Prof. Mikio Furuta from the University of Tokyo gave a talk at the Math Seminar on February 25, 2020. The title of his talk was "Index of the Wilson-Dirac operator revisited: a discrete version of Dirac operator on a finite lattice". His talk was based on his recent collaboration with both mathematicians and physicists. The main goal of his talk is to give an equality between the index of the Dirac operator, which is defined on a continuous space, and that of the Wilson-Dirac operator, which is defied on a discrete lattice. This equality is given in a suitable K-group, which is defined as a collection of (some equivalence classes of) pairs of Hilbert spaces and operators acting on them. The key point in the proof of the main result is to compare two different Hilbert spaces somehow, and he explained an idea of the construction of a map needed for this comparison. This talk included many new ideas, and both of mathematicians and physicists enjoyed it very much.

The article written by Dr. Tomoki Ozawa, "Study of Topological Lattice Models with Synthetic Dimensions" was published in the April 2020 issue of Butsuri, the monthly magazine published by Physical Society of Japan. The cover of the same issue was based on a figure from the article by Dr. Ozawa. For more details, please refer to the article by him in this issue.

The CNET Japan Live 2020 held on February 19, various performances talk about the theme of "Innovation indispensable for corporate growth". Mr. Hiroyasu Kodama at G's ACADEMY and Dr. Tsukasa Tada at Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) in RIKEN are trying to create and nurture innovators and work on co-creation with companies. A panel discussion entitled “Developing and co-creating innovators” was held.

My name is Ryusuke Hamazaki. I am a senior research scientist at iTHEMS and also a RIKEN Hakubi leader of a team on nonequilibrium statistical mechanics. So far I have worked on foundation of equilibrium quantum statistical mechanics, namely how isolated quantum many-body systems relax to thermal equilibrium after long time. Extending this framework, I am currently trying to understand laws of nonequilibrium quantum statistical mechanics. Another motivation of mine is to apply the theory to other nonequilibrium science, such as biology or high-energy physics. I am eager to discuss and collaborate with one another to contribute to interdisciplinary fields through universality of statistical mechanics!

I am Masaki Taniguchi, a mathematician, who has been working at iTHEMS/RIKEN since April 2020. My interests cover gauge theory, Floer theory and its applications to 3- and 4-dimensional topology. In a mathematical study of gauge theory, we obtain information of 4-manifolds by observing the moduli space of solutions to a certain non-linear partial differential equation for a given 4-manifold. This method enables us to find interesting phenomena of 3- and 4-dimensional topology which are different from that of other dimensions.
Currently, I am studying the following topics:
1. gauge theory for a class of non-compact 4-manifolds called 4-manifolds with periodic ends and their applications to existence of codimension-1 embedding of 3-manifolds and positive scalar curvature on spin 4-manifolds,
2. a quantitative formulation of instanton Floer homology and its applications to a study of the homology cobordism group which is related to existence of triangulations of topological manifolds, and
3. a study of 2-dimensional knots in the 4-space using gauge theory.
I'm also interested in physical aspects of gauge theory. I'm looking forward to discussing with researchers in various fields at RIKEN.

Hello, I am Akira Dohi, the Junior Research Associate (JRA) student. My research interest concentrates on how neutron stars are cooled or heated. A Neutron star is born as a remnant by supernova explosion of a massive star and basically cools down by many neutrino losses. How to cool or heat the neutron star is connected to the temperature or magnetic field of the surface, which can be estimated using the observations of X-ray astronomical satellite. The cooling and heating processes are believed to be caused in a wide range of density regions even with the above nuclear saturation density. I am studying numerical modeling of neutron stars evolution, and combining some observations, I aim to specify the origin of these processes, which would be useful for elucidation of various physics, above all nuclear theory. iTHEMS’s members have different fields from my area and this would broaden our scientific knowledges and views through communications.

My name is Euki Yazaki and I joined iTHEMS in April 2020.
My research area is biology, and I have been studying evolutionary biology consistently since I started my research career as a student at University of Tsukuba in 2010. I am particularly interested in the molecular phylogeny and molecular evolution of eukaryotic microorganisms (called Protists). Based on large-scale molecular sequence data acquired from many Protists, I have inferred the evolutionary history of genes and phylogenetic relationships of organisms. Ultimately, I hope to elucidate the early evolution of eukaryotes.
I'm very excited to be a member of iTHEMS because the mathematical professionals from diverse backgrounds at iTHEMS give me the opportunity to expand my biology and therefore my science.

Title: Nisnevich topology with modulus
Author: Hiroyasu Miyazaki
arXiv: http://arxiv.org/abs/1910.14579v2

Title: Categorical polynomial entropy
Author: Yu-Wei Fan, Lie Fu, Genki Ouchi
arXiv: http://arxiv.org/abs/2003.14224v1

Title: ΛΛ and NΞ interactions from Lattice QCD near the physical point
Author: Kenji Sasaki, Sinya Aoki, Takumi Doi, Shinya Gongyo, Tetsuo Hatsuda, Yoichi Ikeda, Takashi Inoue, Takumi Iritani, Noriyoshi Ishii, Keiko Murano, Takaya Miyamoto
arXiv: http://arxiv.org/abs/1912.08630v2

Title: MeV-scale reheating temperature and cosmological production of light sterile neutrinos
Author: Takuya Hasegawa, Nagisa Hiroshima, Kazunori Kohri, Rasmus S. L. Hansen, Thomas Tram, Steen Hannestad
arXiv: http://arxiv.org/abs/2003.13302v1

Title: The HAL QCD potential in I=1 ππ system with the ρ meson bound state
Author: Yutaro Akahoshi, Sinya Aoki, Tatsumi Aoyama, Takumi Doi, Takaya Miyamoto, Kenji Sasaki
arXiv: http://arxiv.org/abs/2004.01356v1

Title: The KO-valued spectral flow for skew-adjoint Fredholm operators
Author: Chris Bourne, Alan L. Carey, Matthias Lesch, Adam Rennie
arXiv: http://arxiv.org/abs/1907.04981v2

Title: Analysis for Lorentzian conformal field theories through sine-square deformation
Author: Xun Liu, Tsukasa Tada
arXiv: http://arxiv.org/abs/2004.01930v1

Title: Semi-Dirac transport and anisotropic localization in polariton honeycomb lattices
Author: B. Real, O. Jamadi, M. Milićević, N. Perent, P. St-Jean, T. Ozawa, G. Montambaux, I. Sagnes, A. Lemaître, L. Le Gratiet, A. Harouri, S. Ravets, J. Bloch, A. Amo
arXiv: https://arxiv.org/abs/2004.03478