Este minicurso se realizará los días martes 4, jueves 6, lunes 10, martes 11 y jueves 13 de septiembre desde las de 15:30 a 16:30 hrs. en sala 1 de la Facultad de Matemáticas. The famous Ergodic Theorem may be viewed as a counterpart of Law of Large Numbers. It is also fruitful to study Central Limit Theorem, Exponential Decay of Correlations and Law of Iterated Logarithm for certain maps and their invariant measures. In this mini-course I will focus on rational maps of Riemann Sphere. In this setting it´s natural to study the class of measures called equilibrium states with Holder continuous potentials, introduced by Denker, Przytycki and Urba_ski. I want to talk about recent results with Anna Zdunik and Mariusz Urba_ski in which we apply theory of Young´s towers and deduce aforementioned strong statistical properties in this context. Although our methods work in complex projective spaces of any dimension, I will focus only on one-dimensional case.
Este minicurso se realizará los siguientes días:
Lunes 3 de septiembre a las 17:00 hrs, sala 1 de la Fac. de Matemáticas UC. (seminario introductorio, en el seminario SCS-D).
Martes 4, miércoles 5 y jueves 6 de septiembre a las 16.30 hrs. en la sala 1 de la Fac. de Matemáticas UC
El curso tendrá tres sesiones los días 19, 20 y 21 de marzo, entre las 17:00 y 18:20 horas, y se realizará en el Auditorio Ninoslav Bralic de la Facultad de Matemáticas de la Pontificia Universidad Católica de Chile y está dirigido a académicos y estudiantes de postgrado
El cursillo se realizará los dias lunes 12, martes 13, miercoles 14 de marzo de 2012 a las 16:00 Hrs. en el Auditorio Ninoslav de la PUC.
Abstract: An elliptic surface is an algebraic surface which admits a fibration with a fibre an elliptic curve. An example of such a surface is the blow-up of base points of a pencil of plane cubic curves. Although a general fibre is a nonsingular curve, some fibres can be singular, and their classification reveals a surprising relationship with Dynkin diagrams of simple Lie algebras. I will try to be non-technical, explaining most of the theory for the case of pencils of plane cubic curves, and their generalizations, Halphen pencils of plane elliptic curves of degree 3m with 9 m-multiple singular points. The theory of such pencils is ultimately related to old problem in algebraic geometry: finding a geometric construction of fake projective planes.