Mechanics and all that
Gabriele Tornetta (University of Glasgow)
Friday 1st February, 2013 04:00-05:00 516
The topic of the seminar is Analytical Mechanics, and the discussion will develop from concrete Newtonian systems to some more abstract algebraic structures. But in the end mechanics will just a pretext to convince you that "all that" is actually a great deal of mathematics, e.g. calculus of variations, smooth manifolds and structures thereof. I'll introduce the notion of symmetries for Lagrangean systems, which will take us to the theory of Lie groups as well, and the celebrated Noether's theorem will be stated and proven. Finally the shift to Hamiltonian mechanics will be motivated, and the natural symplectic structure arising from the theory is highlighted, which lead to algebraic structures such as Poisson algebras. If time permits, the C*-algebraic approach to mechanics will be briefly discussed as well.
(Hopefully illuminating) examples will be provided during the talk.