Symplectic geometry of Frobenius structures

The purpose of the notes is to reiterate and expand the viewpoint, outlined in the paper math.AG/0110142 of T. Coates and the author, which recasts the concept of Frobenius manifold in terms of linear symplectic geometry and exposes the role of the twisted loop group L^{(2)}GL_N of hidden symmetries. New applications include a several line proof of the genus 0 Virasoro constraints and the quantum Hirzebruch-Riemann-Roch theorem in the theory of cobordism-valued Gromov-Witten invariants.