Related papers: Quantum Geometric Description of Cosmological Mode…

A slightly extended version, with a footnote added on December 19, 1997, of a contributed Abstract to the Eight Marcel Grossmann Meeting, Jerusalem, June 1997.

We give a brief survey of many of the high-lights of our present understanding of the young subject of quantum metric spaces, and of quantum Gromov-Hausdorff distance between them. We include examples.

With the two most profound conceptual revolutions of XXth century physics, quantum mechanics and relativity, which have culminated into relativistic spacetime geometry and quantum gauge field theory as the principles for gravity and the…

We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for…

This is a summary report of the workshop D2 in GR15. In this workshop rather diverging problems related to quantum gravity and quantum cosmology were discussed. Since it is almost impossible to summarize all these discussions in coherent…

This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical…

This is an expository lecture, for the Abel bicentennial (Oslo, 2002), describing some recent work on the (small) quantum cohomology ring of Grassmannians and other homogeneous varieties.

This is a review of the paper "Anomalies in Quantum Field Theory and Cohomologies of Configuration Spaces" (arXiv:0903.0187).

These notes partly touch the topic of the talk given by the author at the XXXVIII Workshop on Geometric Methods in Physics, hold in June-July 2019 in Bia\l{}owie\.{z}a, Poland. They consist of a short and self-contained introduction to the…

These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.

This is the draft version of a review paper which is going to appear in "Advances in Imaging and Electron Physics"

We summarize the talks presented at the QG4 session (loop quantum gravity: cosmology and black holes) of the 13th Marcel Grossmann Meeting held in Stockholm, Sweden.

In this short note we provide a review of some developments in the area of homotopy quantum field theories, loosely based on a talk given by the second author at the Xth Oporto Meeting on Geometry, Topology and Physics.

I present a selection of conceptual and mathematical problems in the foundations of modern physics as they derive from the title question. Contribution to a panel session, "Springer Forum: Quantum Structures -- Physical, Mathematical and…

We remark the importance of adding suitable pre-geometric content to tensor models, obtaining what has recently been called tensorial group field theories, to have a formalism that could describe the structure and dynamics of quantum…

This is a review article for The Review of Particle Physics 2006 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters as at May 2006. Topics included are Parametrizing the Universe; Extensions…

This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…

This introductory review is addressed to beginning researchers. Some of the distinguishing features of loop quantum gravity are illustrated through loop quantum cosmology of FRW models. In particular, these examples illustrate: i) how…

Invited talk delivered at the International Conference on General Relativity and Cosmology (ICGC), Ahmedabad, India; 13 - 18 December 1991. To appear in its proceedings.

After introducing the basic ingredients of Loop Quantum Cosmology, I will briefly discuss some of its phenomenological aspects. Those can give some useful insight about the full Loop Quantum Gravity theory and provide an answer to some…