About:

This lecture was part of the workshop Singularity Formation in General Relativity and Dispersive PDEs

About the talk:

Dr. Rodnianksi discussed the role that self-similarity plays in singularity formation in PDE's and illustrated it on two examples.

The first was the role of self-similar solutions of the compressible Euler equations in the proof of a finite time blow up for the energy super-critical nonlinear Schrodinger and the compressible Navier-Stokes equations.

The second example was in the context of the Einstein vacuum equations of general relativity and involved a geometric notion of “twisted self-similarity” which plays an important role in the proof of existence of vacuum spacetimes with naked singularities.

About the speaker:

Igor Rodnianski (he/him) was born in Kyiv, Ukraine. After receiving his undergraduate degree in Physics from the St-Petersburg State University in 1995 and PhD in Mathematics from Kansas State University under the direction of Lev Kapitanski in 1999, he came to Princeton as an Instructor and has been there since. He is currently a Professor and the Department Chair at Princeton.

Rodnianski’s research interests lie broadly in the subjects of partial differential equations and mathematical physics and, more specifically, in the areas of hyperbolic and dispersive equations and general relativity. He was a recipient of the Clay Fellowship, the Fermat Prize, Simons Investigator Award and the Bôcher Prize.