Geometry and Topology Seminar - Chao-Ming Lin - The deformed Hermitian—Yang—Mills equation, the Positivstellensatz, and the Solvability
Title: The deformed Hermitian—Yang—Mills equation, the Positivstellensatz, and the Solvability
Abstract: The deformed Hermitian—Yang—Mills equation, which will be abbreviated as the dHYM equation, was discovered around the same time in the year 2000 by Mariño—Minasian—Moore—Strominger and Leung—Yau—Zaslow using different points of view.
In this talk, first, I will skim through Leung—Yau—Zaslow’s approach and some known solvability results. Then, I will introduce some Noetherian ascending type cones, which are generalizations of the C-subsolution cone introduced by Székelyhidi (see also Guan). Last, I will show some of my recent work on the conjecture by Collins—Jacob—Yau when the complex dimension equals four. This conjecture states that their existence theorem of the dHYM equation can be improved when the phase is close to the supercritical phase. To be more precise, I proved that when the complex dimension equals four, if there exists a C-subsolution, then the dHYM equation is solvable.
Location: Virtual, Zoom
ID: 931 8760 7131
Password: Second word in Geometry and Topology