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Graduate Organized Seminar - An Introduction to Symplectic Geometry with Relations to Mechanics

Joey Palmer, Department of Mathematics, Washington University in St. Louis

August 8, 2012 - 4:00 pm to 5:00 pm
Location: Cupples I, Room 6 | Host: Timothy Chumley

Abstract: I will be giving a brief introduction to Symplectic Geometry for people who are not familiar with the field followed by the beginnings of its connections to Classical Mechanics. We will define symplectic manifolds, lagrangian submanifolds, and the cannonical and tautological forms. We will be using the cotangent bundle as a motivating example, with smooth sections being the lagrangian submanifolds and explain how these can be generated by smooth functions and why these submanifolds are so important. We will then derive the Hamiltonian equations and explain how a Hamiltonian function can contain all of the information about the dynamics of a classical system.