Titles and Abstracts


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Funding and registration




Conference description

Supported by the National Science Foundation, this CBMS conference will be held at Tulane University, New Orleans, from May 17 to May 21, 2010. The principal speaker will be Professor Wei-Ming Ni of University of Minnesota, who will deliver ten lectures with the central theme The Mathematics of Diffusions that are described below. In addition, there will be five speakers each giving a related talk. The five speakers will be:

  • Chris Cosner (University of Miami),
  • Manuel del Pino (Universidad de Chile),
  • Changfeng Gui (University of Connecticut),
  • Kening Lu (Brigham Young University),
  • Juncheng Wei (The Chinese University of Hong Kong).

It is well-known that diffusion in single equations tend to suppress pattern formation; on the other hand, diffusion in systems may trigger and enhance patterns (e.g, nonconstant steady states)--as was first discovered by Alan Turing more than 50 years ago. Of the most biological/physical significance are steady states that concentrate highly in small areas, such as spikes. The first mathematical theory of "spike-layer'' solutions was rigorously established by Ni and Takagi in a series of papers from 1986 to 1993. Since then, the area has attracted many first rate analysts as well as applied mathematicians, and has enjoyed a tremendous growth. Multi-peak solutions and solutions with multi-dimensional concentration sets, and their stabilities, have been studied for the Gierer-Meinhardt system, nonlinear Schrodinger equations, and biological systems with cross-diffusion (including chemotaxis systems); the methods developed in this direction have recently led to a complete resolution of the 30-year-old DeGiorgi conjecture in phase transition for the dimensions higher than 8.

Ten Lectures of Professor Ni:
  • Lecture 1. Introduction/Overview of pattern formation from the point of view of diffusion, including the backgrounds of various models.
  • Lecture 2. (Turing's approach) Gierer-Meinhardt system and its shadow system:Global existence and finite time blow-ups.
  • Lectures 3-4. Spike-layers and steady states with multidimensional concentration sets in Gierer-Meinhardt system and related topics.
  • Lecture 5. Stability of steady states and dynamics of Gierer-Meinhardt system and its shadow system.
  • Lecture 6. Lengyel-Epstein system and CIMA reaction: The first experiment in chemistry to verify Turing's "diffusion-driven instability". We will devote this hour to describing the mathematical progress on this topic.
  • Lecture 7. Negative taxis - Shigesada, Kawasaki and Teramoto's cross-diffusion model in population dynamics.
  • Lecture 8. Positive taxis - Keller-Segel system in chemotaxis. To compare the mathematics involved in positive- and negative-taxis.
  • Lectures 9-10. Spatially inhomogeneous equations and systems --diffusion and biased movements in mathematical ecology.
Throughout the lectures, open problems, conjectures, and new directions will be discussed.


Conference program in pdf or here.


Participants list in pdf or here.

Registration and financial support

To help us better organize the conference, the participant should register, with no fees, by simply sending an email to, stating your full name, title, organization and email address. To apply for financial support (transportation and lodging), the applicant should also provide the employment status (postdocs, junior/senior researcher, graduate student, etc), the research field, and indicate to what extend the support is needed (travel expense, or hotel, or both).?About 30 participants will be supported. Priority will be given to postdocs, junior researchers, graduate students and under represented groups, in closely related research fields. Graduate students should also have short endorsing letters from their advisers sent to the organizer.


Participants whose lodging will be supported by the conference will stay in?

with reservations made through the confernece organizer;?Other participants who will pay for their own lodging should make their own reservations in the same hotel or the following addtional ones:?

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Astor Crowne Plaza,
739 Canal Street,
New Orleans LA 70130

Hotel Front Desk: (504)962-0500
Hotel Fax: (504)962-0501


The taxi fare from the airport to the hotels is about $35 and the ride is approximately 30 minute-long.The Mathematics Department of Tulane is located at 6823 St. Charles Ave., and the easiest way to get there from the hotels is by the street car which runs along St. Charles Ave. The street car can be boarded near the hotels listed above.

At the airport, the Airport Shuttle which is located just outside of the baggage claim area will take you to the Astor Crowne Plaza Hotel 739 Canal St. at Bourbon St. The fare is $20 one way and the route is about 1 hour. A taxi from the airport is about $35 and that ride is approximately 30 minutes.

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