Americas Conference on Differential Equations and Nonlinear Analysis

By Hinke Osinga
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Americas VI, Pan-American Advanced Studies Institute
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.

Group photo taken at the welcome reception, Monday January 17 2005
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. Laguna del Inca, Portillo; photograph taken by Graca Carita (Carnegie Mellon University)
Laguna del Inca, Portillo.

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.

Talks were filmed so that the audience could enjoy them in two rooms. 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.
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.
The audience at the welcome reception, January 17, 2005 Raúl Manásevich addresses the audience at the welcome reception, January 17, 2005
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.

Jack Hale, Raúl Manásevich, David Kinderlehrer and Irene Fonseca at the banquet, January 20, 2005 Xiaoho Wang, Marty Golubitsky, Barbara Keyfitz, and Steve Schecter at the banquet, January 20, 2005
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). 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. 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); copyright James Muldowney (University of Alberta)
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).

The conference was sponsored by:
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.
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