Upcoming Talks

Title: Cut Locus, Injectivity Radius, and their Stability

Speaker:  Dr. Arita Bhowmick (Kerala School of Mathematics)

Venue: Ramanujan Hall, Department of Mathematics
Date and Time: 30 July 2026,  ,15:00 pm
Abstract:
Given a fixed point p on a Riemannian manifold (M, g), the cut locus Cut(p, g) is the collection of points q in M such that there exists a distance- minimizing geodesic from p to q, any extension of which fails to be distance- minimizing from p. In a sense, the nontrivial topology of the manifold is contained in the cut locus of a point: if one removes the cut locus, then what remains is diffeomorphic to an open ball of appropriate dimension. More generally, we shall define the cut locus of a submanifold N ⊂ M, and the distance between them is defined as the injectivity radius of N.
In the first part of the talk, we shall define the cut locus and some related concepts. We shall see examples to demonstrate the importance of studying the cut locus. Then, in the second part, we shall see how the injectivity radius behaves continuously if we perturb the metric. As a consequence, we shall get the Hausdorff stability of the cut locus as well. Once the technical definitions are over, the heart of the proofs are quite elementary.
Everyone is cordially welcome! There will be pictures.