Mathematics & Computer Science Department Northern Kentucky University Seminar leader 1994-96: Kevin Kirby Participants: Leon Arriola, Dan Curtin, Maria Falbo-Kenkel, Don Krug, Kristin Pfabe, Gail Wells, Steve Wilkinson

- From Lagrangian to Hamiltonian mechanics
- Trajectories of
*dX/dt = J grad H*and level curves of*H* - Linearization; Symplectic and Hamiltonian matrices
- Poisson brackets (of functions on phase space)
- Liouville's Theorem

- Gaussian optics: translation & refraction
- The thin lens; conjugate planes; telescopic systems
- Theorem: Matrices are optical iff symplectic
- The eikonal function

- Gauging field theories
- Conformal gravity

- Groups preserving bilinear forms: O(n) vs. Sp(2n)
- Lie algebras as tangent spaces of Lie groups

- Vectors and algebraic k-forms
- Duality: sharps and flats
- Wedge products, interior products
- The canonical symplectic form on V x V*
- From symplectic vector spaces to symplectic manifolds
- The canonical symplectic form on a cotangent bundle

Photo (top) by Klaus-Peter Zauner