Wednesday, April 28, 13:30- Information Theory SG Seminar
Thursday, April 29, Shōwa Day (National Holiday!)
Friday, April 30, 12:30- Coffee Meeting

On April 13, Dr. Takuju Zen from Kochi University of Technology gave a talk entitled “Self-adjoint extension in quantum mechanics and non-Rydberg spectra of one-dimensional hydrogen atom” at the iTHEMS Math-Phys joint seminar.

In the first part, he briefly explained the necessity of self-adjointness of operators in quantum mechanics and gave some important examples of such operators. Besides, he mentioned that the self-adjointness of Laplacian is equivalent to flux conservation in one dimension. Finally, he introduced studies of quantum particles on graphs.

In the second part, the speaker discussed one dimensional Coulomb problem. Mainly, he noted that a simple self-adjoint extension of such hamiltonian could not be used. Then he provided a concrete procedure to study the solutions of one dimensional Coulomb problem and explained his interesting results.

Reported by Yukimi Goto

On April 16, 2021, 13:30-15:00 (JST) 0:30-2:00(EDT), Professor Kenji Fukaya, Simons Center for Geometry and Physics, Stony Brook University, gave a colloquium talk by zoom. The title was "Mirror symmetry and KAM theory". His talk began at the origin of symplectic geometry, namely, the Hamiltonian dynamics. He reviewed completely integrable Hamiltonian systems, where the first integrals define foliation by half dimensional Lagrangian tori with linear flows. The KAM (Kolmogorov-Arnold-Moser) theory describes perturbation of this system and shows that almost all tori persist. Then Professor Fukaya explained the Lagrangian torus fibration found by Strominger-Yau-Zaslow, with the example of the complex projective space. For the complex projective n-space, the image of the moment map is an n-simplex and the regular fibers are Lagrangian n-tori. The inverse image of the boundary of the simplex corresponds to the singular fiber of the holomorphic fibration (the product of homogeneous coordinates) to a disk, By choosing a symplectic form, around the singular fiber of holomorphic fibration, there is defined the monodromy map by using the Hamiltonian flow of the Hamiltonian function that is the absolute value of the fibering. Professor Fukaya told that for this example in dim n = 2, the monodromy near the singular fiber exhibits the KAM theoretic behavior, but in dim n = 3, it is not the case with respect to the Fubini-Study symplectic form. However, he expects it can be the case with respect to the Calabi-Yau Kaehler form. This correspondence between symplectic manifolds (the torus fibration of the complex projective space) and complex manifolds (the holomorphic map to the disk) is an introductory example of the mirror symmetry. His talk might enter much deeper part related with homological mirror symmetry, but he stopped and concluded by saying that the KAM theory explains the transition from completely integrable systems to chaos and it should be possible to find alternative in mirror symmetry or field theory which will explain the transition from stable system to chaos. The talk of Professor Fukaya was really stimulating and his enthusiasm impressed the audience.

Reported by Takashi Tsuboi

Following last year’s precedent, iTHEMS held an online lecture event for the general public with the help of Academist Inc., on April 18th, 2021. The event was planned as an alternative for the lectures at RIKEN’s annual open house.
The event was started by Kanato Goto with his talk on Blackhole and its information problem. His compelling narrative evoked a lot of questions from high school students; some of them were very sharp.
Next, Jeffery Fawcett talked about genome science. Among other topics he studied, he also mentioned the mutation of COVID-19 virus. During the lunch break, Program Director Hatsuda talked with Mr. Shibato from Academist about related books, the exhibition of Black Hole Recorder at Miraikan, and the attempts with RIKEN SUURI.
In the afternoon, Sugiura-san talked about the supercomputers and the analysis of subatomic physics, followed by Naomi Tsuji's talk on supernovae and their remnants. The talk included several polls from the audience.
Keita Mikami concluded the event with his talk on Mathematics, in particular inequality and differential equations.
All the talks were compered by Ms. Michibayashi from Academist; Her facilitation with a wit kept the talks accessible even to high school students. The event was viewed by as many as more than three hundred audiences at one time.

Title: Born-Oppenheimer potential energy surfaces for Kohn-Sham models in the
local density approximation
Author: Yukimi Goto
arXiv: http://arxiv.org/abs/2104.09057v1

Title: Note on the Goldbach Conjecture and Landau-Siegel Zeros
Author: D. A. Goldston, Ade Irma Suriajaya
arXiv: http://arxiv.org/abs/2104.09407v1