The deformed Hermitian—Yang—Mills equation, the Positivstellensatz, and the Solvability
Time: 2022-03-17
Published By: Wenqiong Li
Speaker(s): Chao-Ming Lin(University of California-Irvine)
Time: 09:00-10:00 March 23, 2022
Venue: Online
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, e.g., Collins—Jacob—Yau, Chen, and Chu—Lee-Takahashi. Then, I will introduce some filtration 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.
Speaker:
Chao-Ming Lin is currently a fifth year PhD student at University of California-Irvine under the supervision of Professor Zhiqin Lu and Xiangwen Zhang. He was awarded the Von Neumann Outstanding Performance as a Graduate Student Award in 2021. His research interests lie in special PDEs in complex geometry and differential geometry. Right now, in particular, the deformed Hermitian—Yang—Mills equation and the general inverse $\sigma_k$ equation. For more details about him, please visit: https://www.math.uci.edu/~chaominl/.
Zoom:
Link: https://us02web.zoom.us/j/87454487019?pwd=cnlsdkRMZ056bFpuVHVYdTN1TlJXQT09
ID: 874 5448 7019
Password: 606066
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, e.g., Collins—Jacob—Yau, Chen, and Chu—Lee-Takahashi. Then, I will introduce some filtration 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.
Chao-Ming Lin is currently a fifth year PhD student at University of California-Irvine under the supervision of Professor Zhiqin Lu and Xiangwen Zhang. He was awarded the Von Neumann Outstanding Performance as a Graduate Student Award in 2021. His research interests lie in special PDEs in complex geometry and differential geometry. Right now, in particular, the deformed Hermitian—Yang—Mills equation and the general inverse $\sigma_k$ equation. For more details about him, please visit: https://www.math.uci.edu/~chaominl/.
Zoom:
Link: https://us02web.zoom.us/j/87454487019?pwd=cnlsdkRMZ056bFpuVHVYdTN1TlJXQT09
ID: 874 5448 7019
Password: 606066
