Video Lectures

Abstract: It is a basic open question in geometric measure theory to understand regularity of a stationary integral varifold. Even a.e. regularity remains an open question. The central issue is analyzing the varifold near a point Z with a tangent...

Abstract: Let M be a compact Riemannian manifold. Morse theory for the energy function on the free loopspace LM of M gives a link between geometry and topology, between the growth of the index of the iterates of closed geodesics on M, and the...

Abstract: Finding non-constant harmonic 3-spheres for a closed target manifold N is a prototype of a super-critical variational problem. In fact, the
direct method fails, as the infimum of the Dirichlet energy in any homotopy class of maps from the...

Abstract: The spacetime positive mass theorem says that an asymptotically flat initial data set with the dominant energy condition must have a timelike energy-momentum vector, unless the initial data set is in the Minkowski spacetime. We will review...

Abstract: Functional Determinants are quantities constructed out of spectra of conformally covariant operators, and are explicit in dimension two and four, due to formulas by Polyakov and Branson-Oersted. Extremizing them in a conformal class...

Abstract: I will talk about periodic geodesics, geodesic loops, and geodesic nets on Riemannian manifolds. More specifically, I will discuss some curvature-free upper bounds for compact manifolds and the existence results for non-compact manifolds...

I will talk about a recent result showing that some well-studied polynomial-based error-correcting codes (Folded Reed-Solomon Codes and Multiplicity Codes) are "list-decodable upto capacity with constant list-size".

At its core, this is a statement...

Abstract : What are the possible limits of smooth curvatures with uniformly bounded $L^p$ norms ?

We shall see that the attempts to give a satisfying answer to this natural question from the calculus of variation of gauge theory brings us to numerous...

The emerging theory of High-Dimensional Expansion suggests a number of inherently different notions to quantify expansion of simplicial complexes. We will talk about the notion of local spectral expansion, that plays a key role in recent advances in...

It is conjectured that contact manifolds admitting flexible fillings have unique exact fillings. In this talk, I will show that exact fillings (with vanishing first Chern class) of a flexibly fillable contact (2n-1)-manifold share the same product...