Jan 20, 2015
Tuesday
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09:15 AM - 09:30 AM
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Welcome
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- Location
- SLMath: Eisenbud Auditorium
- Video
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--
- Abstract
- --
- Supplements
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--
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09:30 AM - 10:30 AM
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Conformal Dynamics
Yves Benoist (Centre National de la Recherche Scientifique (CNRS))
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
This minicourse is an introduction to the group of conformal transformations of the sphere. We will focus on its action on the space of non-singleton compact subsets of the sphere.
1. Conformal autosimilarity: we will see that the compact subsets whose orbit is closed are exactly the limit sets of convex cocompact subgroups.
2. Quasicircles: we will see that the compact subsets whose orbit closure contains only Jordan curves are exactly the quasicircles.
3. Minimal orbits: we will construct compact subsets of the sphere whose orbit is not closed but whose orbit closure is minimal.
- Supplements
-
--
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10:30 AM - 11:00 AM
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Tea
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- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
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11:00 AM - 12:00 PM
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Introduction to the study of Riemannian Symmetric Spaces
Marc Burger (ETH Zürich)
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
Symmetric spaces are special Riemannian manifolds where at each point the geodesic symmetry is an isometry. Such a space has a Lie group of isometries acting transitively and we will study the structure of these spaces by using the interplay between the Riemannian and the Lie group theory aspect. For instance we will see that a symmetric space is a product of irreducible ones, and that the latter come in three types: compact type (positive curvature), Euclidean type (zero curvature) and non-compact type (negative curvature), with a remarkable duality between the compact and non-compact type. Then we will turn to symmetric spaces of non-compact type and establish the connection between regular elements and maximal flat totally geodesic subspaces; with this at hand, we will obtain the root space decomposition. In the last part we will study more closely the symmetric spaces that admit an invariant complex structure (hermitian symmetric). These form the natural framework for the study of that part of higher Teichmueller theory concerned with maximal representations of surface groups.
Prerequisite: some basic knowledge of differential and Riemannian geometry, ideally corresponding to the eight first chapters of M. do Carmo, "Riemannian Geometry", Birkhauser, 1992; the book is freely available in pdf format on google.
- Supplements
-
--
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12:00 PM - 02:00 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
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02:00 PM - 03:00 PM
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Anosov representations
Anna Wienhard (Max Planck Institute for Mathematics in the Sciences)
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
- --
- Supplements
-
--
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03:00 PM - 03:30 PM
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|
Tea
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
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03:30 PM - 04:30 PM
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The GL(2,R) action on moduli spaces of translation surfaces
Alexander Wright (Stanford University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
This three lecture mini-course will assume no prior background. The first lecture will introduce translation surfaces and their moduli. The second lecture will discuss the GL(2,R) action on these moduli spaces, and the connection to dynamical problems on translation surfaces. The third lecture will discuss orbit closures for the GL(2,R) action.
- Supplements
-
--
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04:30 PM - 06:20 PM
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Reception
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- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
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Jan 21, 2015
Wednesday
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09:30 AM - 10:30 AM
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Dynamics on character varieties
Yair Minsky (Yale University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
- --
- Supplements
-
--
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10:30 AM - 11:00 AM
|
|
Tea
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
11:00 AM - 12:00 PM
|
|
Conformal Dynamics
Yves Benoist (Centre National de la Recherche Scientifique (CNRS))
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
This minicourse is an introduction to the group of conformal transformations of the sphere. We will focus on its action on the space of non-singleton compact subsets of the sphere.
1. Conformal autosimilarity: we will see that the compact subsets whose orbit is closed are exactly the limit sets of convex cocompact subgroups.
2. Quasicircles: we will see that the compact subsets whose orbit closure contains only Jordan curves are exactly the quasicircles.
3. Minimal orbits: we will construct compact subsets of the sphere whose orbit is not closed but whose orbit closure is minimal.
- Supplements
-
--
|
12:00 PM - 02:00 PM
|
|
Lunch
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
02:00 PM - 03:00 PM
|
|
Introduction to the study of Riemannian Symmetric Spaces
Marc Burger (ETH Zürich)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
Symmetric spaces are special Riemannian manifolds where at each point the geodesic symmetry is an isometry. Such a space has a Lie group of isometries acting transitively and we will study the structure of these spaces by using the interplay between the Riemannian and the Lie group theory aspect. For instance we will see that a symmetric space is a product of irreducible ones, and that the latter come in three types: compact type (positive curvature), Euclidean type (zero curvature) and non-compact type (negative curvature), with a remarkable duality between the compact and non-compact type. Then we will turn to symmetric spaces of non-compact type and establish the connection between regular elements and maximal flat totally geodesic subspaces; with this at hand, we will obtain the root space decomposition. In the last part we will study more closely the symmetric spaces that admit an invariant complex structure (hermitian symmetric). These form the natural framework for the study of that part of higher Teichmueller theory concerned with maximal representations of surface groups.
Prerequisite: some basic knowledge of differential and Riemannian geometry, ideally corresponding to the eight first chapters of M. do Carmo, "Riemannian Geometry", Birkhauser, 1992; the book is freely available in pdf format on google.
- Supplements
-
--
|
03:00 PM - 03:30 PM
|
|
Tea
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
03:30 PM - 04:30 PM
|
|
Anosov representations
Anna Wienhard (Max Planck Institute for Mathematics in the Sciences)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
- --
- Supplements
-
--
|
|
Jan 22, 2015
Thursday
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09:30 AM - 10:30 AM
|
|
The GL(2,R) action on moduli spaces of translation surfaces
Alexander Wright (Stanford University)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
This three lecture mini-course will assume no prior background. The first lecture will introduce translation surfaces and their moduli. The second lecture will discuss the GL(2,R) action on these moduli spaces, and the connection to dynamical problems on translation surfaces. The third lecture will discuss orbit closures for the GL(2,R) action.
- Supplements
-
--
|
10:30 AM - 11:00 AM
|
|
Tea
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
11:00 AM - 12:00 PM
|
|
Dynamics on character varieties
Yair Minsky (Yale University)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
- --
- Supplements
-
--
|
12:00 PM - 02:00 PM
|
|
Lunch
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
02:00 PM - 03:00 PM
|
|
Anosov representations
Anna Wienhard (Max Planck Institute for Mathematics in the Sciences)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
- --
- Supplements
-
--
|
03:00 PM - 03:30 PM
|
|
Tea
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
03:30 PM - 04:30 PM
|
|
Introduction to the study of Riemannian Symmetric Spaces
Marc Burger (ETH Zürich)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
Symmetric spaces are special Riemannian manifolds where at each point the geodesic symmetry is an isometry. Such a space has a Lie group of isometries acting transitively and we will study the structure of these spaces by using the interplay between the Riemannian and the Lie group theory aspect. For instance we will see that a symmetric space is a product of irreducible ones, and that the latter come in three types: compact type (positive curvature), Euclidean type (zero curvature) and non-compact type (negative curvature), with a remarkable duality between the compact and non-compact type. Then we will turn to symmetric spaces of non-compact type and establish the connection between regular elements and maximal flat totally geodesic subspaces; with this at hand, we will obtain the root space decomposition. In the last part we will study more closely the symmetric spaces that admit an invariant complex structure (hermitian symmetric). These form the natural framework for the study of that part of higher Teichmueller theory concerned with maximal representations of surface groups.
Prerequisite: some basic knowledge of differential and Riemannian geometry, ideally corresponding to the eight first chapters of M. do Carmo, "Riemannian Geometry", Birkhauser, 1992; the book is freely available in pdf format on google.
- Supplements
-
--
|
|
Jan 23, 2015
Friday
|
09:30 AM - 10:30 AM
|
|
Introduction to the study of Riemannian Symmetric Spaces
Marc Burger (ETH Zürich)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
Symmetric spaces are special Riemannian manifolds where at each point the geodesic symmetry is an isometry. Such a space has a Lie group of isometries acting transitively and we will study the structure of these spaces by using the interplay between the Riemannian and the Lie group theory aspect. For instance we will see that a symmetric space is a product of irreducible ones, and that the latter come in three types: compact type (positive curvature), Euclidean type (zero curvature) and non-compact type (negative curvature), with a remarkable duality between the compact and non-compact type. Then we will turn to symmetric spaces of non-compact type and establish the connection between regular elements and maximal flat totally geodesic subspaces; with this at hand, we will obtain the root space decomposition. In the last part we will study more closely the symmetric spaces that admit an invariant complex structure (hermitian symmetric). These form the natural framework for the study of that part of higher Teichmueller theory concerned with maximal representations of surface groups.
Prerequisite: some basic knowledge of differential and Riemannian geometry, ideally corresponding to the eight first chapters of M. do Carmo, "Riemannian Geometry", Birkhauser, 1992; the book is freely available in pdf format on google.
- Supplements
-
--
|
10:30 AM - 11:00 AM
|
|
Tea
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
11:00 AM - 12:00 PM
|
|
The GL(2,R) action on moduli spaces of translation surfaces
Alexander Wright (Stanford University)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
This three lecture mini-course will assume no prior background. The first lecture will introduce translation surfaces and their moduli. The second lecture will discuss the GL(2,R) action on these moduli spaces, and the connection to dynamical problems on translation surfaces. The third lecture will discuss orbit closures for the GL(2,R) action.
- Supplements
-
--
|
12:00 PM - 02:00 PM
|
|
Lunch
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
02:00 PM - 03:00 PM
|
|
Dynamics on character varieties
Yair Minsky (Yale University)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
- --
- Supplements
-
--
|
03:00 PM - 03:30 PM
|
|
Tea
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
03:30 PM - 04:30 PM
|
|
Conformal Dynamics
Yves Benoist (Centre National de la Recherche Scientifique (CNRS))
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
This minicourse is an introduction to the group of conformal transformations of the sphere. We will focus on its action on the space of non-singleton compact subsets of the sphere.
1. Conformal autosimilarity: we will see that the compact subsets whose orbit is closed are exactly the limit sets of convex cocompact subgroups.
2. Quasicircles: we will see that the compact subsets whose orbit closure contains only Jordan curves are exactly the quasicircles.
3. Minimal orbits: we will construct compact subsets of the sphere whose orbit is not closed but whose orbit closure is minimal.
- Supplements
-
--
|
|