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SUMMARY:Networks of continuous time open systems
DTSTART:20150602T141500
DTEND:20150602T153000
DTSTAMP:20260511T140035Z
UID:6369866648ee4b55d35cbca74c2aaa5c22d1c307848c0a9fb789d5a8
CATEGORIES:Conferences - Seminars
DESCRIPTION:Eugene Lerman (UIUC)\n(This talk is based on collaborations wi
 th Lee DeVille and with Dmitry Vagner and David Spivak) Dynamics on networ
 ks has been studied from many different points of view. I prefer to think 
 of a complex continuous time system ("a network") as a collection of inter
 acting subsystems. These subsystems are open (i.e.\, control) systems. The
 re are two rather different aspects of these collections. Given a collecti
 on of open systems one can interconnect them to obtain a new open system. 
 The interconnection process can be iterated: collections of open systems o
 btained by interconnecting smaller open systems can be interconnected agai
 n. The iterative aspect of interconnection of open systems is captured wel
 l by viewing the collection of all open systems as an algebra over a color
 ed operad. This is an instance of an approach advocated by Spivak. On the 
 other hand one of the fundamental problems in the theory of (closed) dynam
 ical systems is constructing maps between dynamical systems or\, failing t
 hat\, proving their existence. For example\, a map from a point to our fav
 orite closed system is an equilibrium\, periodic orbits are maps from circ
 les and so on. Thus it is desirable to have a systematic way of constructi
 ng maps of dynamical systems out of appropriate maps between collections o
 f open systems. It is these kinds of considerations that underlie the deve
 lopment of the groupoid formalism for coupled cell networks of Golubitsky\
 , Steward and their collaborators and its reinterpretation and extension b
 y DeVille and Lerman. The two considerations/viewpoints suggest that netwo
 rks of open systems in general should be an algebra over some sort of a do
 uble monoidal category. I will outline one such possible construction.
LOCATION:CM 113
STATUS:CONFIRMED
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