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Timetable (RGMW01)

Instructional Workshop for Younger Researchers

Monday 12th January 2015 to Friday 23rd January 2015

Monday 12th 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
Tuesday 13th January 2015
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
Wednesday 14th January 2015
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
Thursday 15th January 2015
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
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
19:30 to 22:00 Conference Dinner at Emmanuel College
Friday 16th January 2015
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
Monday 19th January 2015
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
Tuesday 20th January 2015
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
Wednesday 21st January 2015
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
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
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
Thursday 22nd January 2015
09:00 to 10:00 Schramm-Loewner Evolution 6 INI 1
10:00 to 11:00 Random Planar Maps 6
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
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
Friday 23rd January 2015
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
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
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons