The aim of the School
The purpose of the school is to provide current PhD students, potdocs and
other researchers with an uptodate introduction to the main research
topics of the network: loop quantum gravity, spin foam models, matrix
models, and the application of noncommutative 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 2complexes and
cosmological applications. The lectures will present the current perspective
on the construction of these models in terms of 2complexes.
Harold Steinacker  Noncommutative geometry and matrix models (slides: 1, 2)
Noncommutative 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 threedimensional quantum gravity via
ChernSimons 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
noncommutative 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_{q}L(2,C) (lecture notes: 1, 2, 3)
Following the introduction on noncommutative spaces this lecture will
introduce the quantum deformation of the Lorentz group S_{q}L(2,C). Quantum
deformations of SU(2) are a key area of application of noncommutative
geometry as a technical tool in quantum gravity models and S_{q}L(2,C)
deformations are expected to play a similar role in the future.
Maja Burić/Harald Grosse  Renormalisation of the GrosseWulkenhaar 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 GrosseWulkenhaar model. This theory is a nontrivial quantum field
theory on a noncommutative 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_{q}L(2,C) EPRLK model (see lecture notes: 1, 2, 3)
Schedule of lectures
 1213  1314  1415  1515:30  15:3016:30  16:3017:30  17:3018  1819  1920   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 minibus transfers from Krakow Balice airport to Zakopane.
 There are buses from Kraków Główny train station to Zakopane every 3040 min, the trip lasts 2 hours modulo trafic, the cost is about 17zł/4eu (see www.transfrej.com.pl and www.szwagropol.eu)
 There are trains from Kraków Główny train station to Zakopane few times a day, the trip takes 34 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 12 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


 

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 (30second 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, Zakopanelife.pl and Zakopane.pl.
Ski rental: Montana  Ski Service (Hotel Bevedere, 5 minutes walk from Hyrny)

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