This will be an informal and introductory seminar series with the aim of studying how modern mathematical structures arise from physical systems. Hopefully, a deeper understanding of these structures may be gained by considering them within a physical context. No background in physics is supposed. The outline of the seminar is roughly as follows:

- symplectic geometry and Poisson geometry in classical mechanics;
- the various quantization schemes and basic quantum field theory;
- Dirac structures;
- G-torsors and gauge theory - the moduli space {gauge connections}/{gauge equivalence};
- K-theory, spin geometry and the index theorem(s);
- representation theory and the space-algebra correspondence;
- groupoids and categorification;
- noncommutative geometry.

Of course, this is not a complete list of potential topics.