Partial Differential Equations Seminar:
Speaker: Ramesh Mete (IISc. Bengaluru)
Title: The J and dHYM equations, and corresponding natural flows.
Time, Day and Date: 11:30 a.m., Tuesday, August 27
Venue: Online (Zoom): https://us06web.zoom.us/j/88652942508?pwd=5qyzxKZbRXYOSTwwDDJZpjQah0qcLl.1

Abstract: 

The J-equation and deformed Hermitian-Yang-Mills (dHYM) equation are two important examples of complex Hessian equations which have received considerable attention in last two decades. The J-equation, introduced independently by S.K. Donaldson and X.X. Chen (1999) from different viewpoint, is related to the cscK problem in K\"{a}hler geometry. The dHYM equation, introduced by Leung-Yau-Zaslow (2000), has connection to mirror symmetry in string theory. It is well-known that each equation admits a (unique) smooth solution if and only if certain cone (or sub-solution) condition holds, or equivalently, if and only if a Nakai-Moishezon type criterion holds (which is the so-called "stable" situation). In this talk, we will focus on the existence and uniqueness of (singular) solutions for both equations in the unstable case on compact K\"{a}hler surfaces and higher dimensional K\"{a}hler manifolds with Calabi symmetry using some natural flows. Based on a joint work with Dr. Ved Datar (IISc Bengaluru) and Prof. Jian Song (Rutgers University).

4. Algebraic Groups Seminar:
Speaker: Dibyendu Biswas (IIT Bombay)
Title: Bruhat Decomposition
Time, Day and Date: 4:00 p.m., Tuesday, August 27
Venue: Ramanujan Hall, Department of Mathematics
Abstract:We will study Bruhat decomposition in reductive groups.