–From the latest theories and observations to the explanation of the Nobel Prize in Physics! An introduction to black holes from active physicists–

The 2020 Nobel Prize in Physics was awarded to Sir Roger Penrose, Prof. Dr. Reinhard Genzel and Prof. Andrea Ghez for their contributions to the theory and observation of black holes. Black holes have continued to provide hot topics in recent years, such as gravitational waves from black hole coalescence and black hole imaging, but do you really know what black holes are? Three cutting-edge black hole researchers will explain its identity and mystery.

Levinson’s theorem is a surprising result in quantum scattering theory, which relates the number of bound states and the scattering part of the underlying quantum system. For the last about ten years, it has been proved for several models that once recast in an operator algebraic framework this relation can be understood as an index theorem for the Møller wave operators. Resulting index theorems are called topological version of Levinson’s theorem or shortly topological Levinson’s theorem. In this talk, we first review the background and the framework of our investigation. New analytical and topological results are provided for Schrödinger operators on the half-line. This talk is based on my Ph.D thesis.

We propose a manifestly covariant definition of a conserved charge in gravity. We first define a charge density from the energy momentum tensor with a Killing vector, if exists in the system, and calculate the energy (and angular momentum) of the black hole by a volume integral. Our definition of energy leads to a correction of the known mass formula of a compact star, which includes the gravitational interaction energy and is shown to be 68\% of the leading term in some case. Secondly we propose a new method to define a conserved charge in the absence of Killing vectors, and argue that the conserved charge can be regarded as entropy, by showing the 1st law of thermodynamic for a special case. We apply this new definition to the expanding universe, gravitational plane waves and the black hole. We discuss future directions of our research.

December 14 at 10:00-11:30, 2020 (JST)
December 13 at 20:00-21:30, 2020 (EST)

In the history of mathematical study in pattern formation, the effect of domain has been considered as an important factor that can regulate spatial patterning. However, it is still unknown in biology how the geometry of the domain such as nuclear or cellular shapes can directly regulate the cell fate. In this talk, I will introduce two studies of spatial reorganization in chromatin and cellular dynamics and show that the domain is likely to play a critical role in determining the cell function.

M2-brane is an interesting object in M-theory and string theory. A three-dimensional 𝒩=6 super conformal Chern Simons theory with gauge group U(𝑁1)×𝑈(𝑁2), called ABJ theory, describes the low energy behavior of M2-brane On the one hand, it has been considered that when |𝑁1−𝑁2| is larger than the absolute value of Chern Simons level, the supersymmetry is broken. On the other hand, it was predicted that an interesting phenomenon called duality cascade occurs, and supersymmetry is not broken in some cases.

Motivated by this situation, we performed non-perturbative tests by focusing on the partitionfunction on 𝑆3. The result strongly suggests that the duality cascade indeed occurs. We also proposed that the duality cascade occurs in theories with more general gauge groups and we performed non-perturbative tests in the same way. I will review and explain our physical prediction in the first half of my talk. In the second half of my talk , I will explain the non-perturbative tests . This part is mathematical because the partition function reduces to a matrix model by using the supersymmetric localization technique.

Development of methods for classical statistical mechanics is desired for accurate predictions of the structures and thermodynamic properties of liquids. A powerful framework to describe classical liquids is density functional theory (DFT). In the quantum case, there have been recent attempts to develop accurate methods with combining DFT and the functional renormalization group (FRG), which is another framework to deal with many-body systems utilizing evolution equations, and such approaches are expected to work also in the classical case. In this presentation, I will talk about a new approach for classical liquids aided by FRG. The formalism and some ideas to incorporate higher-order correlation functions to systematically improve the accuracy will be shown. I will also present a numerical demonstration in a one-dimensional exactly solvable system and discuss the results by comparing to other conventional methods such as the hypernetted chain.