Collective Power of Science ~ from the High-Energy Atmospheric Physics to our New Exploration of the Universe ~
Teruaki Enoto (Extreme natural phenomena RIKEN Hakubi Research Team)
Lightning discharges and thunderstorms have been recently revealed to exhibit unexpected high-energy phenomena, such as electron acceleration by atmospheric electric fields and photonuclear reactions by gamma rays from accelerated electrons. Our "Extreme natural phenomena RIKEN Hakubi Research Team" is a new group launched in January 2020, and working to create a new interdisciplinary field called the "high-energy atmospheric physics." We are constructing a new observation network for winter thunderclouds along the coast of the Sea of Japan. The heart of this research approach is the "Collective Power of Science". It is an attempt to create science not with a single large instrument, but with a combination of small, scalable instruments. We plan to apply this idea to space X-ray observations using CubeSats and lunar exploration to search for water on its surface using neutron signals generated by cosmic rays. Here I introduce our group activities.
Neural Turing Machines
田中 章詞 (数理創造プログラム 上級研究員)
I would like to review how to design 'trainable computer' in the context of recent deep learning techniques: arxiv: 1410.5401
Peeling tape as a reaction-diffusion system
Keisuke Taga (Waseda Universtiy)
When you peel a tape with appropriate velocity, you will find a sierpinski-gascket like fractal pattern on the peeled trace. It is known that this pattern is caused by a switching of a peeling front structure. In this talk, I will introduce a new model of reaction-diffusion system, which can describe this pattern formation.
On the ionization problem
後藤 ゆきみ (数理創造プログラム 基礎科学特別研究員)
From experiments, it seems that a neutral atom can only bind one or two extra electrons. This is a long standing open problem, sometimes referred to as the ionization conjecture. In this talk, I will briefly present the status of the conjecture.
Knots in Quantum Field Theory
太田 敏博 (数理創造プログラム 研修生 / 大阪大学 大学院理学研究科)
In our three dimensional space knots (or links) are ubiquitous, not only in physics or mathematics, but also in biology, chemistry etc. (Rather, knots might be more common in biology and chemistry...) When knots appear in our world, they often look too complicated to be classified or distinguished. In this talk I will briefly explain a way to deal with the classification of knots using the general ideas of quantum field theory.
What should we do about COVID-19?
カトゥリン・ボシゥメン (数理創造プログラム 客員主管研究員 / Professor, Department of Physics, Ryerson University, Canada)
We have been analyzing and modelling the data for COVID-19 cases in Tokyo and Saitama. We have built mathematical models to analyze the data and make predictions about where the case counts can be expected to go next, and what the consequences could be. For a while, things were going better and better, and daily cases were going down. With the increasing case count in Tokyo, Saitama, Osaka, etc., we now have some concerns. We would like an opportunity to show you some of our results and observations and hear your thoughts. How do you feel about the recent increases? If you were in charge, what decision would you take? As scientists, do we have a responsibility to make sure this information is provided to the general public so they have a clear understanding of the situation? We hope you will join us and share your thoughts.
Morse theory and Floer theory
谷口 正樹 (数理創造プログラム 基礎科学特別研究員)
In a study of topology, Morse theory provides a way to decompose a manifold into elementary parts. We first review a fundamental method in Morse theory. In Floer theory, we consider infinite-dimensional versions of Morse theory for nice functionals. We explain an idea of Floer theory.
Observational study of suprenova remnants
辻 直美 (数理創造プログラム 特別研究員)
Supernova remnants, leftovers of supernova explosion, are believed to be factories of heavy elements and high-energy particles (cosmic rays). These ideas can be probed by observations of electromagnetic waves from supernova remnants. I will give a review talk of the observational studies; what we can learn from observations.
Markdown - the next generation markup language
田中 章詞 (数理創造プログラム 上級研究員)
Markdown is a lightweight markup language. Important features are easy to use, beautiful document output, and TeX rendering support. Thanks to these fascinating features, Markdown has been already one of common markup languages at least in engineering perspectives. But, I guess, there will be benefits even in scientific research perspectives. So, I would like to introduce how to use it and its applications.
Does Neutron Finite Size Affect Nuclear Structure?
内藤 智也 (U Tokyo/QHP)
Atomic nuclei consist of protons and neutrons, which interact via Coulomb and nuclear interactions. Since protons and neutrons have finite charge radii instead of point particles, these finite-size effects for the Coulomb interaction should be considered in the theoretical calculations. Nevertheless, since the contribution of the Coulomb interaction to the nuclear properties is weaker than that of the nuclear force, it was not considered properly. Recently, we have taken the finite-size effect to the Coulomb interaction into account for the calculation of nuclear structures. We found that the finite-size effects give a non-negligible contribution to the nuclear binding energy .  T. Naito, X. Roca-Maza, G. Colò, and H. Liang. Phys. Rev. C Accepted (arXiv: 2003.03177).
Knot theory and topological semimetals
チンカイ・チウ (Kavli Institute for Theoretical Science, Beijing, China)
Topological nodal line semimetals host stable chained, linked, or knotted line degeneracies in momentum space protected by symmetries. We use the Jones polynomial as a general topological invariant to capture the global knot topology of the oriented nodal lines. We show that every possible change in Jones polynomial is attributed to the local evolutions around every point where two nodal lines touch. As an application of our theory, we show that nodal chain semimetals with four touching points can evolve to a Hopf link. We extend our theory to 3D non-Hermitian multiband exceptional line semimetals and provide a recipe to understand the transition of the knot topology for protected nodal lines.
Basics of evolution and the evolution of Sars-CoV-2
ジェフリ・フォーセット (数理創造プログラム 上級研究員)
Next-generation method to derive the basic reproduction number of infectious disease models
入谷 亮介 (数理創造プログラム 研究員)
In response to the recent, increasing interest in epidemiology, I will talk about the mathematical framework to derive the basic reproductive number for compartmental disease models: the Next-Generation Theorem (NGT). In general, whether diseases spread or not is determined by the leading eigenvalue (spectral radius) of a disease-free steady state(s). For an SI-model, for instance, the conventional wisdom is that the instability of (S, I) =(S_0, 0) around the ODE for the model is determined by the real part of the eigenvalue. As the number of infected-class compartments grows, however, it becomes increasingly difficult to determine the spectral radius of the associated matrix. NGT partially resolves this issue by (i) reducing the size of the matrix or dimension, (ii) making the matrix relatively sparse, and (iii) clarifying the biological meaning. I will talk about this theorem per se, though do not give its proof, with some illustrative applications (one of which is actually unsolved and therefore a quiz for you all!) as well as why graph-theory and stochastic analyses may be of great use in the discipline of epidemiology. The purpose of this talk is to facilitate future interactions between biologists including me and theoreticians who are interested in graph theory, matrix calculus, and/or dynamical systems.
Quantum physicists now study non-Hermiticity
濱崎 立資 (数理創造プログラム 上級研究員 / 理化学研究所 開拓研究本部 (CPR) 濱崎非平衡量子統計力学理研白眉研究チーム 理研白眉研究チームリーダー)
On COVID-19 spreading
パスカル・ネドン (理化学研究所 仁科加速器科学研究センター (RNC) 量子ハドロン物理研究室 専任研究員)
Multi-meesenger Search for sources of high energy neutrino
Haoning He (ABBL)
Mathematical models of epidemics
三好 建正 (数理創造プログラム 副プログラムディレクター / 理化学研究所 計算科学研究センター (R-CCS) データ同化研究チーム チームリーダー)
Motivic homotopy theory and modular representation theory
Shane Kelly (Tokyo Institute of Technology)
On the geodesics of regular polyhedra
児玉 大樹 (数理創造プログラム 客員研究員 / 東北大学 材料科学高等研究所 (AIMR) 助教)
Report on RIKEN iTHEMS - Berkeley Math Visiting Scholar Program (Lunch Meeting)
三上 渓太 (数理創造プログラム 研究員)