Jan 20, 2015
Tuesday

09:15 AM  09:30 AM


Welcome

 Location
 SLMath: Eisenbud Auditorium
 Video


 Abstract
 
 Supplements



09:30 AM  10:30 AM


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 nonsingleton 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



10:30 AM  11:00 AM


Tea

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 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 noncompact type (negative curvature), with a remarkable duality between the compact and noncompact type. Then we will turn to symmetric spaces of noncompact 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



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


The GL(2,R) action on moduli spaces of translation surfaces
Alexander Wright (Stanford University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
This three lecture minicourse 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



04:30 PM  06:20 PM


Reception

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements




Jan 21, 2015
Wednesday

09:30 AM  10:30 AM


Dynamics on character varieties
Yair Minsky (Yale University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
 
 Supplements



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 nonsingleton 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 noncompact type (negative curvature), with a remarkable duality between the compact and noncompact type. Then we will turn to symmetric spaces of noncompact 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

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 minicourse 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 noncompact type (negative curvature), with a remarkable duality between the compact and noncompact type. Then we will turn to symmetric spaces of noncompact 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 noncompact type (negative curvature), with a remarkable duality between the compact and noncompact type. Then we will turn to symmetric spaces of noncompact 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 minicourse 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 nonsingleton 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



