Teresópolis (RJ), 20-24 June 2016
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Description: This workshop is an introduction to the study of group actions on manifolds, especially addressed to students and young researchers. One of the main aspects of this subject is represented by the Zimmer program: big groups don't act on small manifolds. In the recent years, several results have been obtained in this direction, mixing techniques of algebraic, geometrical, probabilistic and dynamical nature.

The workshop will be organised in the model proposed by the France-Brazil network in mathematics (intensive workshops for young researchers), which intends to deal with specific though important subjects, with the aim of disseminating to Brazilian and French young researchers.

Practical information: The workshop will take place in Sítio Assunção, a monastery in Teresópolis, a small town which is about 100km far from the center of Rio de Janeiro, in the inland and 900m above the sea. There are several buses connecting Rio de Janeiro to Teresópolis daily.

Scientific committee:

  • Étienne Ghys (CNRS & ENS Lyon)
  • Victor Kleptsyn (CNRS & Université de Rennes)
  • Kathryn Mann (UC Berkeley)
  • Fabio Armando Tal (Universidade de São Paulo)
  • Andrés Navas (Universidad de Santiago de Chile)

Organizers:

  • Sébastien Alvarez (IMPA)
  • Alejandro Kocsard (UFF)
  • Andrés Koropecki (UFF)
  • Emmanuel Militon (Université de Nice)
  • Michele Triestino (UFF)

Preliminary Program
List of registered participants
Brazilian-French Network in Mathematics

Mini-course, by Aaron Brown:
Lecture notes: Entropy, smooth ergodic theory and rigidity of group actions, by Aaron Brown.
With appendices by Sébastien Alvarez, Dominique Malicet, Davi Obata, Mario Roldán, Bruno Santiago and Michele Triestino. Edited by Michele Triestino. Ensaios Matemáticos 33 (2019), Soc. Brasil. Mat. [Ensaios Matemáticos, [arXiv]].
Brown, Rodriguez-Hertz and Wang, Global smooth and topological rigidity of hyperbolic lattice actions
Outline of the mini-course
Topics for students and bibliography: we ask young participants to give talks on topics from the mini-course
List of references suggested by participants who gave talks:
Ledrappier-Young:

  • Ledrappier-Young. "The Metric Entropy of Diffeomorphisms: Part I: Characterization of Measures Satisfying Pesin's Entropy Formula". Ann. Math. (2) 122.3 (1985): 509-39. [JStor]
  • Climenhaga-Katok. "Measure theory through dynamical eyes" (2012). [arXiv]
  • Jiagang Yang. "Entropy along Expanding Foliations" [arXiv]
  • L-S Young. "Ergodic Theory of Differentiable Dynamical Systems". [link]
  • Potrie. "Introduction to non-uniform and partial hyperbolicity" [link]
  • Katok-Hasselblatt. "Introduction to the Modern Theory of Dynamical Systems". Cambridge University Press (1995).
  • Mañé. "Ergodic Theory and Differentiable Dynamics", Springer-Verlag (1987).

Groups:

  • Benoist. "Five lectures on lattices in semisimple Lie groups", available here.
  • Katok. "Fuchsian groups". The University of Chicago Press, Chicago (1992).
  • Maskit. "On Poincaré's theorem for fundamental polygons". Adv. in Math. 7, p. 219-230, (1971).
  • Raghunathan. "Discrete subgroups of Lie groups". Springer-Verlag, Berlin-Heidelberg-New York, (1972).
  • Witte. "Introduction to arithmetic groups" [arXiv]
  • Ghys. "Actions de réseaux sur le cercle". Invent. Math (1999).
  • Witte-Morris. "Can lattices in SL(2,R) act on the circle?" In Geometry, Rigidity, and Group Actions, University of chicago press, 2011.
  • Ghys. "Groups acting on the circle" Ens. Math, (2001)
  • Navas. "Groups of circle diffeomorphisms" University of chicago press (2011) [arXiv]. Also available in spanish: "Grupos de difeomorfismos del circulo", Ensaios Matemáticos, (2007).
  • Katok-Lewis. "Local rigidity for certain groups of toral automorphisms". Israel J. Math. 75 (1991), 203-241.
  • Fisher. "Local rigidity of group actions: past, present, future", Recent Progress in Dynamics, Volume 54, 2007.
  • Hurder. "Affine Anosov Actions" Michigan Math. J. Volume 40, Issue 3 (1993), 561-575. [article]
  • Hurder. "Rigidity for Anosov Actions of Higher Rank Lattices". Ann. Math. (2) volume 135, no. 2 (1992), 361—410.
  • Farb-Shalen. "Real-analytic actions of lattices". Invent. Math. 135 (1999), no. 2, 273–296.
  • Franks-Handel. "Distortion elements in group actions on surfaces". Duke Math. J. 131 (2006), no. 3, 441–468.