Janko Latschev

Seminar "Topics in Symplectic Geometry", Summer term 2025

Symplectic geometry can be described as the geometry underlying the Hamiltonian formalism for describing classical conserative mechanical systems. However, its appeal lies in the fact that it is connected to (and it interacts well with) many other topics in mathematics, most notably differential topology, dynamical systems and algebraic geometry. Our aim will be to study the foundations of symplectic geometry, as well as some of the motivating questions of current research.

As background we will assume a working knowledge in differential geometry, i.e. familiarity with the following notions: manifolds, vector bundles, differential forms, vector fields, flows and Lie derivative of various geometric objects in the direction of a vector field. Other topics will be reviewed as necessary.

The seminar will be run as a reading seminar. Each week, participants will all read some specific text(s), and we will discuss the details and implications of the content in class. Participants will take turns being the designated discussion leader.