known. I will explain how some of these examples shed light on conjectures of Collins, Jacob, and Yau.