Seminar Event Detail


MCAIM Colloquium

Date:  Wednesday, April 13, 2022
Location:  4448 East Hall (3:00 PM to 4:00 PM)

Title:  Emergence of General Relativity from a (Diffeomorphism Invariant) Gauge Theory

Abstract:   Space-time metric and Einstein's equations lie at the foundation of general relativity. Somewhat surprisingly, one can start with an SU(2)-gauge theory, write down the simplest equations one can, without making reference to any background field, and show that the Riemannian geometry and Einstein's equations emerge by setting up an appropriate dictionary. Equations of the `fundamental' gauge theory are simple low order polynomials. Complexity of Einstein's equations can be traced back to the fact that the explicit dictionary from the gauge theory to general relativity is rather intricate. The gauge theory framework provides new insights into general relativity, including an interesting interplay between the Lie algebra of volume-preserving diffeomorphisms and the 'integrable' sector of (anti-)self-dual solutions to Einstein's equations. It also leads to a new infinite dimensional Lie algebra that generalizes the Lie algebra of the diffeomorphism group, opening up
directions for new mathematical work. I will make a special e ort to make the summary of these structures and results accessible to mathematicians as well as physicists.

Event will take place in-person and online via Zoom:

Zoom Info:

Join Zoom Meeting
https://umich.zoom.us/j/91494048285

Meeting ID: 914 9404 8285
Passcode: 387662

Files:


Speaker:  Abhay Ashtekar
Institution:  The Pennsylvania State University

Event Organizer:   Lydia Bieri    math-mcaim@umich.edu

 

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