Reading Seminar on Geometry and Topology

Research Cluster in Low-dimensional Geometry and Topology at University of Luxembourg

Spring Semester sessions of the Academic year 2019-2020

Organizer: Binbin Xu, Miguel Acosta

There will be two parallel reading groups this semester. The first group is about Cannon-Thurston maps for hyperbolic 3-manifolds. The second group is about the realtion between the arithematic properties fo quadratic forms and the hyperbolic geometry.

References

Sessions

  • Thursday 2 July, 11h00 to 12h30, Venue: Webex
    Diptaishik Choudhury (University of Luxembourg)
    The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms. - VI

  • Thursday 25 June, 11h00 to 12h30, Venue: Webex
    Diptaishik Choudhury (University of Luxembourg)
    The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms. - V

  • Tuesday 16 June, 14h00 to 15h30, Venue: Webex
    Binbin Xu (University of Luxembourg)
    Group invariant Peano curves - XVI
    Abstract: The figure eight knot complement and the Peano map in this non-compact case (sections 16-17).

  • Tuesday 9 June, 14h00 to 15h30, Venue: Webex
    Binbin Xu (University of Luxembourg)
    Group invariant Peano curves - XV
    Abstract: The figure eight knot complement and the Peano map in this non-compact case (sections 16-17).

    Thursday 11 June, 11h00 to 12h30, Venue: Webex
    Diptaishik Choudhury (University of Luxembourg)
    The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms. - IV

  • Tuesday 2 June, 14h00 to 15h30, Venue: Webex
    Nhat Minh Doan (University of Luxembourg)
    Group invariant Peano curves - XIV
    Abstract: How to understand the Peano map sections 14-15

    Thursday 4 June, 11h00 to 12h30, Venue: Webex
    Diptaishik Choudhury (University of Luxembourg)
    The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms. - III

  • Tuesday 26 May, 14h00 to 15h30, Venue: Webex
    Nhat Minh Doan (University of Luxembourg)
    Group invariant Peano curves - XIII
    Abstract: How to understand the Peano map sections 14-15

  • Tuesday 19 May, 14h00 to 15h30, Venue: Webex
    Nhat Minh Doan (University of Luxembourg)
    Group invariant Peano curves - XII
    Abstract: How to understand the Peano map sections 14-15

    Thursday 21 May, 11h00 to 12h30, Venue: Webex
    Diptaishik Choudhury (University of Luxembourg)
    The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms. - II

  • Tuesday 12 May, 14h00 to 15h30, Venue: Webex
    Nhat Minh Doan (University of Luxembourg)
    Group invariant Peano curves - XI
    Abstract: How to understand the Peano map sections 14-15

  • Thursday 07 May, 11h00 to 12h30, Venue: Webex
    Diptaishik Choudhury (University of Luxembourg)
    The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms. - I

  • Tuesday 28 April, 14h00 to 15h30, Venue: Webex
    Miguel Acosta (University of Luxembourg)
    Group invariant Peano curves - X
    Abstract: I'll speak about the extension of the main theorem to the one-sided degenerate case (mostly about the ideas of the proof). section 6-7

  • Tuesday 21 April, 14h00 to 15h30, Venue: Webex
    Miguel Acosta (University of Luxembourg)
    Group invariant Peano curves - IX
    Abstract: I will speak about the extension of the main theorem to the one-sided degenerate case (probably I will only explain what the single degenerate case is and leave the proof for the next week). section 6-7

  • Tuesday 14 April, 14h00 to 15h30, Venue: Webex
    Thi Hanh Vo (University of Luxembourg)
    Group invariant Peano curves - VIII
    Abstract: How to construct pseudo-Anosov diffeomorphisms (in particular we will see why they exist !)

  • Tuesday 7 April, 14h00 to 15h30, Venue: Webex
    Filippo Mazzoli(University of Luxembourg)
    Group invariant Peano curves - VII
    Abstract: Proof of the main theorem. section 4-5

  • Tuesday 31 March, 14h00 to 15h30, Venue: Webex
    Filippo Mazzoli(University of Luxembourg)
    Group invariant Peano curves - VI
    Abstract: Proof of the main theorem. section 4-5

  • Tuesday 10 March, 14h00 to 15h30, Venue: Webex
    Diptaishik Choudhury (University of Luxembourg)
    Group invariant Peano curves - IV
    Abstract: Measured laminations and pseudo-Anosov diffeomorphisms. section 11-12

    Thursday 12 March, 14h00 to 15h30, Venue: Webex
    Diptaishik Choudhury (University of Luxembourg)
    Group invariant Peano curves - V
    Abstract: Measured laminations and pseudo-Anosov diffeomorphisms. section 11-12

  • Tuesday 25 February, 14h00 to 15h30, Venue: Webex
    Wai Yeung Lam(University of Luxembourg)
    Group invariant Peano curves - III
    Abstract: Geodesic laminations section 8-9-10

  • Thursday 20 February, 14h00 to 15h30, Venue: Webex
    Wai Yeung Lam(University of Luxembourg)
    Group invariant Peano curves - II
    Abstract: Geodesic laminations section 8-9-10

  • Tuesday 4 February, 14h00 to 15h30, Venue: Webex
    Miguel Acosta(University of Luxembourg)
    Group invariant Peano curves - I
    Abstract: Introduction section 1-2-3

Fall Semester sessions of the Academic year 2019-2020

Organizer: Binbin Xu

There will be two parallel reading groups this semester. The first group is about Mirzakhani's work on the ergodicity of earthquake flow on Teichmüller space. The second group is about uniform lattices of some semi-simple Lie groups.

References

Sessions

  • Thursday 19 December, 11h30 to 12h30, Venue: Room MNO 6B
    Diptaishik Choudhury (University of Luxembourg).
    Mirzakhani's work on the ergodicity of earthquake flow on Teichmüller space - VIII

  • Thursday 12 December, 11h30 to 12h30, Venue: Room MNO 6B
    Diptaishik Choudhury (University of Luxembourg).
    Mirzakhani's work on the ergodicity of earthquake flow on Teichmüller space - VII

  • Tuesday 3 December, 10h00 to 11h00, Venue: Room MNO 5A
    Sourav Ghosh (University of Luxembourg).
    Uniform lattices of some semi-simple Lie groups - V

    Thursday 5 December, 11h30 to 12h30, Venue: Room MNO 6B
    Diptaishik Choudhury (University of Luxembourg).
    Mirzakhani's work on the ergodicity of earthquake flow on Teichmüller space - VI

  • Tuesday 19 November, 10h00 to 11h00, Venue: Room MNO 5A
    Binbin Xu (University of Luxembourg).
    Uniform lattices of some semi-simple Lie groups - IV
    Abstract: Discuss the representation of sl(2) and the sl(2)-triple.

    Thursday 21 November, 11h30 to 12h30, Venue: Room MNO 6B
    Diptaishik Choudhury (University of Luxembourg).
    Mirzakhani's work on the ergodicity of earthquake flow on Teichmüller space - V

  • Tuesday 12 November, 10h00 to 11h00, Venue: Room MNO 5A
    Binbin Xu (University of Luxembourg).
    Uniform lattices of some semi-simple Lie groups - IV
    Abstract: Discuss the representation of sl(2) and the sl(2)-triple.

    Thursday 14 November, 11h30 to 12h30, Venue: Room MNO 6B
    Diptaishik Choudhury (University of Luxembourg).
    Mirzakhani's work on the ergodicity of earthquake flow on Teichmüller space - V

  • Tuesday 29 October, 10h00 to 11h00, Venue: Room MNO 5A
    Sourav Ghosh (University of Luxembourg).
    Uniform lattices of some semi-simple Lie groups - III

    Thursday 31 October, 11h30 to 12h30, Venue: Room MNO 6B
    Yan Mary He (University of Luxembourg).
    Mirzakhani's work on the ergodicity of earthquake flow on Teichmüller space - IV

  • Tuesday 22 October, 11h00 to 12h00, Venue: Room MNO 6A
    Sourav Ghosh (University of Luxembourg).
    Uniform lattices of some semi-simple Lie groups - II

    Thursday 24 October, 11h30 to 12h30, Venue: Room MNO 6B
    Yan Mary He (University of Luxembourg).
    Mirzakhani's work on the ergodicity of earthquake flow on Teichmüller space - III

  • Tuesday 15 October, 11h00 to 12h00, Venue: Room MNO 6A
    Sourav Ghosh (University of Luxembourg).
    Uniform lattices of some semi-simple Lie groups - I

    Thursday 17 October, 11h30 to 12h30, Venue: Room MNO 6A
    Diptaishik Choudhury (University of Luxembourg).
    Mirzakhani's work on the ergodicity of earthquake flow on Teichmüller space - II

  • Thursday 10 October, 11h30 to 12h30, Venue: Room MNO 6A
    Diptaishik Choudhury (University of Luxembourg).
    Mirzakhani's work on the ergodicity of earthquake flow on Teichmüller space - I

Spring Semester sessions of the Academic year 2018-2019

Organizer: Binbin Xu

There will be two parallel reading groups this semester. The papers for the first group are "Symplectic natural of fundamental groups of surfaces" by Goldman and "Moment maps in differential geometry" by Donaldson. The second group is about thermodynamic formalism and pressure metric.

References

Sessions

  • Thursday 27 June, 14h00 to 15h00, Venue: Room MNO 6A
    Filippo Mazzoli (University of Luxembourg)
    Hyperkähler structure on moduli space - XVI

    Friday 28 June, 11h00 to 12h00, Venue: Room MNO 6A
    Yan Mary He (University of Luxembourg)
    The pressure metric for Anosov representations - VII

  • Friday 14 June, 11h00 to 12h00, Venue: Room MNO 6A
    Yan Mary He (University of Luxembourg)
    The pressure metric for Anosov representations - VI

  • Thursday 6 June, 14h00 to 15h00, Venue: Room MNO 6A
    Filippo Mazzoli (University of Luxembourg)
    Hyperkähler structure on moduli space - XV

    Friday 7 June, 11h00 to 12h00, Venue: Room MNO 6A
    Yan Mary He (University of Luxembourg)
    The pressure metric for Anosov representations - V

  • Thursday 23 May, 14h00 to 15h00, Venue: Room MNO 6A
    Filippo Mazzoli (University of Luxembourg)
    Hyperkähler structure on moduli space - XIV

  • Friday 10 May, 11h00 to 12h00, Venue: Room MNO 6A
    Yan Mary He (University of Luxembourg).
    The pressure metric for Anosov representations - IV

  • Thursday 2 May, 14h00 to 15h00, Venue: Room MNO 6A
    Filippo Mazzoli (University of Luxembourg).
    Hyperkähler structure on moduli space - XIII

  • Thursday 25 April, 14h00 to 15h00, Venue: Room MNO 6A
    Filippo Mazzoli (University of Luxembourg).
    Hyperkähler structure on moduli space - XII

    Friday 26 April, 11h00 to 12h00, Venue: Room MNO 6A
    Binbin Xu (University of Luxembourg).
    The pressure metric for Anosov representations - III
    Abstract: I'll talk about the definition of Anosov representations and their associated flows.

  • Thursday 18 April, 14h00 to 15h00, Venue: Room MNO 6A
    Filippo Mazzoli (University of Luxembourg).
    Hyperkähler structure on moduli space - XI

    Friday 19 April, 11h00 to 12h00, Venue: Room MNO 6A
    Binbin Xu (University of Luxembourg).
    The pressure metric for Anosov representations - II
    Abstract: I'll talk about the definition of Anosov representations and their associated flows.

  • Friday 5 April, 11h00 to 12h00, Venue: Room MNO 6A
    Yan Mary He (University of Luxembourg).
    The pressure metric for Anosov representations - I
    Abstract: Discuss the Teichmüller space case to have an idea about the pressure metric

Fall Semester sessions of the Academic year 2018-2019

Organizer: Binbin Xu

There will be two parallel reading groups this semester. The papers for the first group are "Symplectic natural of fundamental groups of surfaces" by Goldman and "Moment maps in differential geometry" by Donaldson. The paper for the second group is "Anosov representations: Dynamical and geometric characterizations" by Kapovich-Leeb-Porti.

References

Sessions

  • Tuesday 22 January, 10h45 to 11h45, Venue: Room MNO 5A
    Andrea Seppi (University of Luxembourg)
    Hyperkähler structure on moduli space - X

  • Tuesday 18 December, 12h45 to 13h45, Venue: Room MNO 6A
    Andrea Seppi (University of Luxembourg)
    Hyperkähler structure on moduli space - IX

  • Tuesday 11 December, 12h45 to 13h45, Venue: Room MNO 6A
    Andrea Seppi (University of Luxembourg)
    Hyperkähler structure on moduli space - VIII

  • Tuesday 4 December, 12h45 to 13h45, Venue: Room MNO 6A
    Andrea Seppi (University of Luxembourg)
    Hyperkähler structure on moduli space - VII
    Abstract: I will continue the construction of Teichmüller space as a symplectic reduction.

    Thursday 6 December, 14h00 to 15h00, Venue: Room MNO 6A
    Louis Merlin (University of Luxembourg)
    Anosov representations in higher rank Lie groups - VII

  • Tuesday 27 November, 12h45 to 13h45, Venue: Room MNO 6B
    Andrea Seppi (University of Luxembourg)
    Hyperkähler structure on moduli space - VI
    Abstract: I will start talking about the construction of Teichmüller space as a symplectic reduction.

    Thursday 29 November, 14h00 to 15h00, Venue: Room MNO 6A
    Louis Merlin (University of Luxembourg)
    Anosov representations in higher rank Lie groups - VI

  • Tuesday 13 November, 10h45 to 11h45, Venue: Room MNO 5A
    Filippo Mazzoli (University of Luxembourg)
    Hyperkähler structure on moduli space - V

  • Tuesday 6 November, 12h45 to 13h45, Venue: Room MNO 5A
    Filippo Mazzoli (University of Luxembourg).
    Hyperkähler structure on moduli space - IV
    Abstract: I will continue to talk about symplectic geometry and symplectic reduction on hyperkahler structures.

  • Tuesday 30 October, 10h45 to 11h45, Venue: Room MNO 5A
    Filippo Mazzoli (University of Luxembourg).
    Hyperkähler structure on moduli space - III

    Thursday 1 November, 14h00 to 15h00, Venue: Room MNO 6A
    Vincent Pecastaing (University of Luxembourg).
    Anosov representations in higher rank Lie groups - V

  • Tuesday 23 October, 10h45 to 11h45, Venue: Room MNO 5A
    Filippo Mazzoli (University of Luxembourg).
    Hyperkähler structure on moduli space - II

    Thursday 25 October, 14h00 to 15h00, Venue: Room MNO 6A
    Vincent Pecastaing (University of Luxembourg).
    Anosov representations in higher rank Lie groups - IV

  • Tuesday 16 October, 11h00 to 12h00, Venue: Room MNO 5A
    Andrea Seppi (University of Luxembourg).
    Hyperkähler extensions of Teichmüller space - I
    Abstract: In the first meeting I will recall some notions on the Weil-Petersson geometry of Teichmüller space, Kähler geometry, and I will give an outline of general results which permit to construct hyperkähler extensions of the Weil-Petersson metric.

    Thursday 18 October, 14h00 to 15h00, Venue: Room MNO 6A
    Vincent Pecastaing (University of Luxembourg).
    Anosov representations in higher rank Lie groups - III

Spring Semester sessions of the Academic year 2017-2018

Organizer: Binbin Xu

There will be two parallel reading groups this semester. The paper for the first group is "A topological characterisation of hyperbolic groups" by Bowditch. The paper for the second group is "Lectures on Anosov representations I: Dynamical and geometric characterizations" by Kapovich-Leeb-Porti.

References

Sessions

  • Tuesday 29 May, 10h30 to 11h30, Venue: Room MNO 6B
    Binbin Xu (University of Luxembourg)
    A topological characterization of hyperbolic groups - VII
    Abstract: We will introduce path quasi metric, system of annuli, and the relations among them and cross-ratio. After this, we should be able to sketch the proof of the main theorem. We will skip some details to save some time.

    Thursday 31 May, 11h00 to 12h00, Venue: Room MNO 6B
    Binbin Xu (University of Luxembourg)
    A topological characterization of hyperbolic groups - VIII
    Abstract: We will introduce path quasi metric, system of annuli, and the relations among them and cross-ratio. After this, we should be able to sketch the proof of the main theorem. We will skip some details to save some time.

  • Tuesday 24 April, 10h20 to 11h20, Venue: Room MNO 6A
    Filippo Mazzoli (University of Luxembourg)
    A topological characterization of hyperbolic groups - VI

  • Monday 16 April, 16h00 to 17h00, Venue: Room MNO 6A
    Filippo Mazzoli (University of Luxembourg)
    A topological characterization of hyperbolic groups - V

  • Tuesday 10 April, 10h20 to 11h20, Venue: Room MNO 6A
    Filippo Mazzoli (University of Luxembourg).
    A topological characterization of hyperbolic groups - IV

  • Tuesday 27 March, 10h30 to 11h30, Venue: Room MNO 6B
    Binbin Xu (University of Luxembourg).
    A topological characterization of hyperbolic groups - III

    Abstract : Recall some background on hyperbolic groups.

    Thursday 29 March, 11h00 to 12h00, Venue: Room MNO 6B
    Vincent Pecastaing (University of Luxembourg).
    Anosov representations in higher rank Lie groups - II

    Abstract : Informal discussion about the paper and related topics.

  • Tuesday 20 March, 10h30 to 11h30, Venue: Room MNO 6B
    Binbin Xu (University of Luxembourg).
    A topological characterization of hyperbolic groups - II

    Abstract : Recall some background on hyperbolic groups.

    Thursday 22 March, 11h00 to 12h00, Venue: Room MNO 6B
    Vincent Pecastaing (University of Luxembourg).
    Anosov representations in higher rank Lie groups - I

  • Tuesday 13 March, 16h00 to 17h00, Venue: Room MNO 6B
    Funda Gultepe (University of Luxembourg).
    A topological characterization of hyperbolic groups - I

Fall Semester sessions of the Academic year 2017-2018

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 group will meet after lunch on Tuesdays at 13:30 for a minicourse on symmetric spaces.

References

Sessions

  • Tuesday 05 December, 11h00 to 12h30, Venue: Room MNO 6B
    Andrew Yarmola (University of Luxembourg)
    Random walks on the mapping class group - VII
    Abstract: We plan to finish the proof of the main result.

    Wednesday 06 December, 11h00 to 12h30, Venue: Room MNO 6A
    Vincent Pecastaing (University of Luxembourg)
    Minicourse on symmetric spaces - VIII

  • Tuesday 28 November, 11h00 to 12h30, Venue: Room MNO 6B
    Andrew Yarmola (University of Luxembourg)
    Random walks on the mapping class group - VI
    Abstract: The focus this week will be the proof of the main result.

    Thursday 30 November, 14h00 to 15h30, Venue: Room MNO 6B
    Vincent Pecastaing (University of Luxembourg)
    Minicourse on symmetric spaces - VII

  • Tuesday 14 November, 11h00 to 12h30, Venue: Room MNO 6B
    Andrew Yarmola (University of Luxembourg)
    Random walks on the mapping class group - V
    Abstract: The focus this week will be to prove half of the main result.

    Tuesday 14 November, 13h30 to 15h00, Venue: Room MNO 6B
    Olivier Glorieux (University of Luxembourg)
    Minicourse on symmetric spaces - VI

  • Tuesday 07 November, 13h30 to 15h00, Venue: Room MNO 6B
    Olivier Glorieux (University of Luxembourg)
    Minicourse on symmetric spaces - V

  • Tuesday 24 October, 11h00 to 12h30, Venue: Room MNO 6B
    Funda Gultepe (University of Luxembourg).
    Random walks on the mapping class group - IV
    Abstract: The focus this week will be on the outline of the proof.

    Tuesday 24 October, 13h00 to 14h30, Venue: Room MNO 6B
    Vincent Pecastaing (University of Luxembourg).
    Minicourse on symmetric spaces - IV
    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 real-split simple Lie algebras, and also describe some non-split 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.

  • Tuesday 16 October, 11h00 to 12h30, Venue: Room MNO 6B
    Funda Gultepe (University of Luxembourg).
    Random walks on the mapping class group - III

    Abstract : The focus this week will be on the the curve complex and relative hyperbolicity.

    Tuesday 16 October, 13h30 to 15h00, Venue: Room MNO 6B
    Vincent Pecastaing (University of Luxembourg).
    Minicourse on symmetric spaces - III

  • Monday 9 October, 15h00 to 16h30, Venue: Room MNO 6A
    Olivier Glorieux (University of Luxembourg).
    Minicourse on symmetric spaces - II

    Tuesday 3 October, 11h00 to 12h30, Venue: Room MNO 6B
    Binbin Xu (University of Luxembourg).
    Random walks on the mapping class group - II

  • Tuesday 3 October, 11h00 to 12h30, Venue: Room MNO 6B
    Binbin Xu (University of Luxembourg).
    Random walks on the mapping class group - I

    Tuesday 3 October, 13h30 to 15h00, Venue: Room MNO 6B
    Vincent Pecastaing (University of Luxembourg).
    Minicourse on symmetric spaces - I

Spring Semester sessions of the Academic year 2016-2017

Organizers: Andrew Yarmola and Vincent Pecastaing

The first half of the semester will be devoted to the proof of the Zimmer Conjecture.

References

Sessions

  • Thursday 6 April, 11h00 to 12h30, Venue: Room S.5A
    Olivier Glorieux (University of Luxembourg)
    Abstract: 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)
    Abstract: 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)
    Abstract: 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)
    Abstract: 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.

Fall Semester sessions of the Academic year 2016-2017

Organizers: Daniel Monclair and Andrew Yarmola

Unless otherwise specified, the reading group will meet on Tuesday, 12h30 - 14h00, Room G002
Contact: 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

After this, we will study the recent solution by Benoist and Hulin of the Schoen-Li-Wang conjecture: every quasiisometric map between rank one symmetric spaces is within bounded distance of a (unique) harmonic map.

References

Sessions

  • Tuesday 17 January, 12h30 to 14h00, Venue: Room G002
    Daniel Matei (IMAR Bucharest)
    Analytic and topological torsion
    Abstract: We discuss the Ray-Singer analytic torsion and the Reidemeister-Franz topological torsion of odd-dimensional 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 so-called arc metric, was studied.It is a naturalproblem whether the Thurston metric is well-defined 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 Anti-de Sitter 3-manifolds.
    Abstract: Motivated by the work of Brock that provides estimates for the volume of the convex core of quasi-Fuchsian manifolds in terms of the Weil-Petersson 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 Weil-Petersson) 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 zeta-regularized 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 zeta-regularized 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 2015-2016

Organizer: Jean-Marc 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, François Labourie and Andrés Sambarino, The pressure metric for Anosov representations, 2013, (ArXiv).

  • François 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).

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

  • 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

Fall Semester sessions of the Academic year 2015-2016

Organizer: Jean-Marc 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 B21
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, François Labourie and Andrés Sambarino, The pressure metric for Anosov representations, 2013, (ArXiv).

  • François 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).

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
    Jean-Marc Schlenker (University of Luxembourg)
    Introduction to pressure metric - II

  • 07 Oct (Wednesday), 1:30 p.m - 2:30 p.m, Venue: Room B21
    Jean-Marc Schlenker (University of Luxembourg)
    Introduction to pressure metric - I

Spring Semester sessions of the Academic year 2014-2015

Organizer: Jean-Marc 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

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
    Jean-Marc Schlenker (University of Luxembourg)
    Anti-de Sitter and Margulis spacetimes (after Danciger-Guéritaud-Kassel).

  • 30 March (Monday)
    Nicolas Tholozan (University of Luxembourg)
    Closed anti-de Sitter spacetimes (after Guéritaud-Kassel).

  • 23 March (Monday)
    Jean-Marc Schlenker (University of Luxembourg)
    Introduction to anti-de Sitter geometry in dimension 3