# Mathematical Sciences Research Institute

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1. # GAAHD Research Seminar: On the classification of C-Fuchsian subgroups of Picard modular groups

Location: MSRI: Simons Auditorium
Speakers: Frédéric Paulin (Centre National de la Recherche Scientifique (CNRS))

Given an imaginary quadratic number field K, we give a classification of the maximal nonelementary subgroups of the Picard modular group PSU_{1,2}(O_K) preserving a complex geodesic in the complex hyperbolic plane. Complementing work of Holzapfel, Chinburg-Stover and Möller-Toledo, we show that these maximal C-Fuchsian subgroups are arithmetic, arising from a quaternion algebra over Q with Hilbert symbol (D,D_K) for some explicit positive integer D and with D_K the discriminant of K. We thus prove the existence of infinitely many orbits of K-arithmetic Cartan chains in Poincaré's hypersphere in the complex projective plane. This is a joint work with Jouni Parkkonen.

Updated on Apr 17, 2015 09:51 AM PDT
2. # 3-Manifold Seminar

Location: 939 Evans Hall
Speakers: Ian Agol (University of California, Berkeley)
The topic this semester is representations of 3-manifold groups into SL_2 C. Topics will include:

- character varieties and curves of characters
- ideal points, R-tree actions, tree actions associated to ideal points of curves
- associating incompressible surfaces to tree actions and measured laminations to R-tree actions
- volumes of representations and Chern-Simons invariant
- Dehn invariants, the Bloch group, and extensions
- volume rigidity, via simplicial volume and the barycenter map
- the A-polynomial

Created on Jan 29, 2015 09:28 AM PST
3. # Open ended seminar: Measures on the boundary minimizing energy

Location: MSRI: Baker Board Room
Speakers: Seonhee Lim (Seoul National University)

Let X be the universal cover of a compact manifold of negative curvature. We will present local limit theorem of the heat kernel and explain how we use equidistribution of large spheres. The equidistribution is based on uniform mixing of geodesic flow with respect to a conformal family of measures on the boundary of X, which is the family associated to the Martin kernel.

This family of measures turns out to be the unique family of measures minimizing the energy (or the Rayleigh quotient of Mohsen). We will also look at the generalized Harish-Chandra function. The normalizing constant which can be defined for any conformal family depends only on the cohomology class of the family of measures.

This is a joint work with François Ledrappier.
Updated on Apr 17, 2015 09:46 AM PDT
1. # Geometry and Analysis of Surface Group Representations: The Area of Convex Projective 2-Orbifolds

Location: MSRI: Baker Board Room

The Hilbert metric on a bounded convex set $\Omega\subset\mathbb R^2$ determines an area 2-form on $\Omega$. One of the coordinates used by Fock and Goncharov assigns to an ideal triangle $T\subset\Omega$ a shape parameter $t >0$. We obtain a lower bound for the area of $T$ in terms of $t$.

Updated on Apr 17, 2015 09:54 AM PDT
2. # DMS Research Seminar: The modular action on PSL(2,R)-characters

Location: MSRI: Simons Auditorium
Speakers: Maxime Wolff (Institut de Mathematiques de Jussieu)

I will present joint work with Julien Marché, in which we investigate the action of the mapping class group on the character variety Hom(\pi_1\Sigma_g,PSL(2,R))/PSL(2,R). When g=2 we prove the action is ergodic on every connected component of the space of conjugacy classes of non elementary representations of non extremal Euler class. The first 45 minutes will be introductory.

Updated on Apr 17, 2015 09:58 AM PDT
3. # DMS Postdoc Seminar: An Overview of the Nahm Transform

Location: MSRI: Simons Auditorium
Speakers: Andres Larrain-Hubach (University of Arizona)

The Nahm Transform is a nonlinear analog of the Fourier Transform, used to construct maps between moduli spaces of solutions of dimensional reductions of Yang-Mills equations. I will discuss several examples and open problems related  to this construction, focusing on the moduli space of solutions to Hitchin equations over a Riemann surface.

Updated on Apr 17, 2015 10:38 AM PDT
4. # GAAHD Postdoc Seminar: Hausdorff dimension of product sets

Location: MSRI: Simons Auditorium
Speakers: Nicolas de Saxce (Université de Paris XIII (Paris-Nord))

Given a subset A of a group G, we want to compare the size the product set AAA of elements that can be written as products of three elements of A with the size of A. I will discuss this problem when G is a simple Lie group and the sets A and AAA are measured by their Hausdorff dimension.

Updated on Apr 17, 2015 10:00 AM PDT
5. # Lorentzian geometric structures seminar

Location: MSRI: Baker Board Room
Created on Feb 23, 2015 11:06 AM PST
6. # MSRI Evans Talk: Topological rigidity theorems and Homogeneous dynamics

Location: 60 Evans Hall
Speakers: Hee Oh (Yale University)

In the hyperbolic plane H^2, horocycles are given by Euclidean circles tangent to the boundary. In 1936, Hedlund showed that in a compact hyperbolic surface Gamma\H^2, every horocycle is dense; this is one of the first theorems on orbit closures in homogeneous spaces.

Hedlund’s approach is based on the study of minimal sets and long time behavior of horocyclic flows. This approach was significantly generalized by Margulis  in his proof of Oppenheim conjecture on values of quadratic forms  in 1989.

In 1991, Ratner gave a complete description of all possible orbit closures on a finite volume homogeneous space under the action of a subgroup generated by unipotent one-parameter subgroups, based on her measure classification theorem.

We will discuss certain topological rigidity theorems in infinite volume hyperbolic manifolds of dimension 2 or 3 which can be approached by generalizing the ideas of Hedlund and Margulis.

Updated on Apr 17, 2015 11:14 AM PDT
7. # GAAHD Research Seminar

Location: MSRI: Simons Auditorium
Updated on Feb 20, 2015 09:49 AM PST
8. # 3-Manifold Seminar

Location: 939 Evans Hall
Speakers: Ian Agol (University of California, Berkeley)
The topic this semester is representations of 3-manifold groups into SL_2 C. Topics will include:

- character varieties and curves of characters
- ideal points, R-tree actions, tree actions associated to ideal points of curves
- associating incompressible surfaces to tree actions and measured laminations to R-tree actions
- volumes of representations and Chern-Simons invariant
- Dehn invariants, the Bloch group, and extensions
- volume rigidity, via simplicial volume and the barycenter map
- the A-polynomial

Created on Jan 29, 2015 09:29 AM PST
9. # Open ended seminar

Location: MSRI: Baker Board Room
Updated on Mar 06, 2015 09:51 AM PST
10. # Geometry and Analysis of Surface Group Representations

Location: MSRI: Baker Board Room
Speakers: Qiongling Li (Rice University), Andrew Sanders (University of Illinois at Chicago)
Created on Jan 22, 2015 04:38 PM PST
11. # DMS Research Seminar

Location: MSRI: Simons Auditorium
Speakers: Marc Burger (Eidgenössische TH Zürich-Hönggerberg), Fanny Kassel (Université de Lille I (Sciences et Techniques de Lille Flandres Artois))
Updated on Jan 28, 2015 02:15 PM PST
12. # DMS Postdoc Seminar

Location: MSRI: Simons Auditorium
Speakers: Guillaume Dreyer (University of Notre Dame), Nicolas de Saxce (Université de Paris XIII (Paris-Nord))
Created on Jan 28, 2015 02:04 PM PST
13. # GAAHD Postdoc Seminar

Location: MSRI: Simons Auditorium
Speakers: Guillaume Dreyer (University of Notre Dame), Nicolas de Saxce (Université de Paris XIII (Paris-Nord))
Created on Jan 28, 2015 02:05 PM PST
14. # Lorentzian geometric structures seminar

Location: MSRI: Baker Board Room
Created on Feb 23, 2015 11:07 AM PST
15. # GAAHD Research Seminar

Location: MSRI: Simons Auditorium
Updated on Feb 20, 2015 09:50 AM PST
16. # Open ended seminar

Location: MSRI: Baker Board Room
Updated on Mar 06, 2015 09:51 AM PST
17. # Geometry and Analysis of Surface Group Representations

Location: MSRI: Baker Board Room
Speakers: Qiongling Li (Rice University), Andrew Sanders (University of Illinois at Chicago)
Created on Jan 22, 2015 04:39 PM PST
18. # DMS Research Seminar

Location: MSRI: Simons Auditorium
Speakers: Marc Burger (Eidgenössische TH Zürich-Hönggerberg), Fanny Kassel (Université de Lille I (Sciences et Techniques de Lille Flandres Artois))
Updated on Jan 28, 2015 02:15 PM PST
19. # DMS Postdoc Seminar

Location: MSRI: Simons Auditorium
Speakers: Guillaume Dreyer (University of Notre Dame), Nicolas de Saxce (Université de Paris XIII (Paris-Nord))
Created on Jan 28, 2015 02:06 PM PST
20. # GAAHD Postdoc Seminar

Location: MSRI: Simons Auditorium
Speakers: Guillaume Dreyer (University of Notre Dame), Nicolas de Saxce (Université de Paris XIII (Paris-Nord))
Created on Jan 28, 2015 02:07 PM PST
21. # Lorentzian geometric structures seminar

Location: MSRI: Baker Board Room
Created on Feb 23, 2015 11:08 AM PST
22. # GAAHD Research Seminar

Location: MSRI: Simons Auditorium
Updated on Feb 20, 2015 09:52 AM PST
23. # Open ended seminar

Location: MSRI: Baker Board Room
Updated on Mar 06, 2015 09:50 AM PST
24. # Geometry and Analysis of Surface Group Representations

Location: MSRI: Baker Board Room
Speakers: Qiongling Li (Rice University), Andrew Sanders (University of Illinois at Chicago)
Created on Jan 22, 2015 04:40 PM PST
25. # DMS Research Seminar

Location: MSRI: Simons Auditorium
Speakers: Marc Burger (Eidgenössische TH Zürich-Hönggerberg), Fanny Kassel (Université de Lille I (Sciences et Techniques de Lille Flandres Artois))
Updated on Jan 28, 2015 02:14 PM PST

seminar
1. # SeminarLorentzian geometric structures seminar: Affine crystallographic and properly discontinuous groups

Updated on Apr 17, 2015 09:56 AM PDT
2. # SeminarGAAHD Postdoc Seminar: Small generators of integral orthogonal groups

Updated on Apr 03, 2015 11:08 AM PDT
3. # SeminarDMS Postdoc Seminar: Parametrizing Hitchin components

Updated on Apr 03, 2015 10:33 AM PDT
4. # SeminarDMS Research Seminar: MCG actions on character varieties

Updated on Apr 03, 2015 10:43 AM PDT
5. # SeminarLorentzian geometric structures seminar: Strip deformations, crooked planes and Margulis spacetimes

Updated on Apr 03, 2015 11:19 AM PDT
6. # SeminarGeometry and Analysis of Surface Group Representations: Asymptotic Teichmüller rays

Updated on Apr 03, 2015 11:10 AM PDT
7. # Seminar3-Manifold Seminar: Local convexity of the renormalized volume for acylindrical convex co-compact hyperbolic 3-manifolds at the geodesic class

Updated on Apr 03, 2015 03:17 PM PDT
8. # SeminarOpen ended seminar: Spectral gap, random walk by isometries of Euclidean space, and smoothness of self-similar measures

Updated on Apr 03, 2015 11:16 AM PDT
9. # SeminarGAAHD Research Seminar: Higher Rank and Rigidity of Actions

Updated on Apr 03, 2015 11:15 AM PDT
10. # SeminarMSRI Evans Talk: Dynamics on moduli spaces of flat surfaces - questions and new directions

Updated on Mar 30, 2015 12:00 PM PDT
11. # SeminarGAAHD Postdoc Seminar: The stable type of the mapping class group and some relatively hyperbolic groups and applications to pointwise ergodic averages

Updated on Mar 26, 2015 03:44 PM PDT
12. # SeminarDMS Postdoc Seminar: Coupled Hitchin Equations

Updated on Mar 26, 2015 04:14 PM PDT
13. # SeminarDMS Research Seminar: Renormalized volume, Weil-Petersson geometry and volumes of hyperbolic 3-manifolds that fiber over the circle

Updated on Mar 27, 2015 03:36 PM PDT
14. # SeminarLorentzian geometric structures seminar: Margulis spacetimes and contracting deformations of hyperbolic surfaces II

Updated on Mar 26, 2015 03:39 PM PDT
15. # SeminarGeometry and Analysis of Surface Group Representations: Introduction to Spectral Networks (II)

Updated on Mar 26, 2015 04:16 PM PDT
16. # Seminar3-Manifold Seminar

Created on Jan 29, 2015 09:25 AM PST
17. # SeminarOpen ended seminar: Quantum ergodicity on large graphs

Updated on Mar 26, 2015 03:48 PM PDT
18. # SeminarGAAHD Research Seminar: Density of lattice orbits on homogeneous varieties

Updated on Mar 26, 2015 03:46 PM PDT
19. # SeminarGAAHD Postdoc Seminar: Gap distributions for saddle connections on the octagon

Created on Mar 20, 2015 12:00 PM PDT
20. # SeminarDMS Postdoc Seminar: Andreev's theorem on projective Coxeter polyhedra

Created on Mar 20, 2015 11:57 AM PDT
21. # SeminarMinicourse

Created on Mar 23, 2015 09:57 AM PDT
22. # SeminarDMS Research Seminar: Stable commutator length on mapping class groups

Updated on Mar 20, 2015 11:42 AM PDT
23. # SeminarGeometry and Analysis of Surface Group Representations: Introduction to Spectral Networks

Updated on Mar 20, 2015 11:38 AM PDT
24. # SeminarOpen ended seminar: From dynamics to flat geometry

Updated on Mar 20, 2015 11:48 AM PDT
25. # SeminarGAAHD Research Seminar: Patterson-Sullivan Theory and Orbit Counting for Subgroups of Mapping Class Groups

Updated on Mar 20, 2015 11:47 AM PDT
26. # SeminarLorentzian geometric structures seminar: Margulis spacetimes and contracting deformations of hyperbolic surfaces

Updated on Mar 20, 2015 11:44 AM PDT
27. # SeminarSimplicial volume, barycenter method, and bounded cohomology

Created on Mar 16, 2015 09:03 AM PDT
28. # SeminarMinicourse

Created on Feb 23, 2015 10:43 AM PST
29. # SeminarGeometry and Analysis of Surface Group Representations: Hitchin representations and equivariant minimal surfaces

Updated on Mar 17, 2015 12:08 PM PDT
30. # Seminar3-Manifold Seminar

Created on Jan 29, 2015 09:23 AM PST
There are more then 30 past seminars. Please go to Past seminars to see all past seminars.