Computable Analysis of Differential Equations (Invited Talk)

In this talk, we discuss some algorithmic aspects of the local and global existence theory for various ordinary and partial differential equations. We will present a sample of results and give some idea of the motivation and general philosophy underlying these results

Unitary One Matrix Models: String Equations and Flows

We review the Symmetric Unitary One Matrix Models. In particular we discuss the string equation in the operator formalism, the mKdV flows and the Virasoro Constraints. We focus on the \t-function formalism for the flows and we describe its connection to the (big cell of the) Sato Grassmannian \Gr via the Plucker embedding of \Gr into a fermionic Fock space. Then the space of solutions to the string equation is an explicitly computable subspace of \Gr\times\Gr which is invariant under the flows.Comment: 20 pages (Invited talk delivered by M. J. Bowick at the Vth Regional Conference on Mathematical Physics, Edirne Turkey: December 15-22, 1991.

International Conference on Nonlinear Differential Equations and Applications

Dear Participants, Colleagues and Friends It is a great honour and a privilege to give you all a warmest welcome to the first Portugal-Italy Conference on Nonlinear Differential Equations and Applications (PICNDEA). This conference takes place at the Colégio Espírito Santo, University of Évora, located in the beautiful city of Évora, Portugal. The host institution, as well the associated scientific research centres, are committed to the event, hoping that it will be a benchmark for scientific collaboration between the two countries in the area of mathematics. The main scientific topics of the conference are Ordinary and Partial Differential Equations, with particular regard to non-linear problems originating in applications, and its treatment with the methods of Numerical Analysis. The fundamental main purpose is to bring together Italian and Portuguese researchers in the above fields, to create new, and amplify previous collaboration, and to follow and discuss new topics in the area

Intersections 2000: What's New in Hadron Physics

Hadron physics is that part of QCD dealing with hadron structure and vacuum structure, almost all of which is nonperturbative in nature. Some of the open problems in this field are outlined. We argue that hadron physics is a distinct subfield, no longer within particle physics, and not at all the same as classical nuclear physics. We believe that it needs to be better organized, and that a first step in doing so might be to establish hadron physics as a new division within the American Physical Society.Comment: Invited Talk at 7th Conference on the Intersections of Particle and Nuclear Physics, Quebec City, Quebec, Canada, May 22-28, 200

Classical and Quantum Mechanical Models of Many-Particle Systems

The topic of this meeting were non-linear partial differential and integro-differential equations (in particular kinetic equations and their macroscopic/fluid-dynamical limits) modeling the dynamics of many-particle systems with applications in physics, engineering, and mathematical biology. Typical questions of interest were the derivation of macro-models from micro-models, the mathematical analysis (well-posedness, stability, asymptotic behavior of solutions), and –to a lesser extend– numerical aspects of such equations