# Program

Talks will be held at Auditorio N. Bralic (in the adjacent building of the Mathematics Building), except on Tuesday 22 where they will take place in Room D 302 (Bachillerato).

see http://pp.mat.puc.cl/content/maps.html

**TENTATIVE PROGRAM**

**MINICOURSES**Antoine DUCROS - U. de Nice:

*Introduction to Berkovich spaces*

Jean-Pierre OTAL - CNRS / U. Paul Sabatier:

*Compactification of spaces of representations (after Morgan and Shalen)*

Nicolas RESSAYRE - U. Montpellier 2:

*Geometric invariant theory: constructing the moduli space of rational maps(after Silverman)*

References

References

*Spectral theory and analytic geometry over non-Archimedean fields. Mathematical surveys and monographs, 33. American Math. Soc., Providence, RI, 1990.*

V. Berkovich:

V. Berkovich:

*Géométrie analytique p-adique, la théorie de Berkovich, Gazette des mathématiciens 111 (2007), 12--27.*

A. Ducros:

A. Ducros:

*J. Morgan and P. Shalen:*An introduction to compactifying spaces of hyperbolic structures by action on trees. Geometry and topology. 228--240 Lecture Notes in Math., 1167, Springer, Berlin, 1985.

*J. Silverman:*The space of rational maps of P

^{1}. Duke Math J. 94 (1998), no1, 41--77

__TALKS__

*Laura DE MARCO: the moduli space of polynomials*

* *

*Jan KIWI: quadratic rational maps*

*John MILNOR: cubic polynomial maps with periodic critical orbit.*

*Mitsuhiro SHISHIKURA : trees associated to Fatou components of rational map*

*Lucien SZPIRO:
1- Potential good reduction and isotriviality.
2- A Shafarevich-Faltings finitness theorem for rational maps.*

Francois BERTELOOT*, Approximation of the bifurcation current for families of rational maps.*

Xander FABER*, Equidistribution and finiteness results.*

Jerome POINEAU,* The berkovich affine line over Z
*