We study birational invariants in order to study birational classifications of varieties. Geography is the study of relations among different invariants. We will focus on two fundamental invariants: canonical volume and geometric genus. For surfaces there are classical results such as Miyaoka-Yau inequality and Noether inequality. I will discuss higher dimensional analogue of them, and introduce our recent work on the optimal Noehter inequality for 3-folds joint with Jungkai Chen and Meng Chen.

*Please contact Keita Mikami's mail address to get access to the Zoom meeting room.

The physics of unconventional superconductors has gained a new dimension in the past decade, thanks to the bloom in the understanding of topological quantum materials. Keeping in mind the success of the symmetry-based diagnosis in the large-scale discovery of topological insulator and semimetal candidates [1], it is natural to ask whether the approach can be generalized to superconducting systems.

In this talk, I provide a unified way to diagnose topology and superconducting nodes in unconventional superconductors. First, I review symmetry-indicator theory for the topological insulators [2]. Also, I also discuss how to generalize the theory to superconductors [3,4,5]. Next, I show that the symmetry-based approach can extensively classify superconducting nodes pinned to high-symmetric momenta [6]. Finally, I show that these results enable us to derive the comprehensive correspondences between pairing symmetries and topological/nodal superconducting nature for each material [7].


*Detailed information about the seminar refer to the email.

The discovery of high-energy cosmic neutrinos opened a new window of astroparticle physics. Their origin is a new mystery in the field, which is tightly connected to the long-standing puzzle about the origin of cosmic rays. I will give an overview of the latest results on high-energy neutrino and cosmic-ray observations, and demonstrate the power of "multimessenger" approaches. In particular, I will show that the observed fluxes of neutrinos, gamma rays, and extragalactic cosmic rays can be understood in a unified manner. I will also highlight the recent developments about astrophysical neutrino emission from supermassive black holes and violent transient phenomena. Possibilities of utilizing high-energy neutrinos as a probe of heavy dark matter may be discussed.