Speaker：Junbang Liu（The Hong Kong University of Science and Technology）
Time: 14:00-15:00, Nov 13, 2026
Venue: room 1124, Material Science Research Building (Section C)
The smooth solvability of the J-equation on a compact Kähler manifold is closely related to numerical positivity of pairs of Kähler classes. When these numerical conditions degenerate or fail, a natural question is whether the equation admits a canonical singular solution. In this talk, I will discuss some recent progress on degenerate J-equations, focusing on the existence, uniqueness, and partial regularity of solutions at the birational minimal slope. I will also describe related results in the J-nef setting, including an analytic characterization of the J-null locus and the finiteness of J-null subvarieties. These results clarify the relationship between numerical obstructions and analytic degeneration.
