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Knot theory and topological semimetals

Ching-Kai Chiu (Senior Research Associate, Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, 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

Jeffrey Fawcett (Senior Research Scientist, iTHEMS)


Next-generation method to derive the basic reproduction number of infectious disease models

Ryosuke Iritani (Research Scientist, iTHEMS)

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

Ryusuke Hamazaki (Senior Research Scientist, iTHEMS / RIKEN Hakubi Team Leader, Nonequilibrium Quantum Statistical Mechanics RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR))


On COVID-19 spreading

Pascal Naidon (Senior Research Scientist, Quantum Hadron Physics Laboratory, RIKEN Nishina Center for Accelerator-Based Science (RNC))


Multi-meesenger Search for sources of high energy neutrino

Haoning He (ABBL)


Mathematical models of epidemics

Takemasa Miyoshi (Deputy Program Director, iTHEMS / Team Leader, Data Assimilation Research Team, RIKEN Center for Computational Science (R-CCS))


Motivic homotopy theory and modular representation theory

Shane Kelly (Tokyo Institute of Technology)


On the geodesics of regular polyhedra

Hiroki Kodama (Visiting Scientist, iTHEMS / Assistant Professor, Advanced Institute for Materials Research (AIMR), Tohoku University)


Report on RIKEN iTHEMS - Berkeley Math Visiting Scholar Program (Lunch Meeting)

Keita Mikami (Research Scientist, iTHEMS)


Algorithms for point set processes

Martin Skrodzki (Visiting Scientist, iTHEMS / Fellow, German Academic Scholarship Foundation, Germany)


Balancing Thermodynamics and Kinetics to Achieve Maximum Rates in Catalysis

Hideshi Ooka (CSRS)


Spintronics: Spin current propagation or susceptibility?

Gen Tatara (CEMS/CPR)



Nagisa Hiroshima (Postdoctoral Researcher, iTHEMS)


Introduction to genetics

Jeffrey Fawcett (Senior Research Scientist, iTHEMS)


Pruning brunches of deep learning

Masato Taki (Senior Research Scientist, iTHEMS)


The new SI units

Tomoki Ozawa (Senior Research Scientist, iTHEMS)


The photospheric origin of the Yonetoku relation in gamma-ray bursts

Hirotaka Ito (Research Scientist, iTHEMS / Research Scientist, Astrophysical Big Bang Laboratory, RIKEN Cluster for Pioneering Research (CPR))


Neutron stars and their oscillations

Hajime Sotani (Research Scientist, Astrophysical Big Bang Laboratory, RIKEN Cluster for Pioneering Research (CPR))


The Efimov Effect

Pascal Naidon (Senior Research Scientist, Quantum Hadron Physics Laboratory, RIKEN Nishina Center for Accelerator-Based Science (RNC))