On October 2, Toshihiro Ota gave a talk at the iTHEMS Math-Phys Joint Seminar. His whole talk was on the interrelation among integrable lattIce models, quiver gauge theories, and hidden TQFT structure.

His first talk was a sort of lecture on TQFT and integrable lattice model at an elementary level. At the beginning of the first talk, he explained quantum mechanics (QM). Then as a variant of QM, he introduced an axiomatic definition of topological quantum field theory as a special class of quantum field theory. He also introduced lattice model which can be seen as a discrete version of quantum field theories. In particular, he mentioned the integrability of the 1-dimensional Ising model.

In the second talk, he focused on the correspondence between Wilson-'t Hooft lines in a class of quantum gauge theories and transfer matrices in the corresponding integrable lattice models. At first, he gave an explanation of “classical integrability” and “quantum integrability” for field theories. In the case of 2-dimensional lattice model, he explained that the integrability is described by the Yang-Baxter equation. Then he moved on to the details of the correspondence. In the lattice model side of the correspondence, he described the transfer matrix in terms of n-copies of L-operators. Moreover, in order to compare to the gauge theory side, he took the trigonometric limit and rewrote the transfer matrix by “more fundamental” L-operators. The gauge theory side is in particular given by 4d N=2 n-node circular quiver theory. The theory is defined on a 4d twisted spacetime S^1 xε R^2 x R, and he gave an expression of the Wilson-'t Hooft line wrapping the circle S^1. As the main result of his joint work with Kazunobu Maruyoshi and Junya Yagi, he gave a relation between these Wilson-’t Hooft lines and transfer matrices. Finally, he gave several comments related to integrability from TQFT in extra dimension.

Visible components of our Universe, such as galaxies, show hierarchical structures. Such structures are always embedded in DM structures called "halos". In the early Universe, there exist small density fluctuations that eventually collapse to halos at some points by their self-gravity. Then, halos grow to form larger structures again by self-gravity and this is the origin of the structure of the current Universe. The large-scale structure of halos as well as their inner structures contain information about the nature of the DM particle.

Cosmological N-body simulation is a powerful computational method to follow that structure formation, by solving multi-body problems numerically. A halo, which is a clump of elementary DM particles, is treated as one smooth particle in N-body simulation. Its prediction power is so strong that the calculation corresponding to the upcoming cosmological survey, for example, has long been awaited. However, its computational costs scale as the square of the particle number N (or N log N when some reduction methods are adopted) and it is almost impossible to cover everything we need.

There are two strategies in the calculation: simulating a large volume with large particle mass, or a small volume with small particle mass. The former is suitable for studies that deal with the large-scale structure while the latter has advantages in studying the properties of each halo. His group has conducted a large high-resolution simulation project which enables us to study both of them. The Uchuu simulation, which uses the cubic of 12800 particles in a 2 Gpc-scale simulation box, enables us to study large-scale structures. The Shin-Uchuu simulation in the same project, which uses the cubic of 6400 particles in a 140 Mpc-scale box, is provided aiming to study the inner structure of DM halos. Analyzing the simulated structure and halo properties, the matter power spectrum covering from the largest to the non-linear regime is obtained. Also, the so-called mass-concentration relation in a wide halo mass range is now available thanks to the project. There is another good news for DM hunters: the results of the simulation are open to the public. This should boost the DM study from many aspects!

The Japan Science and Technology Agency (JST) is pleased to announce that it will hold a seminar titled "Series of Seminars on collaboration between Mathematics, Science and Engineering". There will be 16 sessions in total, covering topics ranging from machine learning to quantum computing, simulation, data science and many more. For more details, please refer to the related link.

I am originally from a city in South of Italy. After my PhD at the University of Rome La Sapienza in 2008 I moved to Jagiellonian University in 2009 as a research assistant and I have been Visiting Scholar in several places all around the globe. I here mention a few: I was already at RIKEN with the JSPS Fellowship in November 2014-January 2015 in the ABBL group under the direction of Nagataki-san and as a visiting researcher in January and February 2019. I was in US at Stanford University with the Fulbright, Marie Curie’ and the American Astronomical Society Fellowship from 2012-2013, and 2015-2018. In all these years I have been studying Gamma-Ray Bursts, selection biases in treating GRB correlations, their application as cosmological tools and as a tool to discriminate among theoretical physical models. More recently I have started working on machine learning for redshift extraction of GRBs and Active Galactic Nuclei and on the selection effects in SNe cosmology in collaboration with Hatsuda-san and Nagataki-san. Last year I started collaborating with Don Warren and Gilles Ferrand to a project that aims to include virtual reality to show GRBs correlations to a broader audience.

Title: Seiberg-Witten Floer homotopy contact invariant
Author: Nobuo Iida, Masaki Taniguchi
arXiv: http://arxiv.org/abs/2010.02132v1

Title: The groups of diffeomorphisms and homeomorphisms of 4-manifolds with boundary
Author: Hokuto Konno, Masaki Taniguchi
arXiv: http://arxiv.org/abs/2010.00340v1

Title: Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
Author: Yoshimasa Hidaka, Muneto Nitta, Ryo Yokokura
arXiv: http://arxiv.org/abs/2009.14368v1