Flat Surfaces and Dynamics on Moduli Space, II (19w5078)


Ferrán Valdez (UNAM)

(University of Toronto)

(Tel Aviv University)

Anton Zorich (Universite Pierre Diderot)


The Casa Matemática Oaxaca (CMO) will host the "Flat Surfaces and Dynamics on Moduli Space, II" workshop from May 26th to May 31st, 2019.

The classical illumination problem (Straus, 1950) asks whether there exists a polygonal room with a pair of points which do not illuminate each other. First examples were found by Tokarsky in 1995 and Boshernitzan (unpublished), and this raised the question of classification and possible cardinality of pairs of points which do not illuminate one another on translation surfaces.

Thanks to breakthrough results by A. Eskin, A. Mohammadi & M. Mirzakhani classical illumination problems can now be solved in full generality adapting methods from dynamics on homogeneous spaces to dynamics on the moduli space of at Riemann surfaces.

Despite this enormous progress in the area, there are many central questions regarding Flat Surfaces and Dynamics on Moduli spaces that remain open. The purpose of this workshop is to push further the techniques developed in the last 5 years to crack these questions in the near future.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT.