Abstract

The Casa Matemática Oaxaca (CMO) will host the "Flat Surfaces and Dynamics on Moduli Space, II" workshop in Oaxaca, from May 26, 2019 to May 31, 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 First examples were found by Tokarsky in 1995 and Boshernitzan (unpublished), and this raised the question of classification and possible cardinality of pairs of points which do not illuminate one another on translation surfaces.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.