<center><h1>Programme</h1></center>
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Courses
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Teichmüller Theory
<b>Vladimir Fock</b>, Université de Strasbourg, IRMA
<b>Abstract:</b>
The main aim of the course is to present a combinatorial approach to Teichmüller spaces of complex structures on Riemann surfaces. We will give an explicit coordinate description of this space using hyperbolic geometry and then proceed to its quantization using quantum dilogarithm. We will also discuss relations of Teichmüller spaces to cluster varieties, Dehn invariant and Bloch group, higher Teichmüller spaces. If time permits the relation to integrable systems will also be discussed. Knowledge of these subjects is not assumed. On the contrary, we hope that the course will serve as an introduction to these branches of mathematics.
A significant part of the course can be found in the following articles:
 V.V. Fock, A.B. Goncharov, Dual Teichmüller and lamination spaces. arXiv:math/0510312
 L.Chekhov, V.V.Fock, Quantum Teichmüller space, arXiv:math/9908165
Elementary knowledge of hyperbolic geometry in two and three dimension and of the notion of Poisson structure is recommended. We also recommend to look through the definitions of Weil representation, Dehn invariant and (Liouville) integrable system.

Deformations of Operator Algebras and the Construction of Quantum Field
Theories
<b>Gandalf Lechner</b>, Universität Leipzig
<b>Abstract:</b> TBA
Geometric Quantization
<b>Gijs Tuynman</b>, Université Lille 1
<b>Abstract:</b>
In this course I intend to describe the geometric quantization procedure in all its details, starting with prequantization and going from to halfdensity quantization to halfform quantization. I will try to emphasize the why of all constructions, starting with the initial motivation from physics for this procedure. I will also give explicit formulas that permit to compute examples. Depending upon on time I will sketch most/some of the proofs.
REFERENCES:
 J.Sniatycki: Geometric quantization and quantum mechanics (Springer, 1980)
 N.Woodhouse: Geometric quantization (Oxford UP, 1980 & 1990)
 D.Simms & N.Woodhouse: Lectures on geometric quantization (LNP, Springer)
 J.M.Souriau: Structure of dynamical systems (Birkhaüser) = Structure des systèmes dynamiques (Dunod, 1970)
In my course I will rely upon basic knowledge concerning symplectic mechanics, Lie groups and fibre bundles (but just the basics). The following references contain certainly (infinitely) much more than I will need. In any case, I will recall (if necessary) what I need.
 R.Abraham & J.Marsden: Foundations of mechanics
 J.M.Souriau: Structure of dynamical systems (see above)
 P.Libermann & C.M.Marle: Symplectic geometry and analytical mechanics (Kluwer)
 Warner: Foundations of differentiable manifolds and Lie groups (Springer GTM)
 Husemoller: Fibre bundles (Springer GTM)
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Schedule
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Time  Monday Sept 15  Tuesday Sept 16  Wednesday Sept 17  Thursday Sept 18 

8:30  Registration  
9:00 
Fock: Teichmüller 1 
Lechner: QFT 3  Lechner: QFT 5  Fock: Teichmüller 4 
10:30  Coffee break  Coffee break  Coffee break  Coffee break 
11:00  Tuynman: GeomQuant 1  Tuynman: GeomQuant2  Fock: Teichmüller 3  Fock: Teichmüller 5 
12:30  Lunch break  Lunch break  Lunch break  Lunch break 
14:00  Lechner: QFT 1 
Lechner: QFT 4  Tuynman: GeomQuant 3 
Tuynman: GeomQuant 5 
15:30  Coffee Break  Coffee Break  Coffee Break  Coffee Break 
16:00  Lechner: QFT 2  Fock: Teichmüller 2  Tuynman: GeomQuant 4  Questions & Discussion 
17:00  Questions & Discussion  Questions & Discussion  Questions & Discussion  
17:30  
19:00  Conference Dinner @ Unicum 
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Lunch Breaks
</center>Lunch will be provided at the university restaurant in the same building. There will be a choice of different dishes, including meat or fish, vegetarian options and a salad bar.
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Conference Dinner
</center>The conference dinner will take place Wednesday, September 17 at 7:00 pm at
the restaurant <b>Unicum</b>, CarlThierschStr.9, 91052 Erlangen. The restaurant is in Erlangen city center and in walking distance from the hotels (Map).