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# Tristan Collins, Special Colloquium

## December 12, 2017 @ 4:00 pm - 5:00 pm

**Title: ***The J-equation and stability.*

**Abstract:** Donaldson and Chen introduced the J-functional in ’99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point. The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.