# The 7th AIMS Conference on Dynamical Systems and Differential Equations

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by Carmen Chicone and Yuri Latushkin

The AIMS biannual conference series on dynamical systems and differential equations started in May 1996 with a conference at Southwest Missouri State University, Springfield, MO, USA (now Missouri State University) and was continued at Shanghai Jiaotong University, Shanghai, China in June 1998; Kennesaw State University, Kennesaw, GA, USA in May 2000; University of North Carolina at Wilmington, Wilmington, NC, USA in June 2002; California State Polytechnic University, Pomona, USA in June 2004; and University of Poitiers, Poitiers, France in June 2006 with a record attendance of 700 mathematicians and scientists from five continents.

While the official attendance at this year's conference at UT-Arlington was 658 participants, a record number of 47 special sessions were organized and 803 talks were presented. (The full conference program is available: http://aimsciences.org/AIMS-Conference/2008/.) It was a large and successful meeting, due to the organization by the Mathematics Department of the University of Texas at Arlington, the sponsorship by the USA National Science Foundation, the University of Texas at Arlington, and the University of North Carolina at Wilmington, and the individual organizers listed below:

• The Scientific Committee: Shouchuan Hu (Chair), Jerry Bona, Alberto Bressan, Adrian Constantin, Amadeu Delshams, Hiroshi Matano, Alain Miranville, Wei-Ming Ni, N.S. Papageorgiou, Jianzhong Su, Jianping Zhu.
• Conference Coordinator: Xin Lu.
• Conference Organization Committee: Jianzhong Su (Chair) , Jianping Zhu (Co-Chair), Tuncay Aktosun, Gaik Ambartsoumian, Alain Bensoussan , Hristo V. Kojouharov, Cecelia Levings , Yue Liu , Peter Moore , Hua Shan.
• Global Organizing Committee: Shouchuan Hu (Chair), Julien Arino, Francisco Balibrea , Mohamed Belhaq, Gunduz G. Caginalp, Xinli Fu, Marty Golubitsky, Laszlo Hatvani, Hassan Hbid, Miaohua Jiang, Peter Kloekden , Tibor Krisztin, Irena Lasiecka, Yuri Latushkin, Xin Lu, Amy Novick-Cohen, Mitsuharu Otani R. Shivaji, Stefan Siegmund, Atanas Stefanov, Jianzhong Su Saleh Tanveer, Weike Wang, Xiaoming Wang, James Ward, Jianping Zhu.

The conference began on Sunday May 18 with the plenary talk given by George Papanicolaou, Stanford University, USA (Problems in scattering theory arising in the imaging of edges). The speaker discussed the mathematics that arises in the imaging of edges, both with full and partial aperture (array) data. In the second plenary talk, Sijue Wu, University of Michigan, USA (Almost global wellposedness of the 2-D full water wave equation) described her proof of the existence of solutions for the infinite depth water wave equations with small data for exponentially long time-scales. Hans Weinberger, University of Minnesota, USA presented the third plenary talk of the first session (Spreading speeds for a partially cooperative two-species reaction-diffusion system), in which he analyzed traveling wave behavior for a two-species system designed to model the interaction of ungulates and grasslands.

After these plenary talks, the participants had a chance to enjoy 19 early afternoon and 22 late afternoon parallel sessions. The authors of this article organized and attended the special session Dynamical systems and applications. This session was designed so that some of the speakers were alloted two consecutive 30-minute slots that kept the speaker's pace slow and the audience's understanding high. This format seemed to be a great success. The speakers for this session were W. Strauss, Z. Lin, V. M. Hur, J. Bona, R. de la Llave, R. C. Calleja, P. Guidotti, A. Scheel, and C. Zeng.

There were 22 morning parallel sessions on Monday May 19. One of us attended the session on Nonautonomous dynamical systems organized by R. Fabbri and C. Nunez, and enjoyed the talks given by D. Damanik and D. Lenz on the subject lying at the intersection of the spectral theory for Schrödinger operators and spectral theory of dynamical systems. The other sampled talks in several special sessions and listened to a very informative talk on Evans's functions presented by Y. Latushkin in the session on Nonautonomous dynamical systems.

In the first plenary talk on Monday (Heat equation and Non-equilibrium (Classical) Statistical Mechanics), Carlangelo Liverani (University of Rome Tor Vergata", Italy) illuminated a path from the classical microscopic description of a macroscopic body to the heat equation. The following speaker, Jean-Claude Saut (Universit'e Paris-Sud, France) surveyed recent progress concerning the existence and qualitative properties of traveling wave solutions to the Gross-Pitaevskii equation posed on the whole space of two and three dimensions in his talk (Traveling waves for the Gross-Pitaevskii equation). After lunch, there were 23 early and 21 late afternoon sessions, including a continuation of the dynamical systems session.

Shouchaun Hu presents plaque to Jianping Zhu, the chair of the UT-Arlington Mathematics Department.

Over 300 conference participants enjoyed an excellent banquet on Monday evening while being entertained by a first-rate mariachi ensemble. Jerry Bona, the after dinner host, mentioned his impression of the first AIMS conference in Springfield, Missouri: (we paraphrase) "I thought it was well done, but not much would happen after that." He then reviewed the amazing growth of the conferences in the series and announced with pride that he had attended all of them. Jerry then introduced Shouchuan Hu, the Director of AIMS, who presented a plaque to the UT-Arlington Mathematics Department to commemorate their hard work organizing the conference. The evening ended with John Graef's recitations of some humorous mathematical anecdotes. A very good time was had by all.

The morning of Tuesday May 20 started with 21 parallel sessions. The authors attended the session on Long time behavior of Hamiltonian and dissipative systems organized by A. Stefanov and M. Stanislavova. The speakers gave an account of the most recent advances in this area, concentrating on applications of harmonic analysis and spectral theory. In two notable talks, H. Chen explained some recent results on the existence and stability of traveling waves and C. Zeng discussed spike solutions of a singular parabolic equation.

Carmen Chicone (middle) between sessions during the conference.

The plenary talk on Tuesday was given by Lassi Paivarinta, University of Helsinki, Finland (Invisibility challenges inverse problems). He discussed invisibility phenomena in the context of the electrical impedance tomography problem (Calderon Problem). In the afternoon there were 21 special sessions followed by a bus trip and walking tour of the historic West End district of downtown Dallas. Carmen was deeply moved by a reverent visit to Dealy Plaza. One of his most important mathematical conversations of the meeting took place later that day over dinner at an upscale Mexican restaurant, where he had the pleasure to meet for the first time in person an admired mathematical colleague, Hans-Otto Walther.

The morning of Wednesday May 21 started with 20 parallel sessions. One of the authors of this report participated in the fourth session on Qualitative behavior of solutions of evolutionary PDEs organized by I. Lasiecka, G. Todorova, and M. Nakao. This session gathered an array of experts working in both parabolic and hyperbolic PDEs and their applications.

The first plenary talk on Wednesday was delivered by Lisa Fauci, Tulane University, USA (Interaction of elastic biological structures with complex fluids). Her energetic talk on the biofluiddynamics of reproduction was complemented with excellent graphics. The second plenary talk was given by Walter Strauss, Brown University, USA (Steady Rotational Water Waves) on existence proofs for waves with large amplitudes for arbitrary vorticity functions. His talk was followed by 18 early and 9 late afternoon parallel sessions. One of the authors of this report attended the session Boundary value problems and control theory organized by Hongqiu Chen, M. Colin and R. Fukuiumi, to listen to several excellent talks on dispersive nonlinear equations.

This professionally organized high-level conference covered the full range of research in dynamical systems: abstract mathematical analysis, modeling, computation, and concrete applications in many areas of science and technology including biomathematics, medicine, fluid mechanics, celestial mechanics, astrophysics, engineering, and economics. The impact of the AIMS conference series on our field is hard to overestimate. We believe we speak for all participants in saying that this conference was a first-rate mathematical experience.

The American Institute of Mathematical Sciences is an international organization for the advancement and dissemination of mathematical sciences well known for its great success in publishing a number of excellent journals including Discrete and Continuous Dynamical Systems (Series A and B), and many others impressive activities. See http://aimsciences.org/index.html.

The 8th AIMS conference will take place at Dresden University of Technology, Dresden, Germany during May 25-28, 2010 (for more information contact Shouchuan Hu (shu@missouristate.edu), Xin Lu (lux@uncw.edu), Stefan Siegmund (stefan.siegmund@tu-dresden.de), or check the AIMS website http://aimsciences.org).

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