Flat Surfaces and Dynamics of Moduli Space (16w5010)

Arriving in Oaxaca, Mexico Sunday, May 8 and departing Friday May 13, 2016

Organizers

(Universidad Nacional Autonoma de Mexico)

(University of Washington)

(Goethe Universität Frankfurt Am Main)

Objectives

We want to bring together international experts on moduli spaces of curves and flat surfaces. For many of the above topics there is a dichotomy of type of results: results that hold almost everywhere and results for especially rich examples. These complementary approaches make the topic challenging both for mathematicians with analytic (or measure-theoretic) backgrounds and for those with rather algebraic backgrounds. \par We remark that in Mexico there are well stablished research groups on moduli spaces of curves, foliations and dynamical systems, however flat surfaces are not yet widely known. By including researches working in Mexico and by locating the conference in Oaxaca, we expect to also expand the local community in flat surfaces and moduli spaces. For these reasons, our first preference for the venue of the proposed meeting is BIRS station in Oaxaca, Mexico. However, we can also carry this meeting in BIRS station in Banff, Canada. \\ \\ Talks on flat surfaces and dynamics on moduli space subject have been given at the last five international congresses of mathematicians: by H.~Masur in Z\"urich, 1994; by A.~Eskin in Berlin, 1998; by G.~Forni in Beijing, 2002; by Y.~Minsky and A.~Zorich in Madrid, 2006; by A.~Avila, U.~Hamenst\"adt, and M.~Mirzakhani in Hyderabad, 2010. {\it{Moreover, in Seoul 2014, two Fields medals have been given to A. Avila and M. Mirzakhani for their work on the proposed topic.}}

In recent years, workshops and conferences on flat surfaces and their relation to the moduli space of curves (and Teichm\"uller space) have taken place at various institutions around the world.



  • May--August 2010 (Trimester at the Hausdorff-Institute, Bonn): ``Geometry
  • and dynamics in Teichm\"uller space'', organized by U. Hamenstaedt, M. M\"oller, A. Zorich.
  • May 2011 (Oberwolfach) ``Billiards, flat surfaces and dynamics on moduli space'',
  • organized by H. Masur, M. M\"oller, A. Zorich.
  • July 2011 (IAS Summer school, Park City): ``Moduli Spaces of Riemann Surfaces'', organized by B. Farb,
  • E. Looijenga, D. Hain.
  • April 2012 (CIRM, Luminy): ``The horocyclic flow in different situations'', organized by F. Dal'bo,
  • P.~Hubert, A.~Zorich.
  • September 2012 (Roscoff, Bretagne): ``Algebraic geometry for the flats'', organized by P.~Hubert, E.~Lanneau, A.~Zorich.
  • August 2012 (University of Illinois at Urbana-Champaign): ``Geometric structures And Representation varieties'', organized by J.~Athreya, C.~Leininger and S.~Bradlow,
  • August 2013 (CCM, Morelia): ``International Conference and Workshop on Surfaces of Infinite type'', organized by J.~Bowman,
  • P.~Hooper,R.~Trevino, F.~Valdez, G.~Weitze-Schmith\"usen.
  • November 2013 (ICERM, Providence) ``Low-dimensional Topology, Geometry, and Dynamics'', organized by
  • M.~Duchin, P.~Hubert, H.~Masur, R.~Schwartz, A.~Zorich.
  • March 2014 (Oberwolfach): ``Flat surfaces and dynamics on moduli space'',
  • organized by H. Masur, M. M\"oller, A. Zorich.
There is thus a tradition of activities in the field to be continued. Moreover, no major conference on flat surfaces or dynamics on moduli spaces is scheduled for 2016 so far.

%REFERENCES

Bibliography





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