Clay Mathematics Institute 2010 Summer School

Búzios, Rio de Janeiro, de 11/07 até 07/08

The 2010 CLAY MATHEMATICS INSTITUTE SUMMER SCHOOL will take place at Hotel Atlantico, Estrada da Usina, 294 – Morro do Humaitá – Armação de Buzios.

Armação dos Búzios, or just Búzios is located 200 km south of Rio de Janeiro. Búzios is one of the most known resort of Brazil: a peninsula surrounded by 8km of islands and beaches of all styles.

Foundational Courses

Large random planar maps and their scaling limits
Jean-Francois Le Gall (Orsay) and Gregory Miermont (Orsay)

Course Description/References (by Jean-Francois Le Gall)

Lecture Notes (by Jean-Francois Le Gall)

Lecture Notes (by Gregory Miermont)

Exercises/Tutorials (by Nicolas Curien)

SLE and other conformally invariant objects
Vincent Beffara (ENS-Lyon)

Lecture Notes

Exercises/Tutorials (by Hugo Duminil)

Noise-sensitivity and percolation
Jeffrey Steif (Chalmers) and Christophe Garban (ENS-Lyon)

Lecture Notes





Nicolas Curieen (1-5)

Nicolas Curieen (6)

Hugo Duminil

Evening Talk

July 13th


  • Expansion, bottlenecks and random processes

Itai Benjamini
(18:30 – 19:30)

July 22th

  • Common zeros of random polynomials

Gady Kozma
(18:30 – 19:30)

July 23th

  • Dimers and analytic torsion

Julien Dubedat
(18:30 – 19:30)

July 26th

  • Critical behavior in inhomogeneous graphs

Remco Van der Hostad
(19:00 – 20:00)

July 27th

  • Random fields of gradients with non-convex interactions

Stefan Adams
(19:00 – 20:00)

July 28th

  • Level sets of the Brownian sheet.

Tom Mountford
(19:00 – 20:00)

July 29th

  • RSW for the Ising model

Pierre Nolin
(19:00 – 20:00)

July 30th

  • Random walks and random growth in dynamic environment

Vladas Sidoravicius
(19:00 – 20:00)


Program at a Glance

Week 1

Week 2

Week 3





Please, click on the links below in order to find where are you will be staying at Búzios:

Barra da Lagoa
Búzios Internacional
Casa Búzios
Luar de Búzios
Rooming List

Transportation to Búzios


We will have transportation from Rio de Janeiro to Búzios, on July 10th (Saturday) at 15:00hs (BUS 1) and on July 11th (Sunday) at 13:30hs (BUS 2). Both days the buses will departure from IMPA.

If you arrive much earlier than the bus departure, you can wait at IMPA’s reading room located at the 2nd floor. There will be some sandwiches and beverages for sale at the tea room, also located at the second floor (we advice you to have some brazilian pocket money – reais). For those who are coming with a notebook, IMPA has wi-fi connection throughout the whole building and its password is: impacastorina
The official address of IMPA is:
Estrada Dona Castorina, 110 – Jardim Botanico. In order to find about further details about our address, please access our website:IMPA

Please, if you intent to use our transportation you must confirm it to us by sending a copy of your passport to informing us if you will take BUS 1 or BUS 2.

For those who can not reach IMPA on time for the buses departures, There are several regular bus lines from Rio de Janeiro to Buzios from Novo Rio Bus Terminal which is located at: Av. Francisco Bicalho, 1 – Santo Cristo. A taxi from the International Airport should cost you around R$ 40,00. Once at the Bus Terminal look for the Viação 1001 sales point located on the first floor. The company Viação 1001 offers many daily departures. To find about the fare and the time departures, please access:autoviação1001

Transportation – AIRPORT TO IMPA

We will provide transportation from the airport to IMPA on Saturday and Sunday. In this direction, please look at the schedule below:

JULY 10th


– MICRO BUS – leaving airport by 6 am (as soon as AF 442 arrives)
– MICRO BUS – leaving airport by 7 am (as soon as AA 2601 arrives)
– MICRO BUS – leaving airport by 9:30 am (CO 129, DELTA 61 and TAM 8085)
– MICRO BUS – leaving airport by 10:30 am (US 800 and AA 905)
– 1 CAR – leaving airport by 11:30 am (TAM 8081)

JULY 11th


– 1 CAR – leaving airport by 6 am (AF 442)
– MICRO BUS – leaving airport by 10:30 am (US 800 and DELTA 61)


– MICRO-BUS – leaving airport at 18:30 (TAP 177, LAN 750, AF 444) – and going directly to Buzios

Videos and Pictures


Webpage maintained at the CMI