In the solar system as elsewhere, we learn most from the unexpected. I will describe three recent observational projects challenging existing ideas about solar system objects, and provoking new ones. The freaks are an interstellar object (‘Oumuamua) and a long-period comet (C/2017 K2), active far beyond Uranus. The conundrum concerns the origin of the Trojans of Neptune in the context of planetary migration.
For a weighted homogeneous polynomial and a choice of a diagonal symmetry group, we define a new Fukaya category based on wrapped Fukaya category of its Milnor fiber together with monodromy information. It is analogous to the variation operator in singularity theory. As an application, we formulate a complete version of Berglund-Hübsch homological mirror symmetry and prove it for two variable cases.