# Coast to Coast Seminar Series: "Poisson Structures investigated with Computer Algebra"

*Dr. Thomas Wolf and Dr. Alexander Odesskii*

### Abstract

This seminar will discuss Poisson Structures, which play an important role in both pure mathematics and applications. After giving a brief explanation of this notion, it will be shown how the computation of Poisson Structures leads to the problem of solving overdetermined algebraic systems. In the following demonstration a package developed by one of the presenters will be used to solve such systems. During the talk extensive comments are made concerning general issues that come up in large scale computer algebra computations. If there is time examples of other large scale computations will be added.

### About the Speaker

Dr Odesski's research interests include Integrable Systems, Mathematical Physics, Computer Algebra, High Performance Computing, Representation Theory, Non-commutative Geometry, Algebraic Geometry. His main research interests are in Mathematical Physics in the sense of Mathematics inspired by ideas that come from Theoretical Physics. More precisely, he is interested in algebraic and geometric structures which come from quantum field theory, statistical mechanics and the theory of integrable systems. Currently he is Brock SharcNet Research Chair.

Dr. Wolf's research interests include differential equations and integrability, computer algebra, General Relativity and special aspects of optimization and artificial intelligence. Dr. Wolf does work with computer algebra concerns algorithms to simplify and solve overdetermined systems of equations (linear/non-linear), (algebraic/ordinary differential (ODEs)/partial differential (PDEs)). These basic algorithms are applied in higher level programs for the determination of symmetries, conservation laws or other properties of differential equations. Applications include the classification of integrable systems of evolutionary scalar PDEs, vector PDEs, single and systems of supersymmetric evolutionary PDEs and recently integrable quadratic Hamiltonians with higher degree first integrals but also discrete integrable system from Discrete Differential Geometry.