Americas VI, Pan-American Advanced Studies Institute |
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Centro de Modelamiento Matemático
Universidad de Chile, Santiago-Chile
January 10-21, 2005 |
The Americas Conferences on Differential Equations and Nonlinear Analysis are held every other year in one of the countries
on the North- and South-American continents. So far, conferences have
been organised in Taxco (Mexico, 1994), Aguas de Lindoa (Brasil,
1996), Atlanta (USA, 1998), Merida (Venezuela, 2000), Edmonton
(Canada, 2002), and now in Santiago de Chile. This year was the first
time that speakers were invited from all over the world, resulting in
a total of 180 participants. It was a very vibrant meeting with a wide
variety of speakers and topics.
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Group photo taken
at the welcome reception, Monday January 17,
2005. |
PASI2005 was split into two parts; the first week
consisted of minicourses, aimed for PhD students. The second part was
the actual conference. During the first week two-hour courses were
given by (in the order of the program) Jack Hale, Luis Caffarelli,
Stuart Antman, Walter Craig, Rafael de la Llave, Takis Souganidis,
Yingfei Yi, James Yorke, Konstantin Mischaikow, John Mallet-Paret, and
Gustavo Ponce. Furthermore, Alfonso Castro, Stig-Olof Londen, and
Michael Sullivan gave one-hour lectures. The PhD students were
enthusiastic about this first week. In particular, the lectures of
Luis Caffarelli were very well received. On the other hand, there was
a clear consensus that the level of the lectures was higher than
expected, and some students suggested to have three-hour lectures, so
that the speakers need not skip the low-level material.
On the Wednesday evening of the second week, many PhD
students displayed their research at the poster session. Despite the
long day of talks, a lot of people showed up for this event and it was
very successful. In fact, the discussions went on well after the
official end of the session (at 8pm!) and the real die-hards were
kicked out while talking mathematics. |
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Laguna del
Inca, Portillo. |
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The program of the actual conference consisted of four
plenary talks in the morning and five other presentations in the
afternoon in two or four parallel sessions. The quality of the talks
was very high and mostly aimed at a level such that non-specialists
could follow the presentation. I particularly enjoyed the
presentations of Shui-Nee Chow, Ivar Ekeland, George Sell and Luca
Dieci. (This does not mean that the other talks were of a lesser
quality!) Shui-Nee Chow talked about information transportation via
electronic circuits. The idea is to use spiking solutions to carry the
information and he explained how to drive the system such that the
output always leads to a specific number of spikes. It is important to
realize here that any initial condition should immediately generate
this prescribed number of spikes; there is no transient time! Ivar
Ekeland discussed a problem from Economics. He described an optimization
problem where two different types of goods (say nuts and bolts) must
be transported to the same place so that they can be put together (a
matching problem). How can you do this in an optimal way? The
nuts and bolts were an entertaining example (especially since he got
them the wrong way around!) and his notation was interspersed with
musical signs, which for the musicians amongst us was quite
helpful. In the second part of his talk, he related this simple
matching problem to so-called hedonic models in
economy. Hedonic models take into account that for certain economic
goods quality is more important than quantity. If the prices of homes
decrease, people do not buy more homes, they buy a better one.
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George
Sell had a very timely presentation that included the prediction of
tsunamis. He explained the modeling problems in wheather forecasting
and discussed several techniques and their justifications. This led
to some interesting debates on how useful a prediction can be if there
is no clear measure of closeness to the actual wheather pattern. Luca
Dieci described algorithms for the computation of Lyapunov
expononents, or more general dichotomies, both for continuous and
discrete systems. More importantly, he explained the underlying
assumptions and gave a proof of correctness for his methods, which
included some very interesting properties and unexpected
counter-intuitive results. In short, the computations do not normally
become more accurate by integrating (iterating) for longer time! Of
course, I should also mention Marty Golubitsky here, who presented his
first results on bifurcations in network architectures; see also the
In The Spotlight article. |
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Talks were filmed so
that the audience could enjoy them in two rooms. The audience in the
other room was present via the TV screen in the
back. |
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Raúl
Manásevich (right) addresses the audience at the welcome
reception on
Monday January 17, 2005. |
The conference included a welcome reception on Monday with lots of
pisco sour, caipirinhas, and fantastic Chilean food. Have you ever
tried raw marinated fish coverd in melted cheese? These Chilean
ceviches are highly addictive! There was also a conference banquet on
Thursday, again with lots of pisco sour, caipirinhas and good
food. Many participants were raving about the food in Chile; the
vegetables and fruits are very flavorful and the steak served at the
banquet definitely was the best steak I ever had. During the
conference banquet there was a special speech for Jack Hale with a
commemorative plaque to thank him for initiating the PASI meetings and
for encouraging interaction between North- and South-America. Clearly
this initiative has created a wealth of opportunities for academics
and students in South-America, but has also been very beneficial and
productive for the North-American side. Unfortunately, the visa
situation in the US has made such interactions far more
difficult. For example, there was a discussion at the
PASI2005 about the fact that it is no longer straightforward to obtain
a work or study visa for the US for people from South-American
countries. The costs of obtaining a visa have gone up dramatically and
the chances of being turned down (for no obvious reasons) is, in
fact, large.
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From left to right:
Jack Hale (Georgia Tech), Raúl Manásevich (Universidad
de Chile), David Kinderlehrer (Carnegie Mellon University) and Irene
Fonseca (Carnegie Mellon University) at the banquet, January 20, 2005
(George Sell, University of Minnesota, is standing in the
back); photograph taken by James Muldowney (University of
Alberta). |
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From left to right: Xiaohong
Wang (Purdue University), Marty Golubitsky (University of Houston),
Barbara Keyfitz (University of Houston), and Stephen Schecter (North
Carolina State University) at the banquet, January 20,
2005; photograph taken by James Muldowney (University of
Alberta). |
A very special thank you goes to the local organizing
committee, Raúl Manásevich (chair), Juan Dávila,
Manuel Del Pino, Patricio Felmer, Marta Garcia-Huidobro, Salomé
Martinez, and to the system administrators at the Universidad de
Chile, who literally were magicians with the multimedia
organization. |
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Clockwise from top left: Katherine Bold
(Princeton University), Alfonso Sorrentino (Princeton University),
Aaron Hoffman (Brown University), Bernardo Sousa (Carnegie Mellon
University), Leo Tzou (University of Washington), Graca Carita
(Carnegie Mellon University), and Adrian Tudorascu (Carnegie Mellon
University); photograph taken by James Muldowney (University of
Alberta). |
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The conference
was sponsored by: |
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Centro de Modelamiento Matemático,
Departamento de Ingeniería Matemática,
US National Science Foundation,
US Department of Energy,
Pontificia Universidata Católica de Chile,
Comisión Nacional de Investigación Cientifica y
Tecnológica,
Office of Naval Research Global,
Facultad de Ciencias Físicas y Matemáticas ---
Universidad de Chile,
International Centre for Theoretical Physics,
Pacific Institute of Mathematical Sciences,
Air Force Office of Scientific Research. |