Universidade Lusófona de Humanidades e Tecnologias

Grupo Lusófona


Second Workshop on Quantum Gravity and
Noncommutative Geometry

Universidade Lusófona, Lisbon 22-24 September 2008

Purpose of the Workshop

To bring together mathematicians and theoretical physicists working on the problems related with quantum gravity and quantum geometry and to provide a forum for exchange of ideas.


There will be morning and afternoon talks, and the venue is in the Auditório Vitor de SÁ (in the university library)

Icone Schedule
Time Monday, 22nd Tuesday, 23rd Wednesday, 24th
09:00-09:45 Registration    
09:45-10:00 Welcome speech    
10:00-11:00 Bertolami Freidel Madore
11:00-11:30 Coffee
11:30-12:30 Steinacker Krasnov Mena-Marugan
12:30-14:00 Lunch
14:00-15:00 Crane Nelson Lewandowski
15:00-15:30 Cofee
15:30-16:00 Zet Sazdovic Martinetii
16:00-16:30 Dawe-Martins Hahn TBA
16:30-17:30 TBA TBA TBA
20:00-23:00 Workshop dinner

T.B.A = To be announced

Icone Abstracts
Paper Author Abstract
Noncommutative quantum cosmology Orfeu Bertolam
Department of Physics, Instituto Superior Técnico, Lisbon, Portugal
We discuss the main features of a phase space noncommutative model in the context of a minisupesrpace Kantowski-Sachs geometry.
Emergent space and gravity from Yang-Mills matrix models Harold Steinacker
Department of Physics, Vienna, Austria
A mechanism for gravity emerging from Yang-Mills-type matrix models is exhibited. The matrix model desribes general noncommutative spaces, which in the semi-classical limit aquire an effective metric depending on the dynamical Poisson structure and an embedding metric. This leads to an emergent gravity intimately related to noncommutativity of space, absorbing the "would-be U(1) gauge fields". The induced gravitational action captures the UV/IR mixing of NC gauge theory. The quantization is discussed qualitatively, which singles out the IKKT model as a prime candidate for a quantum theory of gravity coupled to matter. A mechanism for avoiding the cosmological constant problem is identified.
Model categories and quantum Gravity Louis Krane
Department of Mathematics, Kansas State University, U.S.A.
U(2) gauge theory on noncommutative geometry
Gheorghe Zet
Technical University of Iasi, Romania
We develop a model of gauge theory with U(2) as local symmetry group over a noncommutative space-time. The integral of the action is written considering the U(2) gauge fields coupled with a Higgs multiplet. The gauge fields are calculated up to the second order in the noncommutativity parameter using the equations of motion and Seiberg-Witten map. The solutions are determined order by order supposing that in zero - th order they have a general relativistic analog form. The Wu- Yang ansatz for the gauge fields is used to solve the field equations. Some comments on the quantization of the electrical and magnetical charges are also given, with a comparison between commutative and noncommutative cases.
A question of quantum gravity on the “internal space” of the noncommutative standard model Rachel Martins
Department of Mathematics, Instituto Superior Técnico, Lisbon, Portugal
We suggest that towards a quantization of gravity on a noncommutative manifold, Connes's tangent groupoid and the noncommutative standard model have complementary generalisation questions. Work in progress involves a categorification of real spectral triples using Fell bundle C*-categories to allow us to make and apply a generalisation of the tangent groupoid to these noncommutative manifolds.
Laurent Freidel
Perimeter Institute for Theoretical Physics, Waterloo, Canada.
Plebanski's self-dual gravity without the simplicity constraints Kirill Krasnov
Mathematical Sciences, University of Nottingham, U.K.
As is well-known, in Plebanski's self-dual formulation general relativity is just the SO(3) BF theory supplemented with the so-called simplicity (or metricity) constraints for the two-form B field. Its main dynamical equation states that the curvature of the B-compatible SO(3) connection is self-dual, with the notion of self-duality being defined by the B-field. I describe what happens if one drops the metricity constraints on the B field, keeping only the requirement that the curvature of the B-compatible connection is self-dual. It turns out that the theory one obtains is still a gravity theory, with still just two propagating degrees of freedom as in GR. It could even be that it is quantizable via spin foams, on which I will make some speculative remarks at the end of my talk.
A quantum Goldman bracket (commutator) for intersecting paths on surfaces Jeanette Nelson
Università and INFN Torino, Italy
'll discuss a quantum Goldman bracket (commutator) for intersecting loops on surfaces, which arose in the context of (2+1)--dimensional gravity. The construction uses holonomies of constant connections which generate a $q$--deformed representation of the fundamental group. I'll show how signed area phases relate the quantum matrices assigned to homotopic loops, and explain some features of the resulting quantum geometry.
Type I superstring theory in form of open type II B one, with appropriate choice of boundary conditions Branislav Sazdovic
Institute of Physics, Belgrade, Serbia
'll discuss a quantum Goldman bracket (commutator) for intersecting loops on surfaces, which arose in the context of (2+1)--dimensional gravity. The construction uses holonomies of constant connections which generate a $q$--deformed representation of the fundamental group. I'll show how signed area phases relate the quantum matrices assigned to homotopic loops, and explain some features of the resulting quantum geometry.
Atle Hahn
Mathematical Physics Group, University of Lisbon, Portugal
The noncommutative extension of the Schwarzschild metric based on the frame formalism John Madore
Université de Paris-Sud, France
Hybrid quantum cosmology combining loop and Fock quantizations Guillermo Mena Marugan
Instituto de Estructura de la Materia, Madrid, Spain
As a necessary step towards the extraction of realistic results from loop quantum cosmology, we analyze the physical consequences of including inhomogeneities in loop quantum cosmology. We consider in detail the quantization of a gravitational model in vacuo which possesses local degrees of freedom, namely, the linearly polarized Gowdy cosmologies with the spatial topology of a three-torus. We carry out a hybrid quantization of this model which combines loop and Fock techniques. We discuss the main aspects and results of this hybrid quantization, which include the resolution of the cosmological singularity, the polymeric quantization of the internal time, a rigorous definition of the quantum constraints and the construction of their explicit solutions, the Hilbert structure of the physical states, and the recovery of a conventional Fock quantization for the inhomogeneities.
Jerzy Lewandowski
Institute of Theoretical Physics, Goettingen, Germany
The standard model in noncommutative geometry: extra-dimension from Phythagoras theorem Pierre Martinetti
Institute of Theoretical Physics, Goettingen, Germany
We shall give an overview of Connes'  description of the standard model within the framework
of noncommutative geometry,  emphasizing the metric aspect of the theory. Especially we shall focus on the metric interpretation of gauge fields, and underline the link with other distances defined by connections. As a consequence, we ought to discuss the notion of extra-dimension in this model and see how, from the metric point of view, "some" notion of extra-dimension may arise as a consequence of Pythagoras relation for Dirac operators."

Invited Speakers

John Madore
School of Mathematical Sciences, University of Nottingham, U.K.

Kirill Krasnov
School of mathematical Sciences, University of Nottingham, U.K.

Louis Crane
Department of Mathematics, Kansas State University, U.S.A.

Laurent Freidel
Perimeter Institute for Theoretical Physics, Waterloo, Canada

Jerzy Lewnadowski
Institute for Theoretical Physics, Warsaw, Plenad

Jeanette Nelson
Dipartimento di Fisica Teorica, Università degli Studi di Torino, Italy

Harold Steinacker
Fakultat fur Physik, Universitat Wien and Erwin Schrodinger International Institute for Mathematical Physics, Austria

Guillermo Mena-Marugán
Instituto de Estructura de la Materia, Madrid, Spain

Pierre Martinetti
Institut fur Theoretische Physik, Georg-August Universitat, Goettingen, Germany


Deadline for registration: September, 16th

There will be a registration fee of 30 Euros for the participants who wish to go to the workshop dinner.

If you wish to register in the Second Workshop on Quantum Gravity and Noncommutative Geometry, please an e-mail to:

With the following infos:

  • Last & First Name
  • Home Institution
  • Position ( Student, Professor or Post-Doc)
  • Mailing Adress
  • E-Mail
  • Telephone
  • Fax

If you wish to present a talk, please send it also to:

With the following infos:

  • Tittle
  • Abstract (with around 200 words)
  • Arrival & Departure date
  • Workshop Dinner ( Will attend or Will not attend)
  • Proceedings (Yes or No)

Organizing Commitee

Roger Francis Picken
Mathematics Department, Instituto Superior Técnico

Aleksandar Mikovic
Mathematics Department, Universidade Lusófona

João Nuno Prata
Mathematics Department, Universidade Lusófona

Nuno Costa Dias
Mathematics Department, Universidade Lusófona

André Fonseca
Mathematics Department, Universidade Lusófona


We are at your disposal for any further inquiries.


ULHT - Universidade Lusófona de Humanidades e Tecnologias
Departamento de Matemática
Av. do Campo Grande, 376
1749-024 Lisboa


Roger Picken (rpicken@math.ist.utl.pt)
Aleksandar Mikovic (amikovic@ulusofona.pt)
João Prata (joao.prata@mail.telepac.pt)
Nuno Dias (ncdias@meo.pt)
André Fonseca (andref@ptmat.fc.ul.pt)


(+351) 21 751 5500  ext. 2158  (A. Mikovic, Office)
(+351) 96 885 96 83 (A. Mikovic, Mobile)
(+351) 91 455 66 44 (J.N. Prata, Mobile)


(+351) 21 751 55 12

Hotel and Travel Information

Lusofona University is situated on the eastern side of the Campo Grande park, at a walking distance from the Campo Grande subway(metro) station (yellow and green line).
Street address: Avenida do Campo Grande, 376.

Concerning accommodation, a discount will be given to the participants at the following hotels:

NH Campo Grande (****)
Av. do Campo Grande, 7
Metro station: “Entre Campos” (yellow line)
Tel: (+351) 21 791 7600

Hotel Alif (***)
Campo Pequeno, 51
Metro station: “Campo Pequeno” (yellow line)
Tel: (+351) 21 782 6210

Rooms will be also available at the Lusofona University Residence in the Av. 5 de Outubro
Metro station: “Entre Campos” (yellow line)
For reservations please contact:

  • Mrs. Maria José Almeida (sec.infraestruturas@ulusofona.pt)

A list of the Lisbon hotels, with an on-line reservation service can be found here.

The Lisbon International Airport is close to the Campo Grande district, so that the most convinient transportation mode to the hotels is taxi (5-10 Euros). Otherwise, one can take the AEROBUS, which stops near the Entre Campos metro station (close to the Quality Hotel and the University Residence) as well as in the Avenida da Republica (Hotel Alif) see map. Price is 1,35 Euros, departures every 20 minutes.

You can get to Lusófona University by Bus (7, 36, 47, 78, 106, 108, 701, 750, 767, 777) or Subway (Metro in portuguese, both sites are in english).


If you are interested in knowing what Portugal has to offer to the tourist, please follow these links to the tourism information sites maintained by various Portuguese Institutions.

Visit Portugal - Portugal's official tourism website (in Portuguese, English, Spanish, French or German).

Portugal Virtual - a very complete site (in Portuguese or English) where you may find useful information about accommodation resources, tourism guides, transports, gastronomt, sights, activities, museums, shops, businesses, etc.

Instituto Português de Museus - The Portuguese Institute of Museums (IPM) administers several museums covering art, archaeology and ethnology, where visitors can find outstanding examples of Portuguese heritage that, with the inherent power of real objects, recreate distant ages. Here you can find a list of state museums, with addresses, opening hours, exhibitions, description of the collections including pictures (in Portuguese or English).

Turismo de Lisboa - a very comprehensive guide (in Portuguese, English, Spanish, French, Italian or German). Gives information about museums, monuments and other places of interest, as well as restaurants, hotels and public transports.

Portugal Hotel Guide - A colourful site (in Portuguese, English, Spanish, French, Italian or German) with in-depth hotel listings for Lisbon and Portugal. Complete with photos and web addresses.

Pousadas de Portugal - The Pousadas de Portugal are a chain of over 40 exclusive hotels, located throughout Portugal, and which originated in the 1940’s. Their very name is synonymous with a unique form of quality accommodation, where a warm welcome and personal service await every guest (in Portuguese or English).

Algarve-Web - When the city has worn you down, head south to some of the best beaches in the Algarve region of Portugal (in Portuguese, English or German).

Lonely Planet Lisbon and Portugal - an online version of a well-known guide (in English).

Time Out Guide -This online guide has been taken from Time Out Guide to Lisbon, one in an award-winning series of 35 guides to the world's major cities. A team of local experts has researched all the place has to offer (in English).


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