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Description The Abdus Salam International Centre for Theoretical Physics (ICTP) is organizing an Advanced School and Workshop on Geometry of Discrete Actions, which will be held at the ICTP, Trieste, Italy, from 24 August to 4 September 2015.

The study of discrete actions of groups and semi-groups plays a central role in geometry. This originates in the pioneering work of H. Poincaré over a century ago, studying solutions of certain differential equations on the complex line. This led to the concept of Fuchsian and Kleinian groups: these are discrete groups of automorphisms of the Riemann sphere. They turn out to be closely related to hyperbolic geometry, where Fuchsian and Kleinian groups are groups of isometries of hyperbolic two and three-dimensional spaces. The study of these types of discrete group actions, and their generalizations to higher dimensions and to other geometries, plays a major role in complex geometry and in holomorphic dynamics. There is a vast field of research waiting to be explored, as for instance in complex hyperbolic geometry, holomorphic dynamics in several complex variables, Lorentzian geometry, etc.
The aim of this School and Workshop is to introduce young mathematicians to the foundations of the field, some of its major developments and tools used for its study. The meeting will start with courses to provide the foundations of the theory. Then an advanced workshop will lead the participants to some of the important areas of current research in the topic in the areas of complex and Lorentzian geometry, Teichmüller theory, moduli spaces and holomorphic dynamics.


MAIN TOPICS:
  • Real hyperbolic geometry
  • Complex hyperbolic geometry
  • Kleinian groups
  • Discrete group actions on complex manifolds
  • Complex affine geometry
  • Lorentzian geometry
  • Holomorphic dynamics
  • Endomorphisms of projective spaces. Fatou sets
  • Complex representations of fundamental groups
  • Moduli spaces of dynamical systems and representations
  • Topology and dynamics of character varieties
  • Teichmüller theory 

Courses (24-28 August):
 
Bertrand Deroin (ENS Paris, France):  Complex Dynamics and Character varieties
Todd Drumm (Howard University, U.S.A.): Lorentzian geometry
Romain Dujardin (Université Paris Est Marne la Vallée, France): Introduction to holomorphic dynamics
François Guéritaud (Laboratoire Paul-Painlevé, France): Hyperbolic surfaces and Teichmüller theory
John Parker (Durham University, U.K.): Complex hyperbolic geometry
José Seade (Universidad Nacional Autónoma de México, Mexico): Limit sets of discrete groups
 
Workshop (31 August-4 September):
 
The tentative list of invited speakers for the Workshop includes:
J. Athreya (University of Illinois at Urbana-Champaign, U.S.A.);
S. Baba (University of Heidelberg, Germany);
C. Cabrera (UNAM, Cuernavaca, Mexico);
R. D. Canary (University of Michigan, USA);
A. Cano (UNAM, Cuernavaca, Mexico);
V. Charette (Université de Sherbrooke, Canada);
M. Deraux (Fourier Institut, Grenoble, France);
D. Dumas (University of Illinois at Chicago, U.S.A.);
S. Dumitrescu (Université Nice Sophia Antipolis, France)
E. Falbel (Université Pierre et Marie Curie, Paris, France);
W. Goldman (University of Maryland, U.S.A.);
K. Gongopadhyay (IISER Mohali, India);
A. Guillot (UNAM, Cuernavaca, Mexico);
N. Gusevskii (UFMG, Belo Horizonte, Brazil);
F. Kassel (Université Lille, France);
R. Kellerhals (University of Fribourg, Switzerland);
R. Kulkarni (IIT Mumbai, India);
C. Leininger (University of Illinois at Urbana-Champaign, U.S.A.);
Mahan Mj (RKM Vivekananda University, India);
S. P. Tan (National University of Singapore, Singapore);
C. Series (University of Warwick, U.K.);
N. Tholozan (University of Luxembourg, Luxembourg);
A. Verjovsky (UNAM, Cuernavaca, Mexico);
T. Ward (Durham University, U.K.);
P. Will (Fourier Institut, Grenoble, France).


PARTICIPATION
Applicants from all countries that are members of the United Nations, UNESCO or IAEA may attend. As the School and Workshop will be conducted in English, participants should have an adequate working knowledge of this language. Although the main purpose of the Centre is to help research workers from developing countries through a programme of training activities within a framework of international cooperation, a limited number of students from developed countries are also welcome to attend.
As a rule, travel and subsistence expenses of the participants should be supported by their home Institutions. Every effort should be made by candidates to secure support for their fare, (or at least half fare). However, limited funds are available for some participants, who are nationals of, and working in, a developing country. Such supports are available only to those attending the entire activity.
There is no registration fee.

APPLICATION:
The deadline for application expired on 30 April 2015.

Material

Advanced School and Workshop on Geometry of Discrete Actions | (smr 2750)
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  • Monday, 24 August 2015
    • 08:30 - 18:15
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 08:30 Registration and administrative formalities 1h30' 
        IMPORTANT: From Monday 24 to Friday 28 August included the activity will take place at Adriatico Guest House (Kastler Lecture Room - lower level), while from 31 August to 4 September the venue  of the activity will be Leonardo Building - Budinich Lecture Hall.

Registration will be carried out at Adriatico Guest House, in front of Kastler Lecture Hall.
        Material: Extra Shuttle Service
      • 10:30 Opening 15'
      • 10:45 Course on Lorentzian geometry - Part 1 1h15'
        Speaker: T. Drumm (Howard University - USA)
        Material: Reference material Slides Video
      • 12:00 Lunch Break 2h0' ( Adriatico Guest House - Cafeteria )
      • 14:00 Course on Complex dynamics and character varieties - Part 1 1h15'
        Speaker: B. Deroin (Ecole Normale Supérieure, Paris - France)
        Material: Video
      • 15:15 Break 15'
      • 15:30 Course on Complex hyperbolic geometry - Part 1 1h15'
        Speaker: J. Parker (University of Durham - UK)
        Material: Video
      • 16:45 Break 15'
      • 17:00 Course on Hyperbolic surfaces and Teichmüller theory - Part 1 1h15'
        Speaker: F. Guéritaud (Laboratoire Paul Painlevé, Lille - France)
        Material: Video
  • Tuesday, 25 August 2015
    • 09:00 - 18:15
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 09:00 Course on Limit sets of discrete groups - Part 1 1h15'
        Speaker: J. Seade (UNAM - Mexico)
        Material: Course Material Video
      • 10:15 Coffee Break 30' ( Adriatico Guest House - Terrace )
      • 10:45 Course on Lorentzian geometry - Part 2 1h15'
        Speaker: T. Drumm (Howard University - USA)
        Material: Slides Video
      • 12:00 Lunch Break 2h0' ( Adriatico Guest House - Cafeteria )
      • 14:00 Course on Complex dynamics and character varieties - Part 2 1h15'
        Speaker: B. Deroin (Ecole Normale Supérieure, Paris - France)
        Material: Video
      • 15:15 Break 15'
      • 15:30 Course on Introduction to holomorphic dynamics - Part 1 1h15'
        Speaker: R. Dujardin (LAMA, Université Paris Est Marne la vallée - France)
        Material: Video
      • 16:45 Break 15'
      • 17:00 Informal Discussion 1h15'
  • Wednesday, 26 August 2015
    • 09:00 - 18:15
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 09:00 Course on Limit sets of discrete groups - Part 2 1h15'
        Speaker: J. Seade (UNAM - Mexico)
        Material: Video
      • 10:15 Coffee Break 30' ( Adriatico Guest House - Terrace )
      • 10:45 Course on Complex hyperbolic geometry - Part 2 1h15'
        Speaker: J. Parker (University of Durham - UK)
        Material: Video
      • 12:00 Lunch Break 2h0' ( Adriatico Guest House - Cafeteria )
      • 14:00 Course on Complex dynamics and character varieties - Part 3 1h15'
        Speaker: B. Deroin (Ecole Normale Supérieure, Paris - France)
        Material: Video
      • 15:15 Break 15'
      • 15:30 Course on Hyperbolic surfaces and Teichmüller theory - Part 2 1h15'
        Speaker: F. Guéritaud (Laboratoire Paul Painlevé, Lille - France)
        Material: Video
      • 16:45 Break 15'
      • 17:00 Informal Discussion 1h15'
  • Thursday, 27 August 2015
    • 09:00 - 18:15
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 09:00 Course on Complex hyperbolic geometry - Part 3 1h15'
        Speaker: J. Parker (University of Durham - UK)
        Material: Video
      • 10:15 Coffee Break 30' ( Adriatico Guest House - Terrace )
      • 10:45 Course on Lorentzian geometry - Part 3 1h15'
        Speaker: T. Drumm (Howard University - USA)
        Material: Slides Video
      • 12:00 Lunch Break 2h0' ( Adriatico Guest House - Cafeteria )
      • 14:00 An introduction to higher Teichmüller Theory 1h15'
        Speaker: D. Canary (University of Michigan - USA)
        Material: Slides Video
      • 15:15 Break 15'
      • 15:30 Course on Introduction to holomorphic dynamics - Part 2 1h15'
        Speaker: R. Dujardin (LAMA, Université Paris Est Marne la vallée - France)
        Material: Video
      • 16:45 Break 15'
      • 17:00 Course on Hyperbolic surfaces and Teichmüller theory - Part 3 1h15'
        Speaker: F. Guéritaud (Laboratoire Paul Painlevé, Lille - France)
        Material: Video
  • Friday, 28 August 2015
    • 09:00 - 12:45
      Location: Adriatico Guest House - Kastler Lecture Hall
      • 09:00 Course on Limit sets of discrete groups - Part 3 1h0'
        Speaker: J. Seade (UNAM - Mexico)
        Material: Video
      • 10:00 Coffee Break 15' ( Adriatico Guest House - Terrace )
      • 10:15 Pressure metrics on higher Teichmüller spaces 1h0'
        Speaker: D. Canary (University of Michigan - USA)
        Material: Slides Video
      • 11:15 Break 15'
      • 11:30 Course on Introduction to holomorphic dynamics - Part 3 1h15'
        Speaker: R. Dujardin (LAMA, Université Paris Est Marne la vallée - France)
        Material: Video
  • Monday, 31 August 2015
    • 09:00 - 16:45
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Quaternionic Kleinian modular groups and arithmetic hyperbolic orbifolds over the quaternions 1h0'
        Speaker: A. Verjovsky (UNAM - Mexico)
        Material: Abstract Video
      • 10:30 Coffee Break 30'
      • 11:00 z-Classes in Geometry and Groups 1h0'
        Speaker: R. S. Kulkarni (IIT Mumbai - India)
        Material: Abstract Slides Video
      • 12:00 Lunch Break 2h0'
      • 14:00 Do limit sets move continuously? 1h0'
        Speaker: C. Series (University of Warwick - UK)
        Material: Abstract Video
      • 15:00 Coffee Break 30'
      • 15:30 Commensurability of hyperbolic Coxeter groups 1h0'
        Speaker: R. Kellerhals (University of Fribourg - Switzerland)
        Material: Abstract Video
  • Tuesday, 1 September 2015
    • 09:30 - 22:30
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Geometric structure on complex curves and algebraic differential equations 1h0'
        Speaker: A. Guillot (UNAM - Mexico)
        Material: Abstract Video
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 On representations of the fundamental group of the whitehead link complement in PU(2,1) 1h0'
        Speaker: P. Will (Fourier Institut, Grenoble - France)
        Material: Abstract Video
      • 12:00 Lunch Break 2h0' ( Leonardo Building - Cafeteria )
      • 14:00 Non-arithmetic complex hyperbolic lattices 1h0'
        Speaker: M. Deraux (Fourier Institut, Grenoble - France)
        Material: Abstract Video
      • 15:00 Coffee Break 30' ( Leonardo Building - Terrace )
      • 15:30 Marked length spectral rigidity for flat metrics 1h0'
        Speaker: C. Leininger (University of Illinois at Urbana-Champaign - USA)
        Material: Abstract Video
      • 16:30 Break 30'
      • 17:00 Conjugation classes of pairs in $\SL(4, \C)$ and $\SU(3, 1)$ 1h0'
        Speaker: K. Gongopadhyay (IISER Mohali - India)
        Material: Abstract Slides Video
      • 19:30 Social Dinner 2h0' ( Leonardo Building - Terrace )
  • Wednesday, 2 September 2015
    • 09:30 - 18:00
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Volume of closed anti-de Sitter 3-manifolds 1h0'
        Speaker: N. Tholozan (University of Luxembourg - Luxembourg)
        Material: Abstract Video
      • 10:30 Coffee Break 30' ( Leonardo Building - Terrace )
      • 11:00 Anti-de Sitter 3-manifolds, Margulis spacetimes, and their higher-dimensional analogues 1h0'
        Speaker: F. Kassel (Université Lille - France)
        Material: Abstract
      • 12:00 Lunch Break 2h0' ( Leonardo Building - Cafeteria )
      • 14:00 The Einstein Universe 1h0'
        Speaker: V. Charette (Université de Sherbrooke - Canada)
        Material: Video
      • 15:00 Coffee Break 30' ( Leonardo Building - Terrace )
      • 15:30 The SL(3,C)-character variety of fundamental groups of cusped 3-manifolds. 1h0'
        Speaker: E. Falbel (Université Pierre et Marie Curie, Paris - France)
        Material: Abstract Video
      • 16:30 Break 30'
      • 17:00 Poster Session 1h0' 
        Posters will be displayed in the Poster Gallery in the Leonardo da Vinci Building, near the      Budinich Lecture Hall.
The size of the magnetic boards for the posters is mts 1,25 (height) x 1,22 (width).
  • Thursday, 3 September 2015
    • 09:30 - 15:45
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 On Poincaré extensions and cobordisms of rational functions 1h0'
        Speaker: C. A. Cabrera Ocanas (UNAM - Mexico)
        Material: Abstract Video
      • 10:30 Coffee Break 15' ( Leonardo Building - Terrace )
      • 10:45 Holomorphic geometric structures on parallelizable manifolds 1h0'
        Speaker: S. Dumitrescu (Université Nice Sophia Antipolis)
        Material: Abstract Video
      • 11:45 Lunch Break 2h0' ( Leonardo Building - Cafeteria )
      • 13:30 The Kulkarni limit set of complex hyperbolic groups 1h0'
        Speaker: A. Cano (UNAM - Mexico)
        Material: Abstract Video
      • 14:30 Break 15'
      • 14:45 Neck-pinching of CP^1-structures 1h0'
        Speaker: S. Baba (University of Heidelberg - Germany)
        Material: Abstract
    • 16:00 - 18:00 RAMANUJAN PRIZE CERMONY
      Material: video
  • Friday, 4 September 2015
    • 09:30 - 13:15
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Limits of limit sets 1h0'
        Speaker: Mj Mahan (RKM Vivekananda University - India)
        Material: Abstract Video
      • 10:30 Coffee Break 15' ( Leonardo Building - Terrace )
      • 10:45 Problem Session 1h0'
        Material: Video
      • 11:45 Break 30'
      • 12:15 Identities on hyperbolic surfaces 1h0'
        Speaker: S. P. Tan (National University of Singapore - Singapore)
        Material: Abstract Video
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