Fall Semester sessions of the Academic year 20172018
Organizers: Andrew Yarmola
There will be two parallel reading groups this semester. One group will meet at 11:00 on Tuesdays to go over Random walks on the mapping class group by Maher. The second groupp will meet after lunch on Tuesdays at 13:30 for a minicourse on symmetric spaces.
References
 Maher, Joseph Random walks on the mapping class group, Duke Math. J. Volume 156, Number 3 (2011), 429468.
 Paulin, Frédéric Groupes et géométries, 20132014
 Pecastaing, Vincent Riemannian Symmetric Spaces
 Eberlein, Patrick Geometry of Nonpositively Curved Manifolds, University of Chicago Press, 1996
Upcoming sessions

Tuesday 24 October, 11h00 to 12h50, Venue: Room MNO 6B
Funda Gultepe (University of Luxembourg).
Funda will be continuing our seminar on the paper Random walks on the mapping class group by Maher. The focus this week will be on the outline of the proof. Tuesday 24 October, 13h00 to 14h00, Venue: Room MNO 6B
Vincent Pecastaing (University of Luxembourg).Abstract : In this talk, I will try to illustrate what we have done so far with different examples. I will focus on Weyl chambers in symmetric spaces, and give illustration of classical reduced abstract root systems as restricted root systems of classical realsplit simple Lie algebras, and also describe some nonsplit examples. We then will examine the action of the isotropy on Weyl chambers and relate it to the Weyl group, and we will see it explicitly on the examples.
Past sessions

Tuesday 16 October, 11h00 to 12h30, Venue: Room MNO 6B
Funda Gultepe (University of Luxembourg).
Funda will be continuing our seminar on the paper Random walks on the mapping class group by Maher. The focus this week will be on the the curve complex and relative hyperbolicity. Tuesday 316 October, 13h30 to 14h00, Venue: Room MNO 6B
Vincent Pecastaing (University of Luxembourg).
Vincent will be continuing a reading course on symmetric spaces following the note Groupes et géométries of Frédéric Paulin and Geometry of Nonpositively Curved Manifolds by Patrick Eberlein. 
Monday 9 October, 15h00 to 16h00, Venue: Room MNO 6A
Olivier Glorieux (University of Luxembourg).
Olivier will give the second talk for the minicourse on symmetric spaces. His talk will borrow from Geometry of Nonpositively Curved Manifolds by Partick Eberlein. Tuesday 3 October, 11h00 to 12h30, Venue: Room MNO 6B
Binbin Xu (University of Luxembourg).
Binbin will give the second talk on the paper Random walks on the mapping class group. 
Tuesday 3 October, 11h00 to 12h30, Venue: Room MNO 6B
Binbin Xu (University of Luxembourg).
Binbin will give the first talk on the paper Random walks on the mapping class group. Tuesday 3 October, 13h30 to 14h00, Venue: Room MNO 6B
Vincent Pecastaing (University of Luxembourg).
Vincent will give the first talk for the minicourse on symmetric spaces. His talk will follow the notes Groupes et géométries by Frédéric Paulin.
Spring Semester sessions of the Academic year 20162017
Organizers: Andrew Yarmola and Vincent Pecastaing
The first half of the semester will be devoted to the proof of the Zimmer Conjecture.
References
 Aaron Brown, David Fisher, Sebastian Hurtado Zimmer's conjecture: Subexponential growth, measure rigidity, and strong property (T), 2016.
Past sessions

Thursday 6 April, 11h00 to 12h30, Venue: Room S.5A
Olivier Glorieux (University of Luxembourg).
Olivier Glorieux will give the second talk on uniform subexponential growth of derivatives. A first step in the proof of the Zimmer Conjecture. 
Thursday 30 March, 11h00 to 12h30, Venue: Room S.5A
Olivier Glorieux (University of Luxembourg).
Olivier Glorieux will give the first talk on uniform subexponential growth of derivatives. A first step in the proof of the Zimmer Conjecture. 
Thursday 23 March, 11h00 to 12h30, Venue: Room S.5A
Vincent Pecastaing (University of Luxembourg).
Vincent Pecastaing will give the second talk in a series on the Zimmer Conjecture. He will talk about super rigidity of cocycles. 
Thursday 09 March, 11h00 to 12h30, Venue: Room S.5A
Vincent Pecastaing (University of Luxembourg).
Vincent Pecastaing will give the first talk in a series on the Zimmer Conjecture. He will provide background and talk about super rigidity of cocycles.
Autumn Semester sessions of the Academic year 20162017
Organizers: Daniel Monclair and Andrew Yarmola
Unless otherwise specified, the reading group will meet on Tuesday, 12h30  14h00, Room G002Contact: Daniel Monclair (daniel.monclair at uni.lu) or Andrew Yarmola (andrew.yarmola at uni.lu)
The first sessions will be devoted to the pressure metric on Teichmüller space, finishing the series of talks on the pressure metric for Anosov representations.
References
 Curtis McMullen , Thermodynamics, dimension and the WeilPetersson metric, 2006.
References
 Yves Benoist, Domique Hulin , Quasiisometric harmonic maps between rank one symmetric spaces, 2015.
 P. Li and J. Wang. Harmonic rough isometries into Hadamard space. Asian J. Math., 2:419–442, 1998
 P. Pansu. Métriques de CarnotCarathéodory et quasiisométries des espaces symétriques de rang un. Ann. of Math., 129:1–60, 1989.
Past sessions

Tuesday 17 January, 12h30 to 14h00, Venue: Room G002
Daniel Matei (IMAR Bucharest).
Analytic and topological torsionAbstract: We discuss the RaySinger analytic torsion and the ReidemeisterFranz topological torsion of odddimensional manifolds with a focus on dimension 3, and their connections to volume, homology growth and various zeta functions.

Tuesday 20 December, 12h30 to 14h00, Venue: Room G002
Qiyu Chen (University of Luxembourg).
Heat kernel and determinant of the Laplacian on finite area Euclidean sectors.Abstract: The Thurston metric was originally introduced by Thurston for the study of hyperbolic surfacesof finite type without boundary. For surfaces of finite type with boundary, a modification of the Thurstonmetric, the socalled arc metric, was studied.It is a naturalproblem whether the Thurston metric is welldefined in Teichmüller spaces of surfaces of infinite type. We will show how to generalize thearc metric to hyperbolic surfaces of infinite type with boundary, under a geometric condition ( introduced by K. Matsuzaki). We will also present several examples for these surfaces anddiscuss the relationbetween this geometric condition andthe Shiga's condition.This is a joint work with L. Liu.

Tuesday 13 December, 12h30 to 14h00, Venue: Room G002
Andrea Tamburelli (University of Luxembourg).
The volume of the convex core of GHMC Antide Sitter 3manifolds.Abstract: Motivated by the work of Brock that provides estimates for the volume of the convex core of quasiFuchsian manifolds in terms of the WeilPetersson distance of the conformal structures at infinity, we study the analogous question for the convex core of GHMC AdS manifolds. We will show that the volume of the convex core is roughly equivalent to the L^1 distance between the left and right metrics and we will then compare it to more classical distances (Teichmuller, Thurston and WeilPetersson) defined on Teichmuller space. This is a joint work with F. Bonsante and A. Seppi.

Thursday 29 November, 12h30 to 14h00, Venue: Room G002
Andrew Yarmola (University of Luxembourg).
Quasiisometric harmonic maps between rank one symmetric spaces  VI 
Thursday 22 November, 12h30 to 14h00, Venue: Room G002
Andrew Yarmola (University of Luxembourg).
Quasiisometric harmonic maps between rank one symmetric spaces  V 
Tuesday 15 November, 12h30 to 14h00, Venue: Room G002
Clara Aldana (University of Luxembourg).
Heat kernel and determinant of the Laplacian on finite area Euclidean sectors.Abstract: I will talk about a variational Polyakov formula for the determinant of the Laplace operator on finite area Euclidean sectors. This formula shows how the zetaregularized determinant of the Laplacian varies with respect to the opening angle of the sector. I will not concentrate on the differentiation of the determinant (or the spectral zeta function) but in the actual computation of the variation in terms of the trace of the heat operator multiplied by the operator multiplication by the conformal factor. I will explain how we compute explicitly all the contributions to this formula coming from the different parts of the sector. Time permitting, I will mention how to compute the zetaregularized determinant of rectangular domains of unit area and how this is uniquely maximized by the square. The results presented in the talk are in collaboration with Julie Rowlett.

Thursday 3 November, 14h00 to 15h30, Venue: Room G002
Andrew Yarmola (University of Luxembourg).
Quasiisometric harmonic maps between rank one symmetric spaces  IV 
Tuesday 18 October, 12h30 to 14h00, Venue: Room G002
Qiyu Chen (University of Luxembourg).
Quasiisometric harmonic maps between rank one symmetric spaces  III 
Tuesday 11 October, 11h30 to 13h00, Venue: Room G002
Qiyu Chen (University of Luxembourg).
Quasiisometric harmonic maps between rank one symmetric spaces  II 
Tuesday 4 October, 11h30 to 13h00, Venue: Room G002
Andrea Tamburelli (University of Luxembourg).
Quasiisometric harmonic maps between rank one symmetric spaces  I 
Tuesday 27 September, 13:45 to 15:15, Venue: Room G002
Nicolas Tholozan (University of Luxembourg).
The Pressure Metric on Teichmüller Space  II 
Tuesday 20 September, 11:30 to 13:00, Venue: Room G004
Nicolas Tholozan (University of Luxembourg).
The Pressure Metric on Teichmüller Space  I
Spring Semester sessions of the Academic year 20152016
Organizer: JeanMarc Schlenker, Daniel Monclair and Hengnan Hu
Unless otherwise specified, the reading group will meet on Wednesday, 3:30 p.m  4:30 p.m. at Room B14 (Campus Kirchberg)Contact: Hengnan Hu (hengnan.hu at uni.lu)
References
 Martin Bridgeman, Richard Canary and Andrés Sambarino, An introduction to pressure metrics on higher Teichmüller spaces, 2015, (ArXiv).
 Martin Bridgeman, Richard Canary, Francois Labourie and Andrés Sambarino, The pressure metric for Anosov representations, 2013, (ArXiv).
 Francois Labourie, Anosov Flows, Surface Groups and Curves in Projective Space, 2004, (ArXiv).
 Rufus Bowen, The Equidistribution of Closed Geodesics, 1972, (American Journal of Mathematics).
 Rufus Bowen, Periodic Orbits for Hyperbolic Flows, 1972, (American Journal of Mathematics).
Upcoming sessions

22 June (Wednesday), 3:30 p.m  4:30 p.m, Venue: Room B14
Nicolas Tholozan (University of Luxembourg).
Introduction to Anosov representation  V
Past sessions

11 May (Wednesday), 3:30 p.m  4:30 p.m, Venue: Room B14
Daniel Monclair (University of Luxembourg).
Introduction to Anosov representation  IV 
4 May (Wednesday), 3:30 p.m  4:30 p.m, Venue: Room B14
Daniel Monclair (University of Luxembourg).
Introduction to Anosov representation  III 
27 Apr (Wednesday), 3:30 p.m  4:30 p.m, Venue: Room B14
Daniel Monclair (University of Luxembourg).
Introduction to Anosov representation  II 
20 Apr (Wednesday), 3:30 p.m  4:30 p.m, Venue: Room B14
Daniel Monclair (University of Luxembourg).
Introduction to Anosov representation  I 
11 Apr (Monday), 2 p.m  3 p.m, Venue: Room A02
Daniel Matei ( IMAR, Bucharest).
An Introduction to character varieties  II 
6 Apr (Wednesday), 3:30 p.m  4:30 p.m, Venue: Room B14
Daniel Matei ( IMAR, Bucharest).
An Introduction to character varieties  I
Autumn Semester sessions of the Academic year 20152016
Organizer: JeanMarc Schlenker, Daniel Monclair and Hengnan Hu
Unless otherwise specified, the reading group will meet on Wednesday, 1:30 p.m  2:30 p.m. at Room B21Contact: Hengnan Hu (hengnan.hu at uni.lu)
References
 Martin Bridgeman, Richard Canary and Andrés Sambarino, An introduction to pressure metrics on higher Teichmüller spaces, 2015, (ArXiv).
 Martin Bridgeman, Richard Canary, Francois Labourie and Andrés Sambarino, The pressure metric for Anosov representations, 2013, (ArXiv).
 Francois Labourie, Anosov Flows, Surface Groups and Curves in Projective Space, 2004, (ArXiv).
 Rufus Bowen, The Equidistribution of Closed Geodesics, 1972, (American Journal of Mathematics).
 Rufus Bowen, Periodic Orbits for Hyperbolic Flows, 1972, (American Journal of Mathematics).
Past sessions

2 Dec (Wednesday), 1:30 p.m  2:30 p.m, Venue: Room B21
Nicolas Tholozan (University of Luxembourg).
Introduction to Anosov representation  III 
25 Nov (Wednesday), 1:30 p.m  2:30 p.m, Venue: Room B21
Nicolas Tholozan (University of Luxembourg).
Introduction to Anosov representation  II 
11 Nov (Wednesday), 1:30 p.m  2:30 p.m, Venue: Room B21
Nicolas Tholozan (University of Luxembourg).
Introduction to Anosov representation  I 
4 Nov (Wednesday), 1:30 p.m  2:30 p.m, Venue: Room B21
Andrea Tamburelli (University of Luxembourg).
Geodesic flows on hyperbolic surfaces  II 
28 Oct (Wednesday), 1:30 p.m  2:30 p.m, Venue: Room B21
Andrea Tamburelli (University of Luxembourg).
Geodesic flows on hyperbolic surfaces  I 
21 Oct (Wednesday), 1:30 p.m  2:30 p.m, Venue: Room B21
JeanMarc Schlenker (University of Luxembourg).
Introduction to pressure metric  II 
07 Oct (Wednesday), 1:30 p.m  2:30 p.m, Venue: Room B21
JeanMarc Schlenker (University of Luxembourg).
Introduction to pressure metric  I
Spring Semester sessions of the Academic year 20142015
Organizer: JeanMarc Schlenker, Jérémy Toulisse and Nicolas Tholozan
Unless otherwise specified, the reading group will meet on on Monday, 2:00 p.m to 3:30 p.m Room B14.Contact: Jérémy Toulisse
Past sessions

28 May (Thursday) 2 p.m at Venue: Room ?
Clara Aldana (University of Luxembourg).
Markovich's proof of Schoen's conjecture. 
18 May (Monday) at Venue: Room B21
Jérémy Toulisse (University of Luxembourg).
Geometrization of the Hitchin component in PSL(4,R)  II. 
14 May (Thursday) 2 p.m at Venue: Room B24A
Jérémy Toulisse (University of Luxembourg).
Geometrization of the Hitchin component in PSL(4,R)  I. 
30 April (Thursday) 2 p.m at Venue: Room B24A
JeanMarc Schlenker (University of Luxembourg).
Antide Sitter and Margulis spacetimes (after DancigerGuéritaudKassel). 
30 March (Monday)
Nicolas Tholozan (University of Luxembourg).
Closed antide Sitter spacetimes (after GuéritaudKassel). 
23 March (Monday)
JeanMarc Schlenker (University of Luxembourg).
Introduction to antide Sitter geometry in dimension 3
Other Seminars
 Geometry and Topology seminar.
 Informal lunch seminar Computer Science meets Mathematics.
 Colloquium.
 General Mathematics Seminar.
 Seminar for PhD candidates.