Coupled gauge-gravity perturbations of the Minkowski space
Organizers
Lars Andersson
, Xuefeng Feng
,
Bo Wen Zhao
Speaker
Puskar Mondal
Time
Wednesday, November 23, 2022 9:30 AM - 10:30 AM
Venue
Online
Online
Zoom 537 192 5549
(BIMSA)
Abstract
I will discuss a global gauge-invariant radiation estimate for the perturbations of the $3+1$ dimensional Minkowski spacetime in the presence of Yang-Mills sources. Pure gravitational and electromagnetic perturbations of the Minkowski space were studied previously by several authors in the last 30 years. The coupling to a non-abelian gauge field is important from both physical and mathematical perspectives since it can lead to very non-trivial dynamics. In this talk, I will focus on the simplest scenario of gauge-gravity coupling on a Minkowski background. In particular, I will discuss how the special structure present both in the Bianchi equations and the Yang-Mills equations is utilized crucially to obtain the dispersive estimates necessary to overcome the concentration of energy via non-linear effects and in turn prove the stability theorem. In addition, I will also briefly discuss how this technology can be adapted to handle the issue of rigorous stability-proof Einstein-Yang-Mills solitons recently discovered by Chen&Yau. This is joint work with Prof. Yau.
Speaker Intro
Puskar Mondal is currently a postdoctoral fellow at CMSA (dept. of Mathematics) and a lecturer at the Math department at Harvard University. His mentor is Prof. Shing-Tung Yau. Before this, he was a Ph.D. student at Yale university where he worked on Mathematical General Relativity under the supervision of Prof. Vincent Moncrief.