Optimal transportation problem
Speaker: Sooraj A P, IIT Bombay
Host: Harsha Hutridurga
Title: Topics in Optimal Transportation
Time, day and date: 2:30:00 PM – 3:45:00 PM, Wednesday, April 08
Venue: Room 105
Abstract: -

Mathematics Colloquium
Speaker: Anusha Mangala Krishnan, IIT Bombay
Title: On the long-time behaviour of ancient homogeneous Ricci flows
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, April 08
Venue: Ramanujan Hall
Abstract: The Ricci flow is a means of evolving a Riemannian metric with time, with the goal of improving it, for example, to smoothen it out or to make it more round. The regularizing properties of the Ricci flow have made it a powerful tool in studying problems in geometry and topology.

In many situations, it is important to study the behaviour of the flow near singularities, that is, points where curvature becomes concentrated. Zooming into such a region gives rise to another Ricci flow solution, which then serves as a model for that singularity. Singularity models for the Ricci flow arising in this manner turn out to be ancient, that is, defined for all negative times. The simplest example of an ancient solution is the Ricci flow evolution of an Einstein metric of positive Einstein constant, which evolves by rescaling the metric linearly in time.

On a compact homogeneous space, the Ricci flow restricts to a finite-dimensional dynamical system on the space of left-invariant metrics. Within this setting, I will discuss a symmetry theorem for ancient Ricci flows, and also discuss how ancient solutions essentially emanate from Einstein metrics, possibly on a lower dimensional space.