# Essential Self-adjointness and Quantum Cosmology

## GAP Seminar

## Meeting Details

For more information about this meeting, contact Nigel Higson, Mathieu Stiénon, Ping Xu.

**Speaker:** Abhay Ashtekar, Penn State University

**Abstract:** To account for what was then believed to be a static universe,
Einstein introduced a positive cosmological constant $\Lambda$ in his
equations of general relativity. When Hubble discovered that the
universe is expanding, Einstein removed the constant, calling its
introduction `the greatest blunder' of his life. However, recent
observations have shown that the universe is accelerating (a discovery
that, incidentally, was awarded this year's physics Nobel prize). The
simplest explanation is a $\Lambda$! Interestingly, it turns out that
while the operator generating dynamics in quantum cosmology is
self-adjoint if $\Lambda$ is non-positive, it fails to be essentially
self-adjoint precisely in the physically interesting case of positive
$\Lambda$. But still dynamics appears to be quite robust with respect
to the choice of the self-adjoint extension. This is puzzling from a
physics perspective. The goal of the seminar will be to explain this
issue and seek insight from mathematicians on this intriguing
phenomenon.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 11/01/2011

**Time:** 2:30pm - 3:30pm