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Description 
The discovery of the Stochastic Loewner Evolution (SLE) by Oded Schramm and the ensuing revitalization of 2D critical phenomena as a stochastic evolution of geometry has been the one of the most spectacular theoretical developments in recent years.  This development was honored by a Fields Metal in 2006 awarded to Wendelin Werner for foundational work done on SLE with O. Schramm and Greg Lawler.  SLE has a vast web of interconnections with many areas of theoretical physics, including 2D conformal field theory, 2D quantum gravity, random matrix theory, multifractal properties of stochastic media, stochastic growth phenomena and many others.  Moreover, surprising connections with 2D fully developed turbulence and 2D spin glasses have just recently emerged.

The aim of this School is to provide an overview of these important and far-reaching recent developments by the leading experts in this field.  

Topics include:
•	Stochastic Loewner Evolution
•	2D Conformal Field Theory
•	2D Quantum Gravity
•	Multifractal Properties of Stochastic Systems
•	Stochastic Growth Processes
•	Connections with 2D Turbulence and Spin Glasses

Material

School on Stochastic Geometry, the Stochastic Loewner Evolution, and Non-Equilibrium Growth Processes | (smr 1952)
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  • Monday, 7 July 2008
    • 08:30 - 10:00 Registration at Adriatico Guest House, lower level 1, outside Giambiagi Lecture Hall
      Location: Adriatico Guest House - Giambiagi Lecture Hall Area (Lower Level 1)
      • 08:30 Registration at Adriatico Guest House, lower level 1, outside Giambiagi Lecture Hall 1h30'
    • 10:15 - 10:45 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 10:15 Coffee break 30'
    • 10:45 - 11:00 Opening
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 10:45 Opening 15'
    • 11:00 - 12:30 Introduction to conformally invariant processes - part I
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 11:00 Introduction to conformally invariant processes - part I 1h30'
        Speaker: Gregory F. LAWLER (Dept. Mathematics, Univ. Chicago, Chicago, U.S.A.)
    • 12:30 - 14:00 Lunch break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 12:30 Lunch break 1h30'
    • 14:00 - 15:30 Introduction to conformally invariant processes - part II
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 14:00 Introduction to conformally invariant processes - part II 1h30'
        Speaker: Gregory F. LAWLER (Univ. Chicago, Dept. of Maths, Chicago, U.S.A.)
    • 15:30 - 16:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 15:30 Coffee break 30'
    • 16:00 - 17:30 Some discrete models of growth and interfaces, and their continuum counterpart - part I
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 16:00 Some discrete models of growth and interfaces, and their continuum counterpart - part I 1h30'
        Speaker: Michel BAUER (CEA Saclay, DSM IPhT, Gif-sur-Yvette, France)
        Material: lecture notes
  • Tuesday, 8 July 2008
    • 09:00 - 10:30 Random conformal geometry and quantum gravity - part I
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 09:00 Random conformal geometry and quantum gravity - part I 1h30'
        Speaker: Bertrand DUPLANTIER (CEN Saclay, Physique Theorique, Gif-sur-Yvette, France)
    • 10:30 - 11:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 10:30 Coffee break 30'
    • 11:00 - 12:30 Some discrete models of growth and interfaces, and their continuum counterpart - part II
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 11:00 Some discrete models of growth and interfaces, and their continuum counterpart - part II 1h30'
        Speaker: Michel BAUER (CEA Saclay, DSM IPhT, Gif-sur-Yvette, France)
        Material: lecture notes
    • 12:30 - 14:00 Lunch brak
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 12:30 Lunch brak 1h30'
    • 14:00 - 15:30 Symmetries of turbulent state - part I
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 14:00 Symmetries of turbulent state - part I 1h30'
        Speaker: Gregory FALKOVICH (The Weizmann Inst., Complex Systems, Rehovot, Israel)
        Material: lecture notes
    • 15:30 - 16:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 15:30 Coffee break 30'
    • 16:00 - 17:30 Quantum gravity: KPZ, SLE, conformal welding and scaling limits - part I
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 16:00 Quantum gravity: KPZ, SLE, conformal welding and scaling limits - part I 1h30'
        Speaker: Scott SHEFFIELD (Courant Institute, Math. Science, New York Univ., U.S.A.)
        Material: lecture notes
    • 19:00 - 21:00 Welcome Reception at Adriatico Terrace
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 19:00 Welcome Reception at Adriatico Terrace 2h0'
  • Wednesday, 9 July 2008
    • 09:00 - 10:30 Introduction to conformally invariant processes - part III
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 09:00 Introduction to conformally invariant processes - part III 1h30'
        Speaker: Gregory F. LAWLER (Univ. Chicago, Dept. Maths, Chicago, U.S.A.)
    • 10:30 - 11:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 10:30 Coffee break 30'
    • 11:00 - 12:30 Random conformal geometry and quantum gravity - part II
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 11:00 Random conformal geometry and quantum gravity - part II 1h30'
        Speaker: Bertrand DUPLANTIER (CEN, Saclay, Physique Theorique, Gif-sur-Yvette, France)
    • 12:30 - 14:00 Lunch break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 12:30 Lunch break 1h30'
    • 14:00 - 15:30 Quantum gravity: KPZ, SLE, conformal welding and scaling limits - part II
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 14:00 Quantum gravity: KPZ, SLE, conformal welding and scaling limits - part II 1h30'
        Speaker: Scott SHEFFIELD (Courant Institute, Math. Science, New York Univ., U.S.A.)
    • 15:30 - 16:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 15:30 Coffee break 30'
    • 16:00 - 17:30 Some discrete models of growth and interfaces, and their continuum counterpart - part III
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 16:00 Some discrete models of growth and interfaces, and their continuum counterpart - part III 1h30'
        Speaker: Michel BAUER (CEA Saclay, DSM IPhT, Gif-sur-Yvette, France)
        Material: lecture notes
  • Thursday, 10 July 2008
    • 09:00 - 10:30 Random conformal geometry and quantum gravity - part III
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 09:00 Random conformal geometry and quantum gravity - part III 1h30'
        Speaker: Bertrand DUPLANTIER (CEN Saclay, Physique Theorique, Gif-sur-Yvette, France)
    • 10:30 - 11:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 10:30 Coffee break 30'
    • 11:00 - 12:30 Symmetries of turbulent state- part II
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 11:00 Symmetries of turbulent state- part II 1h30'
        Speaker: Gregory FALKOVICH (The Weizmann Inst., Complex Systems, Rehovot, Israel)
        Material: lecture notes
    • 12:30 - 14:00 Lunch break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 12:30 Lunch break 1h30'
    • 14:00 - 15:30 Quantum gravity: KPZ, SLE, conformal welding and scaling limits - part III
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 14:00 Quantum gravity: KPZ, SLE, conformal welding and scaling limits - part III 1h30'
        Speaker: Scott SHEFFIELD (Courant Institute, Math. Science, New York Univ., U.S.A.)
    • 15:30 - 16:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 15:30 Coffee break 30'
    • 16:00 - 17:30 Introduction to conformally invariant processes - part IV
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 16:00 Introduction to conformally invariant processes - part IV 1h30'
        Speaker: Gregory F. LAWLER (Univ. Chicago, Dept. Maths, Chicago, U.S.A.)
  • Friday, 11 July 2008
    • 09:00 - 10:30 Quantum gravity: KPZ, SLE, conformal welding and scaling limits - part IV
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 09:00 Quantum gravity: KPZ, SLE, conformal welding and scaling limits - part IV 1h30'
        Speaker: Scott SHEFFIELD (Courant Institute, Math. Science, New York Univ., U.S.A.)
    • 10:30 - 11:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 10:30 Coffee break 30'
    • 11:00 - 12:30 Random conformal geometry and quantum gravity - part IV
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 11:00 Random conformal geometry and quantum gravity - part IV 1h30'
        Speaker: Bertrand DUPLANTIER (CEN Saclay, Physique Theorique, Gif-sur-Yvette, France)
    • 12:30 - 14:00 Lunch break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 12:30 Lunch break 1h30'
    • 14:00 - 15:30 Symmetries of turbulent state - part III
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 14:00 Symmetries of turbulent state - part III 1h30'
        Speaker: Gregory FALKOVICH (The Weizmann Institute, Complex Systems, Rehovot, Israel)
        Material: lecture notes
  • Monday, 14 July 2008
    • 09:00 - 10:30 Conformally invariant random simple curves on Riemann surfaces - part I
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 09:00 Conformally invariant random simple curves on Riemann surfaces - part I 1h30'
        Speaker: Robert BAUER (Univ. Illinois at Urbana-Champaign, Mathematics, Urbana IL, U.S.A.)
        Material: lecture notes
    • 10:30 - 11:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 10:30 Coffee break 30'
    • 11:00 - 12:30 From critical to off-critical interfaces - part I
      Location: Adriatico Guest House Giambiagi Lecture Hall
    • 12:30 - 14:00 Lunch break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 12:30 Lunch break 1h30'
    • 14:00 - 15:30 Stochastic processes in turbulent transport - part I
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 14:00 Stochastic processes in turbulent transport - part I 1h30'
        Speaker: Krzysztof GAWEDZKI (ENS Lyon, Physique Theorique Enslapp, Lyon, France)
        Material: lecture notes
  • Tuesday, 15 July 2008
    • 09:00 - 10:30 Conformal invariance in the 2D Ising model - part I
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 09:00 Conformal invariance in the 2D Ising model - part I 1h30'
        Speaker: Stanislav SMIRNOV (Univ. Geneve, Maths, Geneve, Switzerland)
        Material: lecture notes
    • 10:30 - 11:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 10:30 Coffee break 30'
    • 11:00 - 12:30 Conformally invariant random simple curves on Riemann surfaces - part II
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 11:00 Conformally invariant random simple curves on Riemann surfaces - part II 1h30'
        Speaker: Robert BAUER (Univ. Illinois at Urbana-Champaign, Mathematics, Urbana IL, U.S.A.)
        Material: lecture notes
    • 12:30 - 14:00 Lunch break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 12:30 Lunch break 1h30'
    • 14:00 - 15:30 From critical to off-critical interfaces - part II
      Location: Adriatico Guest House Giambiagi Lecture Hall
    • 15:30 - 16:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 15:30 Coffee break 30'
    • 16:00 - 17:30 Poster Session
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 16:00 Poster Session 1h30'
    • 19:00 - 21:00 Reception at Adriatico Terrace
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 19:00 Reception at Adriatico Terrace 2h0'
  • Wednesday, 16 July 2008
    • 09:00 - 10:30 Stochastic processes in turbulent transport - part II
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 09:00 Stochastic processes in turbulent transport - part II 1h30'
        Speaker: Krzysztof GAWEDZKI (ENS Lyon, Physique Theorique Enslapp, Lyon, France)
        Material: lecture notes
    • 10:30 - 11:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 10:30 Coffee break 30'
    • 11:00 - 12:30 From critical to off-critical interfaces - part III
      Location: Adriatico Guest House Giambiagi Lecture Hall
    • 12:30 - 14:00 Lunch break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 12:30 Lunch break 1h30'
    • 14:00 - 15:30 Conformal invariance in the 2D Ising model - part II
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 14:00 Conformal invariance in the 2D Ising model - part II 1h30'
        Speaker: Stanislav SMIRNOV (Univ. Geneve, Maths, Geneve, Switzerland)
        Material: lecture notes
  • Thursday, 17 July 2008
    • 09:00 - 10:30 Conformal invariance in the 2D Ising model - part III
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 09:00 Conformal invariance in the 2D Ising model - part III 1h30'
        Speaker: Stanislav SMIRNOV (Univ. Geneve, Maths, Geneve, Switzerland)
        Material: lecture notes
    • 10:30 - 11:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 10:30 Coffee break 30'
    • 11:00 - 12:30 Conformally invariant random simple curves on Riemann surfaces - part III
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 11:00 Conformally invariant random simple curves on Riemann surfaces - part III 1h30'
        Speaker: Robert BAUER (Univ. Illinois at Urbana-Champaign, Mathematics, Urbana IL, U.S.A.)
        Material: lecture notes
    • 12:30 - 14:00 Lunch break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 12:30 Lunch break 1h30'
    • 14:00 - 14:45 SEMINAR: Correlated tunneling and the instability of the fractional quantum Hall edge
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 14:00 SEMINAR: Correlated tunneling and the instability of the fractional quantum Hall edge 45'
        Speaker: Oded AGAM (Racah Inst. Physics, The Hebrew Univ., Jerusalem, Israel)
  • Friday, 18 July 2008
    • 09:00 - 09:45 SEMINAR: Exploration processes in the plane and stochastic Loewner evolutions
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 09:00 SEMINAR: Exploration processes in the plane and stochastic Loewner evolutions 45'
        Speaker: Antonio CELANI (Inst. Pasteur, UP Genetique in Silico, Paris, France)
    • 09:45 - 10:30 SEMINAR: Domain walls in Random Potts
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 09:45 SEMINAR: Domain walls in Random Potts 45'
        Speaker: Kay WIESE (ENS, Lab. Physique Theorique, Paris, France)
        Material: lecture notes
    • 10:30 - 11:00 Coffee break
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 10:30 Coffee break 30'
    • 11:00 - 12:30 Stochastic processes in turbulent transport - part III
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 11:00 Stochastic processes in turbulent transport - part III 1h30'
        Speaker: Krzysztof GAWEDZKI (ENS Lyon, Physique Theorique Enslapp, Lyon, France)
        Material: lecture notes
    • 12:30 - 13:00 Closing Remarks
      Location: Adriatico Guest House Giambiagi Lecture Hall
      • 12:30 Closing Remarks 30'