# The J-equation and deformed Hermitian-Yang-Mills equation

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Gao Chen

created by daniele on 20 Sep 2021

modified on 14 Oct 2021

26 oct 2021
-- 14:30

DIMaI, Firenze (online)

Seminari di Geometria Differenziale e Analisi Complessa del Dipartimento di Matematica e Informatica "Ulisse Dini" dell'Università di Firenze

**Abstract.**

The deformed Hermitian-Yang-Mills (dHYM) equation is the mirror equation for the special Lagrangian equation. The ”small radius limit” of the dHYM equation is the J-equation, which is closely related to the constant scalar curvature Kaehler (cscK) metrics. In this talk, I will explain my recent result that the solvability of the J-equation is equivalent to a notion of stability. I will also explain my similar result on the supercritical dHYM equation as well as the application of my results to the cscK problem.