The aim of the School

The purpose of the school is to provide current PhD students, potdocs and other researchers with an up-to-date introduction to the main research topics of the network: loop quantum gravity, spin foam models, matrix models, and the application of non-commutative geometry and quantum groups to quantum gravity as well as more recent developments like group field theory. The emphasize will be on progress made during the four years of the ESF network program Quantum geometry and Quantum Gravity.

 Core lectures

The heart of the program will be a series of core lectures by leading researchers which will give students a solid introduction to the topics of the school.

Abhay Ashtekar - Opening lecture (slides)

Hanno Sahlmann/Kristina Giesel - Loop quantum gravity (notes: 1, 2, 3, 4)

The field of loop quantum gravity is the technically highest developed construction in quantum gravity. As in the last two schools there will be a thorough introduction into the underlying ideas and mathematical methods. The lectures will cover the basic construction of the kinematical hilbert space and some simple operators, working up to the dynamical Hilbert spaces and physical Hamiltonians following from the deparametrization models.

Carlo Rovelli - Spin foams (lectures paper, lecture notes: 1, 2, 3, 4)

The most active field in the network in the last years has been spin foam models, starting with the development of the graviton propagator and the new models, to coherent state techniques and recent asymptotic results, the generalisation to arbitrary 2-complexes and cosmological applications. The lectures will present the current perspective on the construction of these models in terms of 2-complexes.

Harold Steinacker - Non-commutative geometry and matrix models (slides: 1, 2)

Non-commutative geometry is a natural extension of geometry in the context of quantum theories that potentially, may also include gravity.. NCG naturally occurs in particle physics, as shown by Alain Connes, and also appears naturally in the context of three-dimensional quantum gravity via Chern-Simons theory. It is also used as a technical tool in state sum models, particularly via quantum groups, which provide deformations of the usual spin network calculus which can be used to construct quantum gravity models. The lectures will cover the definition and construction of non-commutative spaces as well as the construction of QFTs on them. Another theme will be the relationship to matrix models.

Thomas Krajewski - Group field theories (lecture notes: 1, 2)

Recently group field theories, generalisations of matrix models to higher dimensions, have received renewed attention. In the last year work has begun to take them serious as quantum field theories and analyse their properties using the tools of QFT. The lectures will cover the general structure of GFTs and introduce the QFT tools used to study their renormalisation theory.

Stefan Hollands - Exact QFT in curved backgrounds (lecture notes: 1, 2, 3, 4)

QFT on curved backgrounds is the formulation of QFT which does not require the symmetries of Minkowski or (Anti) de Sitter space times. From the mathematical point of view this is the highest development of QFT. It is also an important intermediate step beetwing the standard QFT and quantum gravity. As an approximation to quantum gravity it supplies some of the most potent intuitions of the field (holography, black hole entropy). The lecture will cover the recent results and successes in the exact construction of these quantum field theories.

 Auxiliary lectures

The lectures of the core program will be augmented by a set of smaller lectures that either deepen a particular aspect of a subject introduced in the core lectures or give brief introductions to related and relevant topics and techniques. Rather than providing a deep technical introduction they should show students further ideas to pursue and study.

Parampreet Singh - Loop quantum cosmology (lecture notes, plots)

Symmetry reduced models are one of the key areas of applications of loop techniques in physically relevant contexts. Following the Core LQG course these lectures will show how to apply these and related techniques in the symmetry reduced sector of GR.

Winston Fairbairn - S_qL(2,C) (lecture notes: 1, 2, 3)

Following the introduction on non-commutative spaces this lecture will introduce the quantum deformation of the Lorentz group S_qL(2,C). Quantum deformations of SU(2) are a key area of application of non-commutative geometry as a technical tool in quantum gravity models and S_qL(2,C) deformations are expected to play a similar role in the future.

Maja Burić/Harald Grosse - Renormalisation of the Grosse-Wulkenhaar model (lecture notes: 1, 2)

Following the core lectures on matrix models and field theories on non commutative space time these lectures will cover the detailed analysis of the Grosse-Wulkenhaar model. This theory is a nontrivial quantum field theory on a non-commutative space time which is fully renormalisable.

Bianca Dittrich - Diffeomorphisms, renormalisation and perfect action in discrete theories (lecture notes)

Spin foam models, when taken as discretisations of a continuum action, require renormalisation to find a continuum limit. This lecture course will introduce the notions of renormalisation and perfect actions in discrete theories with special emphasize on the role of (the breaking of) diffeomorphism invariance.

Jerzy Jurkiewicz - Causal dynamical triangulations (slides: 1, 2)

An alternative approach to the definition of the path integral of quantum gravity is to sum not over geometric moduli of a fixed discretisation, but instead to sum over all discretisations with fixed geometric building blocks. This lecture will give an introductory overview of causal dynamical triangulations, the most successful and sophisticated such technique.

 Planned individual talks

• Claudio Perini - Graviton propagator
• Eugenio Bianchi - Friedmann equation from the EPRL vertex amplitude
• Wojciech Kamiński - EPRL map: SO(4) and SO(1,3), integrability (lecture notes)
• Johannes Brunnemann - Volume operator (notes, slides)
• Simone Speziale - LQG and twisted geometries (slides)
• Aristide Baratin - Geometric constructions of GFTs (lecture notes)
• Winston Fairbairn - S_qL(2,C) EPRLK model (see lecture notes: 1, 2, 3)

 Schedule of lectures

	12-13	13-14	14-15	15-15:30	15:30-16:30	16:30-17:30	17:30-18	18-19	19-20
March 1	lunch	Rovelli	Rovelli	tea break	Giesel	Giesel	coffee break	Sahlmann	Sahlmann
March 2	lunch	Giesel	Giesel	tea break	Sahlmann	Sahlmann	coffee break	Rovelli	Rovelli
March 3	lunch	Giesel	Sahlmann	tea break	Brunnemann	Brunnemann	coffee break	Rovelli	Rovelli
March 4	lunch	Rovelli	Rovelli	tea break	Krajewski	Krajewski	coffee break	Fairbairn	Fairbairn
March 5	lunch	Bianchi	Bianchi	tea break	Fairbairn	Fairbairn	coffee break	Krajewski	Krajewski
March 6	-	-	-	-	-	-	-	-	-
March 7	lunch	Perini	Perini	tea break	Speziale	Speziale	coffee break	Baratin	Baratin
March 8	lunch	Hollands	Hollands	tea break	Dittrich	Dittrich	coffee break	Singh	Singh
March 9	-	-	-	-	-	-	-	-	-
March 10	lunch	Singh	Singh	tea break	Steinacker	Steinacker	coffee break	Hollands	Hollands
March 11	lunch	Steinacker	Steinacker	tea break	Grosse	Grosse	coffee break	Hollands	Hollands
March 12	lunch	Steinacker	Steinacker	tea break	Burić	Burić	coffee break	Hollands	-
March 13	lunch	Jurkiewicz	Jurkewicz	tea break	Kamiński	Kamiński	coffee break	-	-
The opening lecture by Abhay Ashtekar will take place on March 1, at 11:00.

 Transport

• The shuttle service from Car Polonia offers direct mini-bus transfers from Krakow Balice airport to Zakopane.
• There are buses from Kraków Główny train station to Zakopane every 30-40 min, the trip lasts 2 hours modulo trafic, the cost is about 17zł/4eu (see www.trans-frej.com.pl and www.szwagropol.eu)
• There are trains from Kraków Główny train station to Zakopane few times a day, the trip takes 3-4 hours, the cheapest version costs about 20zł/4,5eu, (see pkp), comfortable version costs about 34zł/8eu (see Intercity - from Kraków Główny to Zakopane).
• There is a train from Kraków Airport do Kraków Główny train station every 30 min, the trip takes 15 min and costs 8zł/2eu (see details - from Kraków Balice to Kraków Główny).
• There is a bus (175) from Warsaw Airport to Warsaw Central Station every 30 min, the trip takes 30 min, the cost is about 4zł/1eu (see details).
• There is a train from Warsaw Central Station (Warszawa Centralna) to Kraków Główny Station every 1-2 hours, the trip takes 3 hours - epsilon and costs about 100zł/24eu (see Intercity) or 5 hours + epsilon and costs about 50zł/12eu (see pkp).
• There is a direct train from Warszawa Centralna to Zakopane a few times a day, the trip takes 10 hours and costs about 60zł/14eu (see pkp) or ... (see Intercity).

 Organization

The school is held within the framework of the new ESF research network Quantum Geometry and Quantum Gravity, coordinated by John Barrett and Hermann Nicolai - see http://www.maths.nottingham.ac.uk/qg for further information about the network. Patronage: Janusz Majcher, Major of Zakopane
Scientific Organizing Committee          Local Organizing Committee John Barrett Michał Dziendzikowski Frank Hellmann Wojciech Kamiński Larisa Jonke Marcin Kisielowski Jerzy Lewandowski Ryszard Kostecki Carlo Rovelli Jerzy Lewandowski   Andrzej Okołów   Jacek Puchta       In case of questions write to Marcin Kisielowski.

 Registration & participants

• In order to register fill in the registration form. Note that the first day of the lectures is 1st of March, and the last day of lectures is 13th of March.
• If you have already registered and you want to check or change your data or cancel your registration, you have to log in.
• You can also take a look on the current list of registered participants.
• In case of any questions about registration - ask registration administrator.

 Lecture place, fees & accomodation

School fee: 360PLN (~90EUR), covers the food and beverages during the lunch breaks (~22PLN/day) and two coffee breaks (~10PLN/day) for 11 days, paid upon the arrival to the hotel. (The precise value of the fee may slightly change.)

There are avaible special funds for US students and postdocts to participate in this school.

The lectures will take place at Hyrny guesthouse in Zakopane:

Dom Wczasowy Hyrny
ul. Piłsudskiego 20
Zakopane
tel/fax: +48 18 2015778

The participants of the school can arrange their accomodation in the following hotels:

• Hyrny - the conference venue (alternative reservation links: here and here)
• Rzemieślnik - next door (30-second walk)
• Carlton - nearby (3 minutes walk)
• Patria - nearby hotel (3 minutes walk)
• Litwor - nearby hotel (5 minutes walk)

 Localisation

Zakopane is a tourist and ski resourt in the Tatra Mountains in Poland. During the school it will be also possible to ski, snowboard (down hill, 2000m - 1000 m) or walk in the national park. For more information about Zakopane see Wikipedia, www.ezakopane.pl, Zakopane-life.pl and Zakopane.pl. Ski rental: Montana - Ski Service (Hotel Bevedere, 5 minutes walk from Hyrny)

 Poster

Hi-res (3000x2000) version for print. (Note that this is standard RGB palette picture, so the CMYK palette printout might differ.)