It is our great pleasure to inform you that our iTHEMS colleagues, Nagisa Hiroshima and Yoshiyuki Inoue, are highlighted in RIKEN Annual Report 2020 for their leading role in organizing the iTHEMS "Dark Matter Working Group". This working group aims at creating a new domestic and international network of theoretical and experimental physicists who are interested in dark matter search.

The GAIN Science Slam is all about science communication. The objective is to impart current research results to a diverse audience in an understandable and entertaining way. Science Slams started in German university towns in the mid-2000s: Darmstadt, Braunschweig, Hamburg. Today, Science Slams are held all over Germany on a weekly basis. The virtual GAIN20 Science Slam took place in the Auditorium of the virtual GAIN20 conference on August 28, 2020. The annual GAIN conference is the largest German science and research career fair in the US. Early career researchers and representatives from all areas of the German research landscape come together for two days of exchange, learning and networking in a virtual space.

Seven international researchers from various fields presented their findings in a five-minute pitch in front of the virtual audience. This virtual GAIN audience was the Science Slam Jury. The best slammer received a cash prize of $3,000, proudly presented by the German Center for Research and Innovation (DWIH). This year's winner is Dr. Martin Skrodzki from RIKEN iTHEMS. He gave a talk on seeing, recognizing, and self-driving cars. The talk is available on YouTube.

It is our great pleasure to inform you that the paper on quantum annealing by our iTHEMS colleague, Jason Chang, was ranked No.14 of the most downloaded physics papers published in Scientific Reports in 2019.

The iTHEMS Math-Phys joint seminar was held on August 31st and September 1st, inviting Makiko Sasada from University of Tokyo and Kenichi Bannai from Keio university / RIKEN AIP. This was a series of lectures entitled “Geometric Perspective for the Theory of Hydrodynamic Limits”. They explained to us their recent joint work with Yukio Kametani on hydrodynamic limits from algebraic/geometric view point.

On Day 1, Sasada-san gave an introduction to hydrodynamic limits, and explained the motivation of the joint work and the key ideas. One of the goals of the theory of hydrodynamic limits is to derive macroscopic dynamics from microscopic evolution equations rigorously. There have been many results to this problem, but all of them depend on specific microscopic models. The long term goal of this joint work is to construct an abstract and universal theory of hydrodynamic limits. One of the most important ingredients of the theory of hydrodynamic limits is the “decomposition of closed forms”, which have been obtained by Varadhan and other people using very technical argument depending on models. One of the aims of this work is to give a more general and clear understanding of this type of decompositions. Their strategy is as follows: the microscopic data can be divided into topological (geometric) part and stochastic (analytic) part. For discrete models, the former one is modeled by a directed graph, the set of states at each vertex, and the interaction through edges. A typical analytic datum is the jump rate, i.e., the frequency of interaction. They observed that some important feature of hydrodynamic limits depends only on the geometric data, and as a consequence, they could avoid ad-hoc analytic estimations. Moreover, they obtain a version of Varadhan’s decomposition in a very general setting.

On Day 2, Bannai-san gave a precise mathematical formulation of their main results and proofs. As explained above, the geometric part of microscopic model is given by a directed graph, a pointed set of states, and a function which represents the interaction through edges. From this set of data, we can form a configuration space, each point of which corresponds to a possible state on the graph (The interaction data induce the transition structure on the configuration space). On the configuration space, they consider a special type of functions / forms called “uniformly local functions / forms”, and construct a cohomology theory (uniformly local cohomology) associated to them. Surprisingly, the uniformly local cohomology captures all conserved quantities (macroscopic observables). Moreover, from this fact, they can derive a local form version of Varadhan’s decomposition. An important ingredient of the proof is the group cohomology, which is often used in the field of number theory. They assume the existence of a free group action on the graph (which is valid in many important examples), and apply a general theory of group cohomology. It is very surprising that a fundamental result in hydrodynamic limits is derived from an abstract algebraic theory, and it will provide us a new and clear understanding of this field.

On September 2, Ryosuke Iritani gave a lecture at iTHMES Biology Seminar. In this seminar, Ryo explained the principles of evolution in an easy-to-understand way, using examples such as the diversification of pet dogs and cruciferous plants, and changes in the structure of the gecko's hands. Especially, the formulation of adaptive evolution using Fokker planck equarion was introduced. His seminar will be very useful as a basic knowledge of evolutionary biology and mathematical biology that will be covered in future seminars.

Title: Untangling the complexity of market competition in consumer goods -A complex Hilbert PCA analysis
Author: Makoto Mizuno, Hideaki Aoyama, Yoshi Fujiwara
arXiv: http://arxiv.org/abs/2008.11327v1

Title: Parity operation for Majorana neutrinos
Author: Kazuo Fujikawa
arXiv: http://arxiv.org/abs/2008.11390v1

Title: Barthelonids represent a deep-branching metamonad clade with mitochondrion-related organelles predicted to generate no ATP
Author: Euki Yazaki, Keitaro Kume, Takashi Shiratori, Yana Eglit, Goro Tanifuji, Ryo Harada, Alastair G. B. Simpson, Ken-ichiro Ishida, Tetsuo Hashimoto, Yuji Inagaki
URL: https://royalsocietypublishing.org/doi/10.1098/rspb.2020.1538