## Instructional Workshop for Younger Researchers

**Monday 12th January 2015 to Friday 23rd January 2015**

09:00 to 09:50 | Registration | ||

09:50 to 10:00 | Welcome from Christie Marr (INI Deputy Director) | ||

10:00 to 11:00 |
JP Miller (Massachusetts Institute of Technology)Gaussian Free Field 1 |
INI 1 | |

11:00 to 11:30 | Morning Coffee | ||

11:30 to 12:30 |
Random Planar Maps 1
A map is a gluing of a finite number of polygons, forming a connected orientable topological surface. It can be interpreted as assigning this surface a discrete geometry, and the theoretical physics literature in the 80-90’s argued that random maps are an appropriate discrete model for the theory of 2-dimensional quantum gravity, which involves ill-defined integrals over all metrics on a given surface. The idea is to replace these integrals by finite sums, for instance over all triangulation of the sphere with a large number of faces, hoping that such triangulations approximate a limiting “continuum random surface”.
In the recent years, much progress has been made in the mathematical understanding of the latter problem. In particular, it is now known that many natural models of random planar maps, for which the faces degrees remain small, admit a universal scaling limit, the Brownian map. Other models, favorizing large faces, also admit a one-parameter family of scaling limits, called stable maps. The latter are believed to describe the asymptotic geometry of random maps carrying statistical physics models, as has now been established in some important cases (including the so-called rigid O(n) model on quadrangulations). This mini-course will review the main aspects of these themes. |
INI 1 | |

12:30 to 13:30 | Lunch at Wolfson Court | ||

18:30 to 19:30 | Wine Reception |

12:30 to 13:30 | Lunch at Wolfson Court | ||

13:30 to 14:30 | Schramm-Loewner Evolution 1 | INI 1 | |

14:30 to 15:00 | Afternoon Tea | ||

15:00 to 16:00 |
Random Planar Maps 2
A map is a gluing of a finite number of polygons, forming a connected orientable topological surface. It can be interpreted as assigning this surface a discrete geometry, and the theoretical physics literature in the 80-90’s argued that random maps are an appropriate discrete model for the theory of 2-dimensional quantum gravity, which involves ill-defined integrals over all metrics on a given surface. The idea is to replace these integrals by finite sums, for instance over all triangulation of the sphere with a large number of faces, hoping that such triangulations approximate a limiting “continuum random surface”.
In the recent years, much progress has been made in the mathematical understanding of the latter problem. In particular, it is now known that many natural models of random planar maps, for which the faces degrees remain small, admit a universal scaling limit, the Brownian map. Other models, favorizing large faces, also admit a one-parameter family of scaling limits, called stable maps. The latter are believed to describe the asymptotic geometry of random maps carrying statistical physics models, as has now been established in some important cases (including the so-called rigid O(n) model on quadrangulations). This mini-course will review the main aspects of these themes. |
INI 1 | |

16:00 to 17:00 |
JP Miller (Massachusetts Institute of Technology)Gaussian Free Field 2 |
INI 1 |

09:00 to 10:00 |
Random Planar Maps 3
A map is a gluing of a finite number of polygons, forming a connected orientable topological surface. It can be interpreted as assigning this surface a discrete geometry, and the theoretical physics literature in the 80-90’s argued that random maps are an appropriate discrete model for the theory of 2-dimensional quantum gravity, which involves ill-defined integrals over all metrics on a given surface. The idea is to replace these integrals by finite sums, for instance over all triangulation of the sphere with a large number of faces, hoping that such triangulations approximate a limiting “continuum random surface”.
In the recent years, much progress has been made in the mathematical understanding of the latter problem. In particular, it is now known that many natural models of random planar maps, for which the faces degrees remain small, admit a universal scaling limit, the Brownian map. Other models, favorizing large faces, also admit a one-parameter family of scaling limits, called stable maps. The latter are believed to describe the asymptotic geometry of random maps carrying statistical physics models, as has now been established in some important cases (including the so-called rigid O(n) model on quadrangulations). This mini-course will review the main aspects of these themes. |
INI 1 | |

10:00 to 11:00 | Schramm-Loewner Evolution 2 | INI 1 | |

11:00 to 11:30 | Morning Coffee | ||

11:30 to 12:30 | Office hours | ||

12:30 to 13:30 | Lunch at Wolfson Court |

12:30 to 13:30 | Lunch at Wolfson Court | ||

13:30 to 14:30 | Schramm-Loewner Evolution 3 | INI 1 | |

14:30 to 15:00 | Afternoon Tea | ||

15:00 to 16:00 |
JP Miller (Massachusetts Institute of Technology)Gaussian Free Field 3 |
INI 1 | |

16:00 to 17:00 |
Random Planar Maps 4 This mini-course will review the main aspects of these themes. |
INI 1 | |

19:30 to 22:00 | Conference Dinner at Emmanuel College |

09:00 to 10:00 | Discrete Lattice Models 1 | INI 1 | |

10:00 to 11:00 | Discrete Lattice Models 2 | INI 1 | |

11:00 to 11:30 | Morning Coffee | ||

11:30 to 12:30 | Office hours | ||

12:30 to 13:30 | Lunch at Wolfson Court |

10:00 to 11:00 | Gaussian Multiplicative Chaos 1 | INI 1 | |

11:00 to 11:30 | Morning Coffee | ||

11:30 to 12:30 |
JP Miller (Massachusetts Institute of Technology)Gaussian Free Field 4 |
INI 1 | |

12:30 to 13:30 | Lunch at Wolfson Court | ||

13:30 to 14:30 | Gaussian Multiplicative Chaos 2 | INI 1 | |

14:30 to 15:00 | Afternoon Tea | ||

15:00 to 16:00 | Discrete Lattice Models 3 | INI 1 |

09:00 to 10:00 | Schramm-Loewner Evolution 4 | INI 1 | |

10:00 to 11:00 | Gaussian Multiplicative Chaos 3 | INI 1 | |

11:00 to 11:30 | Morning Coffee | ||

11:30 to 12:30 | Office hours | ||

12:30 to 13:30 | Lunch at Wolfson Court | ||

13:30 to 14:30 | Gaussian Multiplicative Chaos 4 | INI 1 | |

14:30 to 15:00 | Afternoon Tea | ||

15:00 to 16:00 |
JP Miller (Massachusetts Institute of Technology)Gaussian Free Field 5 |
INI 1 |

09:00 to 10:00 | Discrete Lattice Models 4 | INI 1 | |

10:00 to 11:00 | Schramm-Loewner Evolution 5 | INI 1 | |

11:00 to 11:30 | Morning Coffee | ||

11:30 to 12:30 |
Random Planar Maps 5 This mini-course will review the main aspects of these themes. |
INI 1 | |

12:30 to 13:30 | Lunch at Wolfson Court | ||

13:30 to 14:30 | Gaussian Multiplicative Chaos 5 | INI 1 | |

14:30 to 15:00 | Afternoon Tea | ||

15:00 to 16:00 |
J Miller (Massachusetts Institute of Technology)Gaussian Multiplicative Chaos 6 |
INI 1 |

09:00 to 10:00 | Schramm-Loewner Evolution 6 | INI 1 | |

10:00 to 11:00 |
Random Planar Maps 6 This mini-course will review the main aspects of these themes. |
INI 1 | |

11:00 to 11:30 | Morning Coffee | ||

11:30 to 12:30 | Gaussian Multiplicative Chaos 6 | INI 1 | |

12:30 to 13:30 | Lunch at Wolfson Court | ||

13:30 to 14:30 | Office hours | ||

14:30 to 15:00 | Afternoon Tea | ||

15:00 to 16:00 | Discrete Lattice Models 5 | INI 1 |

09:00 to 10:00 |
JP Miller (Massachusetts Institute of Technology)Gaussian Free Field 7 |
INI 1 | |

10:00 to 11:00 | Gaussian Multiplicative Chaos 7 | INI 1 | |

11:00 to 11:30 | Morning Coffee | ||

11:30 to 12:30 | Discrete Lattice Models 6 | INI 1 | |

12:30 to 13:30 | Lunch at Wolfson Court | ||

13:30 to 14:30 | Schramm-Loewner Evolution 7 | INI 1 | |

14:30 to 15:00 | Afternoon Tea | ||

15:00 to 16:00 |
Random Planar Maps 7 This mini-course will review the main aspects of these themes. |
INI 1 |