Over the past three decades, the idea of a path integral over geometries, describing gravity in various dimensions, has become increasingly central to many areas of theoretical physics, including string and Mtheory, holography and quantum aspects of black holes and cosmology.
In each of these areas, the path integral is frequently invoked as a formal device although, as practitioners will admit, except in very special cases the basic formula remains undefined. Typically, classical saddle points are discussed, whether real or complex, but the required integrals are left unperformed.
This state of affairs is untenable because it leaves the theory on a shaky footing and hence does not permit a sound comparison of theoretical predictions with observations. The time has come to critically reassess the foundational ideas of the path integral for gravity, including its definition, evaluation and interpretation; to identify problems with
existing uses and claims based on it, and to seek improvements. The workshop will focus on the continuum theory and its semiclassical limit, with applications to cosmology, black holes and holography. In particular, the notion of a “Euclidean path integral” for a “wavefunction of the universe” will be addressed.
To this effect we intend to revisit discussion of “quantum geometrodynamics” from the path integral viewpoint and to pursue various applications. The developments in this direction that took place in the late 1970's and early 1980's were not incorporated in subsequent efforts, where the emphasis shifted to using a classical background with quantum fluctuations superimposed on it, a split which although useful in particular approximations can hardly be imagined to lie at the foundation of the theory. The revival of the discussion of the foundation of the path integral for gravity is made timely, we believe, by the introduction of new global methods such as PicardLefschetz theory.
The format of the workshop will be unusual. For the first three days, the mornings will begin with a longer, introductory lecture by each of the three organisers, setting out some of the foundational issues. This will be followed by shorter lectures by the participants, tackling the same foundational questions. The morning lectures, held in the Bob room, will be open to all Perimeter residents and visitors. They will be recorded and made available for viewing on PIRSA. Afternoons will be devoted to friendly and informal discussions, with participants invited to offer short contributions which follow up or develop points raised in the mornings, within a relaxed and highly conducive environment. Participation in these afternoon discussion sessions, as well as social events associated with the workshop, will be limited to registered workshop participants. The last two days of the workshop will be an opportunity for participants to continue discussions on topics which emerge as of greatest general interest, as well as to follow up in smaller groups on technical points or new ideas.
Format results

Covariant observables and (quantum) extension theorems
Sumati Surya Raman Research Institute

Gravity and Higgs
Ruth Gregory King's College London  Department of Mathematics

Intrinsic and extrinsic points of view
Lucien Hardy Perimeter Institute for Theoretical Physics

The Path Integral of Unmodular Gravity
Roberto Percacci SISSA International School for Advanced Studies

QuantumMechanical Aspects of Quantum Cosmology
Jonathan Halliwell Imperial College London

Why should (and why can) the path integral serve as the basis for quantum theory?
Rafael Sorkin Perimeter Institute for Theoretical Physics

Consistency of a quantum cosmological bounce
Steffen Gielen University of Sheffield

The NoBoundary Proposal: Alive and Well
Thomas Hertog Katholieke Universiteit Leuven

What is a NoBoundary Quantum State?
James Hartle University of California

Quantum incompleteness of inflation  part I
JeanLuc Lehners Max Planck Institute for Gravitational Physics  Albert Einstein Institute (AEI)  Theoretical Cosmology

Surprises in the Path Integral for Gravity
Neil Turok Perimeter Institute for Theoretical Physics

The path integral for gravity and Fedosov quantization
Stefan Hollands Universität Leipzig