Complex Geometry Talk
Speaker: Dr. Ramesh Mete, IIT Bombay
Host: Saikat Mazumdar
Title: Twisted and coupled cscK metrics on ruled surfaces
Time, day and date: 11:30:00 AM – 12:30:00 PM, Wednesday, October 22
Venue: Ramanujan Hall
Abstract: First we recall the standard canonical metrics in K\"{a}hler geometry. A K\"{a}hler metric is called a constant scalar curvature K\"{a}hler (cscK in short) metric if its scalar curvature is constant. The set of all cscK metrics include the set of all K\"{a}hler-Einstein metrics. Stoppa (2009) introduced the twisted cscK equation by twisting the cscK equation with another equation, called the J-equation. Datar and Pingali (2020) introduced coupled cscK metrics generalizing coupled K\"{a}hler-Einstein metrics defined by Hultgren and Witt Nystr\"{o}m (2019). We study the existence problem of twisted (and coupled) cscK metrics on ruled surfaces using Calabi ansatz. As an application, we give a bound for the Chen-Cheng (2021) invariant on ruled surfaces

Student Seminar
Speaker: Annu Sonkar, IIT Bombay
Host: Santanu Dey
Title: TBA
 Time, day and date: 2:00:00 PM – 2:45:00 PM, Thursday, October 23
Venue: Room 113

Student Seminar
Speaker: Advaith R Nair, IIT Bombay
Host: Santanu Dey
Title: Sard’s Theorem
Time, day and date: 2:45:00 PM – 3:30:00 PM, Thursday, October 23
Venue: Room 113

Commutative Algebra seminar
Speaker: Prof. R. V. Gurjar, TIFR (retd).
Host: Tony Puthenpurakal
Title: Resolution of singularities of algebraic or analytic varieties.
Time, day and date: 4:00:00 PM - 5:00:00 PM, Thursday, October 23
Venue: Ramanujan Hall
Abstract: First I will show how to resolve curve singularities (this must be well-known to many). Then discuss Jung-Hirzebruch argument to get the equation of a surface in three variables in a very simple form, and then resolve its singularities. This will complete the proof of resolution of singularitiies of surfaces. Next, I will discuss some easy but useful results about resolution type results (resolution of indeterminacies, principalization, general notion of resolution of singularities, and their relations to each other).

Analysis seminar
Speaker: Prof. S. Thangavelu
Host: Sanjoy Pusti
Title: On Hardy's inequality for fractional powers of the sublaplacian
Time, day and date: 4:00:00 PM – 5:15:00 PM, Friday, October 24
Venue: Ramanujan Hall
Abstract: In these lectures we plan to give an introduction to Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group. We will recall the case of the standard Laplacian on $ \R^n $ and give a proof of Hardy's inequality for $ (-Delta)^s $ using extension problem and trace Hardy inequality. We will then develop necessary background for studying the modified extension problem for the sublaplacian, establish an analogue of trace Hardy inequality and deduce Hardy's inequality.