Abstracts

Abhay Ashtekar

The big-bang and black holes are perhaps the most dramatic manifestations of the synergistic interplay between geometry and physics. While they both emerge from general relativity, they also bring out its limitations. In this talk, I will illustrate how quantum geometry effects can create new paradigms to resolve some of these difficulties, thereby extending and enhancing the interplay between geometry and physics.

Barry C. Barish

The Laser Interferometer Gravitational-Wave Observatory (LIGO) is being developed with sensitivity that should be capable of the detection of gravitational waves resulting from such astrophysical sources as merging compact binary systems, spinning neutron stars, supernovae explosions and even cosmological sources. LIGO consists of two widely separated long baseline interferometers that can be used standalone or in coincidence. These sophisticated interferometers have been constructed and the commissioning is well along. The detectors are already the most sensitive in the world and are now approaching the design sensitivity of the initial interferometers. The science of gravitational waves, the technology and detector performance, the first upper limits, and finally the prospects for the future will be discussed.

Vladimir Braginsky

Robert Brandenberger

I will argue that, in spite of the spectacular phenomenological success of the inflationary scenario, models of scalar field-driven inflation lead to serious conceptual problems, and a new theoretical paradigm is necessary in order to overcome these problems. I will then discuss the challenges for a new cosmology and attempts to address these in the context of superstring theory.

Jean Pierre Bourguignon

The Ricci curvature was introduced by Grigorio Ricci-Curbastro for purely geometric reasons, and its appearance in the field equations of General Relativity changed its status in Geometry.

All along the XXth century, there has been instances where new developments in relativistic field theory changed the point of view mathematicians had on some geometric quantities or problems. We will recall some of these moments, typically the early days of the Ricci curvature, Hermann Weyl's interest in conformal geometry, the introduction of the Dirac operator and the role of spinor fields, generalized Gauß-Bonnet theorems, and the ADM formalism leading to super-space and the Ricci flow. Almost each time the mathematical techniques needed to take advantage of the new point of view had to be considerably expanded.

Thibault Damour

Reinhard Genzel

Evidence has been accumulating for several decades that quasars, the most luminous objects in the Universe, are powered by accretion of matter onto massive black holes. I will discuss recent observations, employing adaptive optics imaging on large ground-based telescopes that prove the existence of such a massive black hole in the center of our Milky Way, beyond any reasonable doubt. These observations indicate that the Galactic Center black hole may be rotating rapidly and show that massive star formation has been happening recently in its immediate vicinity. I will also briefly discuss our present knowledge about the formation and evolution of these massive black holes in the early Universe.

Michael B. Green

String theory is a promising framework for a consistent unification of Einstein's theory of gravity with the other forces in a manner that is consistent with quantum mechanics. As the talk will explain, string theory was originally formulated in terms of a series of 'perturbative' approximations analogous to the Feynman diagrams that approximate conventional theories. However, recent developments aimed at unravelling the full structure of the theory have led to important insights that will also be described in the talk.

James Hartle

In our quantum universe Einstein's 1915 general theory of relativity governs the deterministic evolution of spacetime geometry over an enormous range of time, place, and epoch. What is the origin of this and other deterministic laws in a quantum universe characterized fundamentally by chance, fluctuation and indeterminism? We seek to answer this question in the contexts of quantum cosmology and the generalized effective quantum theory of spacetime geometry. Two ingredients are essential: First, coarse graining is needed for the decoherence of alternate histories of geometry and coarse graining beyond that is needed to resist the noise that mechanisms of decoherence produce. Second, a restriction is needed on the quantum state of the universe. These requirements will be illustrated in model particle systems and in model cosmologies. The quasiclassical realm of everyday experience is thus an emergent feature of the universe's initial condition and dynamics. We analyze briefly the sensitivity of the existence of a quasiclassical realm to the particular form of the universe's initial quantum state.

Tom Prince

The Laser Interferometer Space Antenna (LISA) is a joint ESA-NASA mission to detect and study gravitational waves. The mission consists of a triangular configuration of 3 spacecraft separated from each other by 5 million kilometers. Gravitational waves will be detected via laser metrology between the spacecraft. LISA is expected to detect thousands of gravitational wave sources including some of the most exotic and energetic sources in the universe. This talk will describe the LISA mission and describe its capabilities for tests of Einstein's theories.

Martin Rees

Richard Schoen

In this lecture we will discuss the geometric question of construction of Riemannian metrics of constant scalar curvature. This problem turns out to have an intimate connection with gravitational mass in relativity. We will discuss this connection and survey the recent activity on the Yamabe problem which has provided a much more thorough understanding of constant scalar curvature metrics both from a variational and heat equation point of view.

Matthias Staudacher

We review recent breakthrough progress in the AdS/CFT correspondence, which is a proposed duality between supersymmetric gauge theories and superstrings on certain curved space-time geometries. The novel connecting link consists in integrable spin chains, which are more commonly studied in condensed matter physics.

Michael Struwe

We review recent progress in the understanding of nonlinear wave equations related to General Relativity.

Michael S. Turner

Einstein's theory provides the basis for our current understanding of the origin and evolution of the Universe. It addition, his theory allows us to frame, but not answer, two of the most basic questions we can ask about the Universe: How did the Universe begin? and How will the Universe end?

Christoph Wetterich

Dark energy - a homogeneously distributed cosmic energy density - seems to explain various cosmological observations. The anisotropies in the microwave background radiation, the formation of structure and the late time acceleration of the Hubble expansion fit into a consistent picture. The role and origin of dark energy are among the greatest mysteries in fundamental physics, touching the question of unification of gravity with the fundamental quantum interactions.

We discuss quintessence - a dynamical form of dark energy - and possible signatures distinctive from a cosmological constant. Quintessence could be related to a new "fundamental" macroscopic force and induce a small time variation of fundamental constants.

Clifford Will

At various times during its 100-year history, relativity was considered the playground of the theorist, not the experimentalist. Although the 1905 special relativity was quickly integrated into mainstream physics and was subjected to numerous experimental tests, the 1915 general relativity remained outside the mainstream for almost half a century. But during the past 40 years a revolution has occurred, and the confrontation between general relativity and experiment is a vigorous, ongoing enterprise. We will review the current status of experimental tests of the theory, and will describe how the future detection of gravitational radiation may provide powerful new tests of the theory in its strong-field, dynamical regime. These tests will rely upon sophisticated calculations of gravitational-wave and strong-field phenomena using both approximation techniques and large scale-numerical computations. The current status of these calculations will be reviewed.

Shing-Tung Yau

Sir Martin Rees