Abstract:

Classical Kleinian groups can be defined as being discrete subgroups of automorphisms of the complex projective line P^1; that is, discrete subgroups of the projective group PSL(2,C). This group is isomorphic to the group of orientation preserving isometries of the real hyperbolic 3-space and its generalization to higher dimensional real hyperbolic spaces is a classical subject that has been and is being studied by many authors. I will speak about a different generalization to higher dimensions: I will consider discrete subgroups of PSL(n+1,C), the group of automorphisms of the complex projective line P^1. I will focus mostly on dimensions n= 2, 3. This includes the discrete groups of holomorphic isometries of the complex hyperbolic space.

Bio:

José Seade obtained his BSc in mathematics from the National University of Mexico (UNAM) in 1976 and his Masters and PhD from the University of Oxford in 1977 and 1980, respectively. Since then, he has worked at the Institute of Mathematics, UNAM, where he has been director since April of 2014.

His present research interests are on singularities theory and complex geometry and he has authored several publications in algebraic topology, algebraic and differential geometry and geometric analysis. He has been awarded the Ferran Sunyer i Balaguer Prize twice (2005 and 2012), was President of the Mexican Mathematical Society (1986-87) and founded the Mexican Mathematics Olympiades. He also founded the Solomon Lefschetz International Laboratory of Mathematics, in Cuernavaca, Mexico, which is associated with the CNRS of France, and is the current Scientific Coordinator of that laboratory. He was a member of the Scientific Council of UMALCA, the Latin American and Caribbean Union of Mathematicians (2001-2009) and since then has been a member of the Executive Committee of UMALCA.

Video: http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=KLEINIAN_GROUPS_IN_SEVERAL_COMPLEX_VARIABLES.html