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.
In conformal field theory, in contrast to gapped theories, S-matrix is not well-defined. Similarly, various inclusive observables which make sense in a gapped theory, such as "energy squared" calorimeters, suffer from IR divergences in CFTs. Using the example of Wilson-Fisher theory, I will discuss how these observables can be renormalized and what is the physical meaning of their anomalous dimensions.
Turbulence is ubiquitous in astrophysical media and plays an essential role in a variety of fundamental astrophysical processes. The turbulent power-law spectra have been observed in the solar wind, the interstellar medium, the intracluster medium, over a vast range of length scales. In our Galaxy, I will discuss pulsars as a unique tool for statistically studying the turbulence in the multi-phase interstellar medium over different ranges of length scales.