Trimester in Combinatorics and Control COCO 2010

Project: Research project

Description

A distinguishing feature of many dynamical systems of practical importance are flows that do not commute. In the context of controlled dynamical systems this feature is exploited to steer systems to any desired states. The key is to judiciously design the order in which control actions are taken. In other settings, such as splitting methods in scientific computing, the lack of commutativity is not a desirable feature, but rather a nuisance and complication. It has been well recognized that underlying such interactions are nontraditional algebraic and combinatorial structures. In control theory, small groups primarily, in the United States and France, have been studying such combinatorial and algebraic structures for several years, but these groups have been somewhat isolated. On the other side, almost exclusively in Europe, there has been a torrent of innovations and insights that exploit newly discovered combinatorial and algebraic structures for applications in large-scale scientific computing and geometric integration. In a three month series of events, COCO 2010 will bring together experts and new trainees from these three subject areas, and from both sides of the Atlantic, to establish new collaborations that will accelerate research innovations in all three areas. Pivots will be the analysis and utilization of structures that supplant classical tools from Lie theory, and which include combinatorial Hopf algebras, Rota-Baxter and dendriform algebras.
StatusFinished
Effective start/end date4/15/103/31/12

Funding

  • National Science Foundation (NSF): $41,250.00

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Combinatorics
Scientific Computing
Algebraic Structure
Dynamical system
Geometric Integration
Splitting Method
Pivot
Commutativity
Commute
Complications
Hopf Algebra
Control Theory
Accelerate
Algebra
Series
Interaction
Innovation