June 21, 2024
Short Thematic Program on Delay Differential Equations

Distinguished Lecture Series
May 4 & 5, 2015 & May 20, 2015
Fields Institute, Room 230

Brown University


Generalized Lecture: Monday May 4, 3:30 p.m.

Recent Advances in Delay Equations

In this talk we survey some aspects of delay-differential equations. The historical roots of the subject date from the early twentieth century. At that time much of the focus was on linear equations arising in applications in science and engineering, and the methods were often formal and ad hoc. Beginning in the 1960’s more attention was paid to nonlinear systems, and a firm theoretical foundation based on infinite-dimensional dynamical systems was established. What has emerged since then is a body of theory with a rich mathematical structure that draws from numerous areas, including dynamics, functional analysis, and topology, and which retains close ties with applications. We shall discuss various recent results and ongoing research in delay equations, and we shall also mention some open problems in the field.


Specialized Lecture: Tuesday May 5, 9 a.m.

C (but not Analytic) Solutions of “Analytic” Functional Differential Equations

While delay equations with variable delays may have a superficial appearance of analyticity, it is far from clear in general that a global bounded solution x(t) (i.e., a bounded solutions defined for all time t) is an analytic function of t; and indeed, very often such solutions are not analytic. In this talk we describe theorems which give sufficient conditions both for analyticity and for non-analyticity (but C ∞ smoothness) of such solutions. In fact these conditions may occur simultaneously for the same solution, but in different regions of its domain, and so the solution exhibits co-existence of analyticity and non-analyticity. In fact, we show it can happen that the set of non-analytic points t of a solution x(t) can be a generalized Cantor set.


Specialized Lecture: Wednesday May 20, 5 p.m.

Tensor Products, Positive Operators, and Delay-Differential Equations




Speakers in the Distinguished and Coxeter Lecture Series have made outstanding contributions to their field of mathematics.