Gravity and the Crossed Product

Edward Witten, IAS
Fine Hall 314

The meaning of entropy in gravitational physics has been mysterious since the beginnings of black hole thermodynamics in the work of Bekenstein and Hawking approximately half a century ago.   By coincidence, another development that occurred at almost the same time was the work of Takesaki and Connes using the ``crossed product'' of a von Neumann algebra by its modular automorphism group to simplify the study of von Neumann algebras of Type III. In this lecture, I will explain in what sense the crossed product sheds light on the meaning of black hole entropy.