Ultrametric Dynamical Days
January 21 to February 1, 2008

PUC, Santiago, Chile.

Description. Building a firm bridge between the relatively new theory of non-archimedean dynamics and the well-established area of complex dynamics, is currently a very active area of research. The interactions between these two fields are particularly striking when dealing with the geometry of parameter spaces of rational or polynomial maps. This  meeting is intended to introduce researchers and graduate students to this problematic.

There will be three mini-courses dealing with the necessary basis of moduli spaces, non-archimedean dynamics and compactification problems. We expect to gather a group of 20 to 30 researchers to create a working atmosphere in order to facilitate scientific interactions:  beside the mini-courses, scheduled talks, informal seminars, and problem sessions will be organized.

Registration. In order to give appropriate facilities we ask each participant to register before December 8 at this website.

Financial support. Limited funds are available to cover travel and/or living expenses. To apply for financial support please register before November 9.

Organizing Committee

Charles FAVRE – CNRS / IMJ, France

Jan KIWI – PUC, Chile

Juan RIVERA-LETELIER – UCN, Chile

Download First Announcement

Download Poster

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

 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


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

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

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 P1. 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

 


 

Francois Berteloot (Toulouse)
Araceli Bonifant (Rhode Island)
Jean-Yves Briend (Marseille)
Mariela Carvacho (Santiago)
Laura DeMarco(Chicago)
Bertrand Deroin (Paris)
Antoine Ducros (Nize)
Romain Dujardin (Paris)
Xander Faber (New York)
Charles Favre (Paris)
Susan Goldstine (Maryland)
Su-Ion Ih (Boulder)
Godofredo Iommi (Santiago)
Shu Kawaguchi (Tokyo)
Jan Kiwi (Santiago)
Victor Kleptsyn (Rennes)
Karl-Olof Lindahl (Vaxjo)
John Milnor (Stony Brook)
Andrés Navas (Santiago)
Jean-Pierre Otal (Toulouse)
Amalia Pizarro (Santiago)
Jerome Poineau (Regensburg)
Alfredo Poirier (Lima)
Mario Ponce (Santiago)
Daniel Pons (Santiago)
Nicolas Ressayre (Montpellier)
Juan Rivera-Letelier (Antofagasta)
Pascale Roesch (Toulouse)
Michael Schraudner (Santiago)
Mitsuhiro Shishikura (Kyoto)
Daniel Smania (Sao Paulo)
Toshi Sugiyama (Kyoto)
Lucien Szpiro (New York)
Ricardo Torres (Santiago)
Eugenio Trucco (Santiago)

Please find bellow directions and practical information that might be of help for you during your stay in Santiago. If you have any questions please send us an email to the following address:

ultrametric08@dynamicalsystems.cl

In case you need to contact us while in Chile you can call Jan Kiwi to the following cell phone number:

(56 9) 96134991
Dial 09 96134991 from phones in Santiago.

1. Accommodation.

At «Hotel & Apart Club Presidente Santiago». It is located three blocks from the «Tobalaba» metro station in the Providencia neighbourhood.

Address:
Hotel & Apart Club Presidente Santiago
Luis Thayer Ojeda 558
Providencia

Phone: (56 2) 233 56 52
Fax: (56 2) 231 69 48

A map and more information regarding the hotel can be found at:

http://www.presidente.cl/english/ClubPresidenteStgo/index_clubSantiago.html

At Residencia Universitaria

It is located three blocks from the «Tobalaba» metro station in the Providencia neighbourhood.

Address:
Residencia Universitaria
Holanda 518
Santiago

http://www.residenciauniversitaria.cl

Phone (56 2) 234 3626

Map Near Residencia

2. From the Airport to the Hotel.

There are several ways to go from Santiago Airport to the Hotel.

2.1 By Taxi, the price should be around 15.000 CLP (arrange the fare with the taxi driver in advance).

2.2 By Bus, there are buses from the airport to the Metro (cost: 2000 CLP) every 30 min. If you are going by bus, you should get off the bus at METRO ESTACION PAJARITOS. Then take the Metro in the «Escuela Militar» direction and get off at METRO TOBALABA. The hotel is three blocks form there.

2.3 By Transfer. This is a small bus that is shared with some other people. They will drive you from the airport to the Hotel. Cost: 5000 CLP. This should be arranged within the airport. There are two companies that offer this service: TRANSVIP and TURBUS.

More information can be found at:

http://www.aeropuertosantiago.cl/contenidos/listado_contenidos.php?s=20040714211755

3. From the Hotel and Residencia to the University.

The conference will be held at Facultad de Matemáticas, Universidad Católica located in Campus San Joaquin of this University (there are several cumpus spread over Santiago).

Campus San Joaquin is located at the San Joaquin Metro Station (Vicuña Mackenna 4860). The easiest way to get there is by Metro.  In the following web-site you can find a map of the metro line and clicking on each metro station you will find a map of the surroundings of the station:

http://www.metrosantiago.cl/planos.php

Directions:

Take the Line 1 (red line) of the metro at Metro Tobalaba  station in direction to San Pablo and get off at Metro Estacion Baquedano.

Transfer to Line 5 (green line) in direction to  Bellavista de La Florida. Get off at estación San Joaquin. You will see the campus.

Then follow the campus map http://pp.mat.puc.cl/content/maps.html

The whole trip should take like 40 minutes.

4. Public transportation.

In order to take a bus in Santiago you need a card, the so called «BIP» card. It can be purchased at any metro station at a cost of 1000 CLP. You need to charge it with certain amount of money and then use it to pay your fare.

The cost of the bus ticket is: 380 CLP.

If you want to use the Metro then you can either buy the tickets at any metro station or use the BIP card.

The cost of a metro ticket is: 420 CLP.

5. Aproximate exchange rate

1 EUR = 715 CLP
1 USD = 498 CLP

You can exchange money at the airport. There are ATM machines all over the city, in particular at the airport. Note that if you want to cash a check you will be asked to show your passport.

6. Weather.

The weather in Santiago during January is normally dry, warm during the
day and cool at night.

The maximum temperature every day should be around 30 degrees Celsius and the minimum 12 degrees Celsius.

7. Places to eat.

There are many places to have lunch and dinner in the Providencia area. Most of them close around 11 pm or later. On Sundays most of the places are closed. Nevertheless, you can find places to eat in a street called «El Bosque norte». It is situated between
the metro stations Tobalaba and El Golf. It is perpendicular to Avenida Providencia.

8. Important entry information: Reciprocity Law.

Passengers from countries which require visa for Chilean citizens (USA, Australia, Canada, Mexico) should pay a reciprocity tax before approaching the International Police

http://www.aeropuertosantiago.cl/contenidos/listado_contenidos.php?s=20040714211544

Research Network on Low Dimensional Dynamics, PBCT/CONICYT, Chile.

Espaces de Berkovich, ANR, France.

Ultrametric Dynamics and Dynamical Moduli Spaces, ECOS/CONICYT, France/Chile.

Facultad de Matemáticas, Pontificia Universidad Católica de Chile.

Francois Berteloot, Hotel & Apart Club Presidente Santiago
Araceli Bonifant, Residencia  Universitaria
Jean-Yves Briend, Residencia  Universitaria
Laura DeMarco, Residencia  Universitaria
Antoine Ducros, Hotel & Apart Club Presidente Santiago
Romain Dujardin,  Residencia  Universitaria
Xander Faber,  Residencia  Universitaria
Charles Favre,  Residencia  Universitaria
Susan Goldstine, Residencia  Universitaria
Su-Ion Ih,Residencia  Universitaria
Shu Kawaguchi, Residencia  Universitaria
Karl-Olof Lindahl, Residencia  Universitaria
John Milnor, Hotel & Apart Club Presidente Santiago
Jean-Pierre Otal, Hotel & Apart Club Presidente Santiago
Jerome Poineau, Residencia  Universitaria
Alfredo Poirier, Residencia  Universitaria
Nicolas Ressayre, Hotel & Apart Club Presidente Santiago
Pascale Roesch, Hotel & Apart Club Presidente Santiago
Mitsuhiro Shishikura, Hotel & Apart Club Presidente Santiago
Daniel Smania, Residencia  Universitaria
Toshi Sugiyama, Residencia  Universitaria
Lucien Szpiro,  Hotel & Apart Club Presidente Santiago