| Abstract | Symplectic geometry was originated from classical mechanics, but this area has been expanding exponentially since 1990's due to the discovery of its striking relations with other area of mathematics, including low-dimensional topology, geometric representation theory, algebraic geometry, etc. The main tool involved in building these relations is Floer theory, which itself can be viewed as a vast generalization of string topology. In this talk, we will give a (very biased) illustration of some aspects of it using our works on dynamics, knot theory and mirror symmetry. |
