The Michelson interferometer is sensitive to the new physics as well as to the gravitational wave. The input laser beam is split in the horizontal and vertical direction, then combined again after times of the round trip in the cavity of each path. The patters of the interference give us the information about the change in path length, forces shifting the reflecting mirrors, and/or the change in the speed of light. During the observing run searching for the gravitational waves, a high-intensity laser form the input source is supplied continuously so it is highly efficient if we can make use of the laser to probe other physics simultaneously. Let us focus on the laser beams after the split. The polarization of the split laser beam changes at each time it is reflected. When axion (or axion-like particle, ALP) coupled to photon exists, the velocity of the right- and left-handed polarized waves should be different. Hence by setting the "bow-tie" cavity to realize different path-length for the right- and left-handed polarized photons, we should see the signature of the ALP in the interference pattern. This idea, which is proposed by Dr. Michimura and his colleagues, is completely new and enable us to probe the unexplored region for ALP lighter than ~0.1 micro-eV. Furthermore, this new search can be done during the gravitational-wave observations and do not affect such observations. He also has shown the expected sensitivity for scalar and vector DM picking up well-motivated examples and told us another idea for the experiment. Such new ideas should open new ways to access the nature of dark matter!
On 8th July, Ph.D. Yui Uchida (RIKEN BDR) gave a talk at the iTHEMS Biology Seminar. Dr. Uchida introduced to us the research field of Evolutionary Developmentary biology (EvoDevo) and talked about her researches on embryogenesis. Her lecture gave a briefly explanation about the background of EvdDevo in general and the important evolutionary questions in vertebrate development that had been tackled by her with mathematical modeling of embryogenesis. I felt her lecture helped many audiences to understand EvoDevo and we had a good discussion. Another highlight of her talk was her talk on the evolution of the five fingers of Tetrapoda excited the physicists! Thank you very much, Dr. Uchida.
On 1 July, Shingo Gibo gave a talk at the iTHEMS Biology Seminar. He talked about his research on using mathematical approaches to understand biological oscillations, such as circadian rhythms. His work is a really nice example of the synergy between different disciplines. He draws ideas from mathematics and physics to solve problems in life science, and then his results developed in life science feeds back to various areas related to mathematics and physics. Another highlight of his talk was his cute zoom background :-) -Jeffrey Fawcett
The iTHEMS Math seminar entitled "Universal Error Bound for Constrained Quantum Dynamics" by Dr. Ryusuke Hamazaki, was held on 24 Jun. In the first part, the speaker first introduced two physical examples of constrained dynamics including Rydberg atoms. Then, he explained the motivation of his study: finding quantitative error estimates of constrained-dynamics in generic gapped quantum systems. He introduced his result about a universal and rigorous error bound for a constrained-dynamics approximation in generic gapped quantum systems. Then, he gave the outline of the proof of the error bound. The proof uses the Schrieffer-Wolf transformation (SWT) and Sylvester equation. In the second talk, he gave a more precise proof of the error bound. In the proof, several computational techniques are used.
Astrophysical observations are really important for understanding the nature of dark matter (DM) in multiple aspects. For example, the measurement of the temperature evolution of the neutron star (NS) provides us with new information about the properties of weakly interacting massive particle (WIMP). Since WIMP can interact with nucleon, of which scattering process is intensively searched in direct detection experiments, WIMP in our Universe should be captured by NSs. When the accumulated WIMPs annihilate inside the NS they heat up to modify the temperature evolution of the NS. Such a phenomenon is especially to probe the WIMP in the mass range of m<O(0.1)GeV and m>O(100)TeV, i.e., the range where it is difficult to probe with on-Earth experiments. In order to detect the effect of the WIMP annihilation, one must understand the temperature evolution of the NS in the standard model process accurately. In general, the surface temperature of NS is the highest at their birth, then cools through the photon and neutrino emission. Some of the NS older than ~Myr shows a higher temperature from the simple expectation in the standard model processes and the gap between the observation and the theoretical prediction was believed to be a room for the DM heating. In the above discussion, the processes of the direct and modified Urca, Bremsstrahlung, and Cooper-pair braking & formation are considered. But another important process so-called the rotochemical heating exists for rotating NSs. The beta equilibrium is not sustained when the NS is rotating and the conversion of the neutron to the proton occurs more frequently than its inverse process. NS heating through this process should be involved when we predict the temperature evolution. The deviation from the beta equilibrium hence the temperature evolution is sensitive to the birth period of the NS. Based on the calculation involiving a detailed treatment of the NS inner structure, Dr. Hamguchi has shown in this seminar that the rotochemical heating should be more efficient than that from the WIMP annihilation for a typical birth period. There might be no rooms for the WIMP annihilation to heat up the NS. However, the observational estimate of the birth period is still a challenging task, and there could be NSs with high birth periods. Furthermore, the number of such systems that are suitable for testing the WIMP heating scenario will increase in the near future. Such kinds of study should accelerate the collaboration between kinds of experiments to solve the DM mystery.
In 17 June, professor Tasuku Soma (The university of Tokyo) gave a seminar on scaling problem and information geometry at the math seminar. In the first part he gave an introductory talk on scaling problem. Assume matrix A is given and each entry of A is positive. Matrix scaling problem is to find good matrix L,R with which LAR and (LAR)* has nice property. He then introduced Sinkhorn algorithm. This is an algorithm to calculate "LAR" in the above problem. He then explained operator scaling, which is quantum analogue of matrix scaling. He explained his recent result on the operator scaling and information geometry. It is known by Csizar that Sinkhorn algorithm for matrix scaling is actually an alternating e-projection, which appears in the information geometry. He then introduced his recent work with Takeru Matsuda. In that work, they proved that operator scaling is also an alternating e-projection.
Report on iTHEMS Intensive Course by Dr. Yoh Iwasa - Sex expression and sex allocation of marine organisms
This month, we hold 4-day intensive course of mathematical biology. This is especially for non-expert. On June 18th, Dr. Yoh Iwasa talked about various mysteries of sex. For instance, anemonefishes (kumanomi, in Japanese) are male when they are born. As they get bigger, they become female. Interestingly, some coral reef fishes are opposite. As they get bigger, they become male. Why do they show such sex expressions? Dr. Iwasa astonished us that various mysteries of sex can be resolved from the view point of game theory. According to him, “Anything related to sexual system can be quantified. In terms of the number of offspring, number of reproductive success, and other things. Success of the male depends on whether there are many more males or females. Obviously, this is the game theoretic view point.” During the lecture, the philosophy behind the mathematical modeling was explained in detail. The lecture on Thursday was attended by more than 160 people through Zoom and Youtube. Dr. Iwasa answered all the uncountable questions from the audience. The wonderful intensive course continues. - Gen Kurosawa
On 10th June, Martin Skrodzki talked about Turing models. Historically, Turing's models have been very successful to describe various pattern-formations on a two dimensional plane. He briefly introduced examples and then talked about three dimensional space, showing amazingly diverse patterns the model can cover. His talk generated stimulation discussion among the audience. Thank you so much for the great talk, Martin! -Ryosuke Iritani
The iTHEMS Theoretical Physics Seminar is hold on June 12, 2020. The speaker is Masaru Hongo in University of Illinois at Chicago/RIKEN iTHEMS. The title is ”Field theoretical approach to relativistic hydrodynamics”. Hydrodynamics is a low-energy effective theory of a conserved charge density, which describes a long-distance and long-time behavior of many-body systems. It is applicable not only to a non-relativistic weakly-interacting dilute gas but also a relativistic strongly-interacting dense liquid like a quark-gluon plasma. The main purpose of this seminar is to explain how we can derive the hydrodynamic equation from the underlying field-theoretical description of systems [1-3]. The derivation is based on the recent development of non-equilibrium statistical mechanics, and they show that the procedure to derive hydrodynamic equations is similar to the so-called renormalized/optimized perturbation theory. Also, to describe transport phenomena in local thermal equilibrium, they give a path-integral formula for a thermodynamic functional, which results in the emergence of thermally induced curved spacetime . These results enable us to derive hydrodynamic equation based on quantum field theories.
Among the numbers of dark matter (DM) scenarios, Weakly Interacting Massive Particle (WIMP) is one of the best-studied particles. It attracts special attention because of its beautiful mechanism to achieve the relic abundance of dark matter which is referred to as the thermal freeze-out. In the early Universe, the annihilation of the WIMP into the standard model (SM) particles and its inverse process are frequent enough to sustain the thermal equilibrium. At a certain point, WIMP decouples from the thermal bath then its number density, which is directly related to the relic abundance, is fixed. The strength of the coupling between WIMP and the SM sector determines the annihilation frequency. The same coupling is also responsible for the energy transfer between the SM particles and WIMP. The constraints on that scattering cross-section (i.e., the energy transfer between two sectors) have already been severely constrained by direct detection experiments. This motivates us to consider such a model that the coupling is so small and the relic abundance is achieved by a resonant annihilation at a certain mass. In this way, we can satisfy the requirements from the results of direct detection experiments. The small coupling between the SM sector and WIMP could lead to a non-equilibrium between them around the freeze-out epoch. Such a situation is referred to as the kinetic decoupling. The kinetic decoupling before the freeze-out affects the calculation of the relic density, which is a crucial part of the WIMP scenario. In this talk, Dr. Abe clarified the effect of the kinetic decoupling in terms of the coupling constant taking two examples of fermionic and scalar DM in the Higgs portal scenario. He calculated the freeze-out process in detail and showed that the scattering cross-section, which is measured at direct detection experiments, should also be different from the case where assumes a complete thermal equilibrium. We could see the signature of such DM in near-future experiments. We should carefully work on the synergy between different types of experiments in this high-precision era of DM search.
In the 6th biology seminar, Hiroshi Yokota (iTHEMS fellow at Kyoto University) talked about his theoretical work on the energy of chromosome loop structure (collaborative work with Masashi Tachikawa). Through the modeling, he talked about the possibility that the chromosome loop structure may occur due to ATP hydrolysis. His work will stimulate future debate over the source of the energy needed for chromosome loops to occur. Great talk, Hiroshi! -Ryosuke Iritani
The second QFT-core seminar entitled “Localization and universality in non-Hermitian many-body systems” given by Dr. Ryusuke Hamazaki (RIKEN Hakubi/iTHEMS) was held on May 29. Non-Hermitian physics is now one of the topics studied actively, and he is one of the world-leading physicists of this topic. In the seminar, first, he introduced the basic ideas of thermalization of the isolated quantum systems and non-Hermitian physics with simple examples. After that, some cutting-edge progress of non-Hermitian many-body localization, and universality of non-Hermitian random matrices were introduced. The seminar was held via the Zoom online conference system. Around 20 people participated in the seminar and joined the active discussion.
On 27 May, Ayaka Kato, The University of Tokyo, gave a talk at the 6th iTHEMS Biology Seminar. In this seminar, Ayaka talked about the results of the research on mathematical modeling of dopamine-related phenomena. It was not previously known how dopamine is involved in motivation, but in Ayaka's previous studies, the mathematical model from several previous experiments was proposed. In this seminar, Ayaka presented a new model that incorporates learning decay and successfully reproduces the real behavior on a computer simulation based on her new model. Since modeling the relationship between dopamine and motivation is very important both psychologically and medically, I felt that the results of these studies would not only benefit basic research but would also serve as a basis for general-purpose practical science and improve their research motivation.
The iTHEMS Math seminar entitled "Knotted 2-spheres in the 4-space and Yang-Mills gauge theory," by Dr. Masaki Taniguchi, was held on 27 May. In the first part, the speaker reviewed that classical knot theory and history of knot. Especially, he introduced that one and two dimensional knot theory, and gave many examples. For one dimensional knot theory, he explained the fundamental problem of knot theory, i.e., the problem of classifying 1-knots up to equivalent. As an example, he introduced a knot invariant coming from 3-colorings. For two dimensional knot theory, he explained the problem of how we write diagrams of 2-knots in four dimensional Euclidean space. Then he introduced the motion picture. In the second part, the speaker focuses on a problem considered in differential topology. First, he explained that the fundamental problem in differential topology. Next, he introduced gauge theory and some examples. Finally, as the main result of the talk, he explained his theorem about the difference between continuous and smooth two dimensional knots. He then introduced that the proof uses Yang-Mills gauge theory for 4-manifolds obtained by the surgery of 2-knots.
The QFT-core seminar series has been started from this fiscal year. The seminar series is hold under the theme of the Quantum Field Theory including elementary particle theory, nuclear theory and Condensed Matter physics. The First seminar in the series was given by Dr.Kengo Kikuchi from the Riken iTHEMS on May 15. The title is “Gradient Flow Equation and Its Applications”. The gradient flow is the one of the methods to suppress the ultraviolet divergence in gauge theories. The any correlation functions in terms of the flowed field, which is defined by the gradient flow equation, are finite without additional renormalizations. Because of this surprising property, the methods has been studied widely, especially in the lattice field theory. In this seminar, he introduce what the gradient flow is briefly, and show his work, “generalized gradient flow equation”, which is the gradient flow equation for field theories with nonlinearly realized symmetry. Applying the formalism to a supersymmetric theory and O(N) non linear sigma model, the SUSY gradient flow and the Large N gradient flow are obtained. He also refer to the current research, the gradient flow of the supersymmetric theory with the non-renormalization theorem and the new formalism to obtain the sphalerons, which is one of the static classical solutions, using gradient flow methods. The seminar was hold via Zoom. There were about 20 participants from iTHEMS and other university. The participants enjoyed meaningful discussions through the seminar.
The first iTHEMS Math seminar of this academic year was held on May 1st on Zoom, inviting our colleague Keita Mikami. The title of the talk was “From Eigenvalues to Resonances”. The main topic was Resonance, which is one of the most studied objects in mathematical study of Schrödinger operators. In the first part, the speaker briefly reviewed spectral theory and how we use it in the study of Schrödinger operators, introducing some basic notions used in the study of Schrödinger operators. Especially, he explained that spectra can be classified into eigenvalues and continuous spectra. Then he introduced scattering theory, which can be used to analyze absolutely continuous spectra. One novelty is that generalized eigenfunction has a representation formula in terms of scattering matrices. In the second part, the speaker gave a brief introduction of resonances and its application to both mathematicians and researchers in other fields. After introducing mathematical definition of resonances, he explained its applications in the other fields. One example was the following experimental result; when one makes a wave with certain frequency in aquarium, there appears special pattern in the distribution of speed. This phenomena can be explained mathematically by considering resonance of pseudodifferential operator on torus.
Math seminar titled "How many electrons can atoms bind?" by Dr. Yukimi Goto was hold on 13 May. In the first part, the speaker started the talk by introducing many body Hamiltonian and Pauli principle. She then introduced the ionization conjecture. She also introduced some known results concerning about this conjecture. In the second part, the speaker introduced approximation methods and its relation to the ionization conjecture. She first introduced Thomas-Fermi theory and see TF functional appears as a leading term of grand state energy for large atom. She introduced Hartree-Fock theory next. She mentioned a variant of the ionization conjecture for HF theory was proven by Solovej, but original conjecture is still open. She then explained HF theory can be regarded as good approximation in terms of volume.
Catherine talked about her general approach for formalizing and quantifying the principle of virological dynamics, namely “virophysics.” She first presented compartmental models to generalize the probability distribution of sojourn time of cells being infective, with parameter estimation in flu data using MCMC, and then talked about COVID-19 modeling and its predictability. I was honestly surprised that increasing the number of compartments can readily change the distribution, and found it promising to apply her approach to not only virology but ecology and evolution as well. Thank you, Catherine, for the great talk! - Ryosuke Iritani
Abiogenesis is the natural process by which life has arisen from non-living matter. Understanding of abiogenesis can tell us one of the most fundamental questions in natural science: “Why are we here?”. However, abiogenesis probability is believed very very low to have us, life, in the universe considering the formation of a long enough polymer having a correct nucleotide sequence by random reactions. Sometimes, this probability is quoted as “Can a monkey hitting a keyboard at random type a complete work of Shakespeare?”. On 11 May 2020, we had iTHEMS Colloquium inviting Prof. Tomonori Totani from the University of Tokyo, with the title of “Emergence of life in an inflationary universe.” Prof. Totani is a renowned professor in astrophysics working on high energy astrophysics and cosmology. As a cosmologist, he visited this abiogenesis issue. Cosmologists believe that the universe created by inflation should extend far beyond the observable universe (13.8 billion light-year radius). Combining the knowledge of this inflationary universe and the RNA formation processes, he provided a new equation describing the abiogenesis probability in an inflationary universe. This new equation showed that, as the inflationary universe contains a large number of stars, it may provide sufficiently many abiogenesis events, even if we consider only the basic random polymerization. However, following his equation, regrettably, we may expect no “aliens” in our universe. Let’s see the results of future telescopes’ search of a second Earth.
On 7 May, Dr. Tomohiko Sano, from École polytechnique fédérale de Lausanne in Switzerland, gave a talk at the 3rd iTHEMS Biology Seminar. In this seminar, Dr. Sano talked about the results of his research on how physical actions in knots occur. It has been empirically known that hitch knots and other knots cannot be untied, but how they work has not been well understood. Dr. Sano explained that he had clarified them through experiments and simulations. Since there are various knots in the three-dimensional structures of DNA and proteins in cells, We felt that Dr. Sano's research could be applied to various structural problems in molecular biology.
On 30 April, Euki Yazaki, who joined iTHEMS in April, gave a talk at the second iTHEMS Biology Seminar. Euki's main research motivation is to understand the diversity and evolution of eukaryotes, especially by focusing on microorganisms called "protists". Most of you probably know nothing about protists. In fact, protist is not a proper phylogenetic group. It is "any eukaryotic organism that is not an animal, plant, or fungus" (from Wikipedia) - i.e. a category to dump all the eukaryotes that most people don't know about and don't care about. Yet, as Euki illustrated, they make up most of the phylogenetic diversity of eukaryotes, and there are still many many species that haven't been discovered. He described his previous research where he isolated an unknown protist from Palau which was different from any other protist that had been discovered, and determined its phylogenetic placement by large-scale DNA sequence data analyses. Euki and I believe that protists hold the key to understanding the origin of eukaryotes and to uncover some new exciting biology. Euki's talk also sparked interest from non-biologists to learn more about phylogenetics, a topic that involves lots of mathematics, which will hopefully be the topic of a seminar in the near future. - Jeffrey Fawcett
At Nerd Night Tokyo on April 22, Don Warren gave a public talk on "First stars". You can watch his superb lecture from YouTube. Enjoy!
Frontier Science Lecture by iTHEMS Researchers for undergraduate students in Univ. of Tokyo was started on April 22, 2020. This year, Yoshiyuki Inoue gave an online lecture on "the History of the Universe looking through the Black Holes". He started the lecture from ancient views of the Universe including the old Japanese tale that the Universe began from the Chaos. Then he moved on to the modern view of the Universe and Matter based on the theory of general relativity and also quantum mechanics. After explaining recent observations of the black holes, he ended his lecture by saying that we are now entering the era of black hole astronomy. On April 29 (although it was a national holiday), Yoshiyuki's lecture was followed by Yoshimasa Hidaka's lecture on "the Origin of Matter". His second lecture will be held on May 13. Frontier Science Lectures in 2018 and 2019 can be checked from the web site below. The 2018 lecture will be published from the Univ. of Tokyo Press in the summer of 2020.
As the first activity of the DM working group in the academic 2020, we have held an online seminar inviting Dr. Sylvia Zhu from DESY. She has introduced her recent work about the axion search using the continuous gravitational waves, which is a new connection between the particle and the gravitational-wave physics. Axions and axion-like particles are good candidates for dark matter, which could simultaneously solve the strong CP problem. When such particles exist around spinning black holes (BHs), they can extract the angular momentum of the BH through the so-called superradiance. In this mechanism, the amplitude of the axion oscillation increases because the wave is scattered off by the rotating BH. Especially for the case of the axion/axion-like particle, this scattering leads to the multiple particle production hence they form a cloud-like structure around the BH, which resembles the electron cloud of the atom. Such a BH-axion cloud object can be the source of the continuous gravitational wave since axions in the cloud are converted to gravitons when they pair-annihilate. The detection of the continuous gravitational wave is really difficult. The key quantities for the detectability are the strength of the gravitational wave and the duration. In addition, the cloud-formation condition has to be satisfied. The larger the mass of the axion as well as the BH is better to form such systems. Also, the strength of the gravitational wave increases along with the mass of the system and the spin of the central BH. On the other hand, the decaying timescale of the gravitational wave emission becomes shorter for heavier systems hence there is a competition between these effects. Combining the mass and spin distribution of the BHs in our Galaxy, we could expect about 100-1000 continuous gravitational-wave signals generated in the axion clouds. We can probe the axion/axion-like particle of which mass is 0.1-1 pico-eV using this method. The sensitivity with the LIGO-Virgo facilities peaks at ~0.5 pico-eV. We could see the signatures of the new physics and/or the hint of dark matter by conducting intensive analyses.
Though this fiscal year started with the confusion for COVID-19, we launched virtual, iTHEMS Biology Seminar. As the first speaker of the seminar series, Asher Leeks, who is appointed with the University of Oxford and visiting Japan as IPA student, gave a talk on his own work on virus-virus interactions. Viruses may disperse (or move) between cells in a group, forming a “collective infectious unit” (CIU). If viruses can interact positively (i.e., larger CIUs enable faster replication), then CIU, albeit physiologically costly, is likely to be favored by natural selection (i.e., evolutionarily advantageous), with the result that fewer but bigger CIUs may emerge. With negative interactions, in contrast, natural selection favors smaller CIUs/no CIUs at all. This is so because, under negative interactions, forming groups would not pay. These contrasting results, therefore, suggest that understanding viral interactions may be of pivotal importance, with potential implications for clinics. He then explained genomic data for comparison and finally talked about our current collaboration project at iTHEMS. Since more and more people are now interested in virology, his new theory may give insight into a wide range of fields, and we learned a lot about what is going on within patients' bodies. Thanks for the excellent talk, Asher! -Ryosuke Iritani (iTHEMS, Research Scientist)
The open house for RIKEN was scheduled on April 18th, but it was cancelled due to the COVID-19 situation. But that did not stop Dr. Yokokura and the other lecturers, Dr. Iritani, Dr. Irie, Dr. Hiroshima, Dr. Miyazaki and Dr. Tanaka. In defiance of the difficulties, they gave the same public lecture on-line with the help by Academist. Dr. Yokokura and other lecturers worked very hard preparing the event; their effort was rewarded by the spectacular success, with as many as over 900 viewers. Some of the positive response can be seen on Twitter.
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.
Strong lensing of the galaxy, which can be seen as arc-like features, is a powerful probe of the small-scale DM halos. The populations of small-scale DM halo give us hints about its particle properties. We need to manage huge parameter spaces (e.g. redshift distribution of the source galaxies, lensing galaxies, mass functions of perturbing subhalos and so on) to determine the subhalo signatures from the strong-lensing image data using likelihood ratio test. The machine-learning based techniques of the reduced likelihood ratio estimator enable us to derive the parameters of subhalo mass function, which are key quantities to access the nature of DM, in an efficient way. The importance of this technique increases for the coming era of large-sized lensing image data. In the near future, we should probe the parameters of the subhalo mass function hence the DM properties from galaxy-galaxy lensing. Furthermore, the method is so flexible that encourages us to consider much wider applications in DM search.
On February 5, 2020, Dr. Yasuo Yasui, a plant geneticist from Kyoto University, gave a talk on his research on buckwheat (=soba) genetics. First, he explained how the current food supply of the world is heavily dependent on a very small number of plants, and that there is a pressing need to increase the yield of many other non-major crops, including buckwheat. He argued that now we have the tools to tackle this problem thanks to the advance in genome sequencing technologies, and that data science, computer science, and mathematical science have important roles to play. He then presented his previous research on buckwheat genetics and genomics, such as the identification of certain genes in buckwheat that are important for buckwheat breeding. He also showed some slides from field trips in South China (mainly Yunnan province) to collect wild buckwheat species, and explained his ongoing research in trying to understand the origin and domestication process of buckwheat, which is a joint effort with Jeffrey Fawcett from iTHEMS, and other researchers in Japan, China, and the UK. The talk was aimed at non-biologists, and many non-biologists from iTHEMS were able to join and ask many questions.
Dr. Martin Skrodzki, who stays at RIKEN iTHEMS as a postdoctoral researcher for the year 2020, gave a talk at the Math Seminar on February 7, 2020. The title of his talk was "Solved and open problems regarding the neighborhood grid data structure". He began with introducing the k-d tree for a finite set with coordinates in the plane and explained that by using this tree one can find the nearest point from a given point in a reasonable time. Then, he looked at the neighborhood grid data structure introduced by Joselli et al. in 2009, which is an n times n matrix filled by pairs of numbers (f(i,j),g(i,j)) where f and g are surjections to the set of numbers from 1 to n squared. He gave the definition of a stable state and explained that any grid data structure can be stabilized and that stabilization can be done in a short time using parallel computation. He explained the correspondence between a generic set of n squared points in the plane and stable grid data structures, and discussed several open questions around this correspondence. The talk was very accessible for everyone and the participants enjoyed it very much.
As ABBL/iTHEMS seminars, Dr. Hajime SOTANI gave a talk about "Neutron stars and nuclear saturation parameters" on 24th January. So far, many equations of state (EOSs) for neutron star matter are proposed, but the EOS is not fixed yet. This is mainly because the difficulty to obtain the information for high density region via terrestrial experiments. Thus, as an inverse problem, neutron stars are a suitable laboratory for probing the nuclear properties in the high density region. In this talk, it has been discussed the possibility for constraining the nuclear saturation parameters via the neutron star observations, especially focusing on the low-mass neutron stars. Any EOSs can be expanded in the vicinity of the saturation point as a function of the baryon number density, where the expansion coefficients correspond to the saturation parameters. So, each EOS has an own set of saturation parameters. Among the saturation parameters, the incompressibility (K0) for symmetric nuclear matter and the so-called slope parameter (L) for pure neutron matter are relatively difficult to constrain, because these are a kind of the derivative around the saturation point. Thus, in particular these two saturation parameters have been focused in this talk. In addition, the EOSs for high density region can not be expressed well only with the saturation parameters, but one may be able to discuss the EOSs with the saturation parameters up to twice the saturation density. In practice, by systematically examining the masses of low-mass neutron stars constructed with various EOSs up to twice the saturation density, the suitable combination of K0 and L for expressing well the low-mass neutron stars has been found successfully, i.e., eta^3 = (K0 * L^2). That is, the neutron star mass and gravitational redshift can be expressed well as a function of eta and the stellar central density. This is suggested that the value of eta and central density could be constrained via the simultaneous observations of neutron star mass and gravitational redshift. Furthermore, using eta, the possible maximum mass of neutron stars has been discussed together with the constraint obtained from the gravitational wave event, GW170817, and NICER observation.
The iTHEMS Math seminar was held on 23 January, inviting Shu Nakamura from Gakushuin university. The title of the talk was “Semiclassical methods in mathematical quantum mechanics”. The topic was semiclassical analysis and scattering theory of Schrödinger operators. In the first part, the speaker gave a introductory talk on the microlocal analysis and semiclassical analysis of Schrödinger operators. He started his talk by introducing a canonical quantization. Then he explained how canonical quantization is understood in the framework of semiclassical and microlocal analysis. Moreover he explained some recent results on this research field. In the second part, the speaker explained his recent results on scattering matrix of Schrodinger operators with long range potentials. At the beginning, he introduced the definition of scattering matrix and some known results. Then he stated his main result on the representation of scattering matrix. As an application, he gave some examples of long range potentials for which he proved several spectral properties of scattering matrix.
The iTHEMS Math seminar was held on 17 December, inviting Shuji Yamamoto from Keio university. The title of the talk was “Multiple Zeta Values: Interrelation of Series and Integrals”. The topic was multiple zeta values (MZVs), which is a generalization of the values of the Riemann zeta function. In the first part, the speaker explained the definition of MZVs, and the statement of the Zagier conjecture, which predicts how many algebraic relations should exist among MZVs. Moreover, he explained several known algebraic relations, including Euler relation, Hoffman relation, duality, sum formula, Ohno relation, etc. He also provided two types of proof of duality, one of which is due to himself and Seki. In the second part, the speaker explained Double Shuffle Relation and Regularization. It is conjectured that these relations generate all the algebraic relations of MZVs, but this is a hard open problem. For example, it is unknown whether the relations imply duality. However, many relations are generated by these relations. The speaker explained some concrete examples, after introducing integral series identity.
The iTHEMS Math seminar was held on 4 December, inviting Wahei Hara from Waseda university. The title of the talk was “Noncommutative crepant resolutions and some higher dimensional flops”. The central topic was singularities of algebraic varieties and representation theory. In the first part, the speaker explained the McKay correspondence as an example of connections between du Val singularities and representation theory of finite subgroups of the special linear group of degree two over the complex number field. In the second part, the speaker talked about noncommutative crepant resolutions of singularities. There are several ways to interpret the Mckay correspondence. The derived McKay correspondence is the interpretation of the McKay correspondence in terms of derived categories. The notion of noncommutative crepant resolutions is the generalization of the derived McKay correspondence to a large class of singularities. We discussed applications of noncommutative resolutions to the study of derived categories in birational geometry.
2nd IPMU-iTHEMS DMWG seminar was held on Dec. 12 at IPMU. Dr. Hikage gave a talk about the weak lensing cosmology by Subaru Hyper Suprime-Cam(HSC) survey. The weak lensing measurement is a powerful tool to probe the matter distribution in the Universe up to redshift z~2. Lots of galaxies are seen in the optical wavelength and the seeing of HSC is fine enough to determine the shape of the galaxy. When massive objects (i.e., dark matter halos and so on) lie on our lines-of-sight, the image of the background galaxies is distorted in a specific pattern. Photometric data of the HSC enables us to tomographically derive the map of the integral of the matter density. This quantity is referred to as the "shear". The power spectrum of the shear map leads to the cosmological parameter such as the total matter density. HSC has revealed that the matter density is in 10-30% of the total energy density of the Universe and previously claimed tension of the cosmological parameters between the measurements may not exist. With future HSC observations, a much precise and deep understanding of the matter distribution in our Universe should become available.
The iTHEMS Math seminar was held on 8 Nov., inviting Atsushi Ito from Nagoya university. The title of the talk was "Some topics in projective geometry of algebraic varieties". The main subject of the talk was the Gauss map and the dual variety of an algebraic variety, which reflect the behavior of the tangent spaces at a moving point of the variety. In the first part, the speaker explained the duality theorem of the dual variety and the original variety, which holds in the usual setting but fails in the unusual (that is, in positive characteristic) setting. In the second part, we considered the dimension of the dual varieties. The main result says that the gap of the dimension of the dual variety from the expected dimension is determined by a fibration structure of the variety with a good fibres.
iTHEMS Public Lectures were held at the 8th floor of the RIKEN IIB building on Nov.9 as a part of the RIKEN Kobe Open Campus 2019. Takumi Doi (RNC/iTHEMS) and Emiko Hiyama (Kyushu U./RNC) gave lectures on computational nuclear and particle physics. Takumi introduced the history and concept of computers with full of Kansai jokes, followed by an explanation of the recent results from massive parallel computers such as the K computer. Emiko explained why quantum systems with more than 3 particles are fundamentally different from the two-body systems, and how to overcome the difficulty by computational approach. Both lectures were pedagogical enough for non-scientists and stimulated interesting questions from the audience.
The iTHEMS Math seminar was held on 24 Oct., inviting Ken Shiozaki from Kyoto university. The title of the talk was "Atiyah-Hirzebruch spectral sequence in band theory". The main subject of the talk was topological K-theory, a branch of topology in mathematics, from the viewpoint of physics. In the theory of condensed matter physics, it is well-understood that a classification of topological phases is given by topological (twisted equivariant) K-theory. Conversely, some physical intuitions help us understanding (or even calculating) K-theory. In the talk, the speaker illustrated "physical meanings" of basic mathematical notions such as the axioms of cohomology theory, the Mayer-Vietoris exact sequence and the Bott periodicity.
Professor Masaki Tsukamoto of Kyushu University, the winner of 2019 Geometry Prize of the Mathematical Society of Japan, visited iTHEMS for October 21 - 23 and gave a series of talks at Math Seminar. The theme of his talks was `Mean dimension of dynamical systems and information theory'. On October 21, 15:30-16:30, 16:40-17:40, he gave survey talks at Okochi Hall; In the first part he explained the notion of mean dimension in relation with information theory as an obstruction to embedding dynamical system to the shift on the Hilbert cube. In the second part he explained the notion of mean dimension in relation with data compression and showed that the mean dimension is obtained by applying to a (mini-max) variational principle to the dynamical rate distortion. His talks on October 22 and 23, 13:30-14:30 at the room 435-437 were on the key observation concerning the embedding problem and that on that concerning the dynamical rate distortion, respectively. The participants enjoyed his clear explanations on this mean dimension defined by Gromov which can play important role in the future study of infinite dimensional dynamical systems.
The 2nd DMWG seminar was held on Oct.21, inviting Dr. Sekiguchi from The Univ. of Tokyo/KEK. Focusing on the weakly interacting massive particle (WIMP) case, he lectured the formation of the minimum mass DM halo in the early Universe and its implications. WIMP is one of the strongest candidates for DM. From a theoretical point of view, neutral wino in the split-SUSY scenario is an example. One important feature of WIMP is that it achieves the current DM density, usually referred to as the relic abundance, via the so-called freeze-out mechanism. In the early Universe, the thermal equilibrium between WIMPs and the standard model (SM) particles is maintained. As the Universe expands, the temperature decreases then the WIMP annihilation rate to the SM particles becomes smaller than the expansion rate of the Universe. At this point, the number density of DM is fixed. This is the thermal freeze-out mechanism to determine the DM relic density. However, the WIMP and the SM particle are still kinetically coupled even after the thermal freeze-out. In this stage, they transfer momentum by each other through the direct scattering. By carefully calculate the epoch of the kinetic decoupling, the minimum halo mass, which is important in characterizing the DM halo properties and the observable signatures, are determined. He showed that the minimum halo mass should be of the order of O(1e-7) solar mass when we consider the neutral wino in the split SUSY scenario. This value is smaller than that expected when we neglect the kinetic decoupling effect. Furthermore, the total number of small-scale halos resides in the larger halo increases. The enhancement in the number of small-scale halos leads to a higher flux for gamma-ray annihilations in present-day halos. We have an increased possibility of detecting DM signatures in the on-going and planned astrophysical observations.
iTHEMS Colloquium was held on 4 Oct. 2019, inviting Prof. Yasuyuki Kawahigashi from the University of Tokyo (he is also a senior visiting scientist of iTHEMS). The title was "Topological phases of matter and operator algebras", and he explained his researches on operator algebra and their relations with theoretical physics. The central subject of the talk was modular tensor category (MTC). A subfactor (an inclusion of simple von Neumann algebra) has the symmetry of a tensor category, in an analogous way to the Galois theory of fields. MTC is an important class of tensor category having an interesting commutativity of the tensor product, and is also a useful tool to describe the anyonic statistics of quasi-particles. A powerful source of MTC is conformal field theory, and a comparison of two mathematical approaches (conformal net and vertex operator algebra) is a recent hot topic. In this talk Prof. Kawahigashi displayed three interesting examples in which a mathematical research, originated from its own motivation, helps the study of mathemtaical physics later. The first is a conjecture by Lan-Wang-Wen about the mathematical formulation of gapped domain wall, which is rejected by a knowledge in subfactor theory. The second is alpha-induction in the theory of MTC, which is now understood as a mathematical formulation of anyon condensation. The third is a work by Bultinck et. al. on tensor network, which turned out to be parallel with the subfactor theory (such as tube algebra and flat connection) studied by Ocneanu, Haagerup and Prof. Kawahigashi in 80-90's. Because the talk was organized coherently, we can enjoy a lot of topics in 90 minutes.
iTHEMS DM working group, which aims to bridge the collider, direct, and indirect dark matter (DM) searches to obtain inclusive understandings of DM and develop new strategies for coming experiments, is launched this summer. The 1st seminar is given by Dr.Rinaldi on Oct. 1st. He talked about composite DM theory. DM is a massive component different from ordinary matters (usually referred to as baryons) in our Universe. The nature of DM is still a big mystery and many kinds of explanations are proposed. Composite DM scenario is motivated by the origin of the mass in the standard model physics. In the standard model, the strong interaction is responsible for the proton and neutron mass hence for the mass of baryons. Considering a similar situation in the dark sector, composites of dark fermions can be DM in our Universe. The dark and the standard model sector are connected through the interaction between the constituent fermions and the standard model particles. Composite DM itself has no direct connection to our sector. This explains the non-detection of DM in the up-to-date collider, direct, and indirect experiments. Also in this scenario, the self-interaction of DM is naturally introduced. Then, it could ameliorate the small-scale problem which appears in more traditional DM scenarios. Starting from the general introduction for composite DM, his recent work based on the lattice calculations for the signatures of composite DM is also introduced. Signals from composite DM could be detected in the near future. A series of seminars and workshops are being planned as the working group activity. Please join us!
iTHEMS Biology Seminar was held on September 13, inviting Prof. Hiroyuki Kubota (Kyushu University) and Dr. Yasufumi Uezu (NTT). The theme of this seminar is “mathematical biology in temporal waveforms.” Prof. Kubota revealed that the temporal patterns of blood insulin concentration selectively regulate downstream molecules depending on network structure and time constant. His discovery is important for understanding the mechanism not only of insulin signaling but also of many signal transduction systems in biology. Dr. Uezu is specialist of voice production research. Textbook in this field often explains vocal fold vibration (sound source) and vocal tract filter are independent. In contrast, he experimentally showed that nonlinear interaction between them is crucial for generating various singing voice, for example falsetto and scream. The seminar attracted a wide range of audience including biologist, physicist, and mathematician, and we enjoyed active discussion.
On Sep. 2 and 3, Dr. Hirotaka Irie (DENSO Corporation / iTHEMS visiting scientist; see his self-introduction in this volume of NewsLetter) gave a series of comprehensive lectures on "Quantum Annealing" which is a quantum computational scheme for hard optimization problems. This was held as a part of the iTHEMS QCoIn WG activity. In the first day, he started the lecture by explaining the fundamental notions of quantum computation and quantum annealing, followed by the basic usage of quantum annealer. In the second day, he discussed the notion of computational complexity in detail, and then showed various examples of the real-world applications of quantum annealer. The lectures were given only by using white-board with detailed explanation of basic equations, which stimulated lots of questions from the audience. Discussions continued during the break and after the lectures.
An Academic-Industrial Innovation Lecture was delivered by Dr. Yuya Nakagawa from QunaSys on September 4th. QuanSys is a venture company specializes in quantum computing and Dr. Nakagawa joined QunaSys shortly after having earned his Ph. D. In the first part, Dr. Nakagawa gave a concise overview of quantum computing. The second part of the lecture consisted of more detailed explanation including the result from QuanSys itself and the application to Quantum Chemistry. The lecture attracted audience not only from RIKEN but also outside RIKEN, especially notable companies. The last part of the lecture turned out to be filled with a lot of questions from the keen audiences, and candid comments were exchanged. We felt that the lecture is really serving as a hub that connects people from academics and industry.
A lecture on “Introduction to quantum many-body system “ by Prof. Hosho Katsura was held from September 5 to 6 at RIKEN. In particular, we studied basic concepts of many-body systems on lattices and how to investigate their properties in analytical and numerical ways. In the first part of the lecture, non-interacting Fermi and Bose systems on lattices were focused and we learned how to calculate energy bands. Such systems included Kitaev chain and Su-Schrieffer-Heeger model for one-dimensional fermions as well as free bosons describing low-energy properties of quantum magnets. In the second part, we studied spin systems such as Affleck-Kennedy-Lieb-Tasaki model from the perspective of frustration-free systems and the concept of matrix product states. The attendees were scientists from various backgrounds; physicists specializing in condensed-matter physics, atomic physics, nuclear physics, and particle physics as well as mathematicians. This lecture was filled with fruitful discussion and instructive to attendees who are not professional in lattice systems.
Program Director of iTHEMS, Prof. Tetsuo Hatsuda gave a talk at the 28th RIKEN Satosho Seminar on Aug. 29, 2019.
As a research activity of RIKEN iTHEMS and Kyushu Univ. collaboration, Dr. T. Doi gave lectures on his research, Lattice QCD and research activity on HAL QCD collaboration from 31th July to 2nd Aug. In his lectures, approximately 25 persons who were mainly PhD students attended and had many discussion with him. It was very fruitful days for them.
General relativity tells us how spacetime is curved by energy distribution and how matter moves in the spacetime. Classical black hole, which is a solution of the classical Einstein equation, has the event horizon and singularity. Event horizon, from which anything cannot escape, is defined at infinite future, and physical quantities such as energy density diverge at the singularity. These properties are not physically acceptable. Then, what are black holes in our universe? Prof. Pei-Ming Ho (National Taiwan University) addressed this question by studying quantum effects in general relativity. The key is the nature of the vacuum. Classical matter always has positive energy, but in quantum field theory the expectation value of energy density can be negative due to quantum fluctuation of the vacuum. The semi-classical Einstein equation connects the expectation value of energy-momentum tensor to the curvature of spacetime. If there is negative energy, traversable wormhole solutions can be constructed. They could be used as time machines for backward time travel, but they would lead to several paradoxes like “Grandfather paradox”. Prof. Ho explained this topic by showing how SF movies were inconsistent with physical laws. Then, he asked “What are the appropriate energy conditions to avoid inconsistencies?” The answer is still unknown, but it should be related to so-called “information paradox” in black holes. Suppose that a star (classical matter) collapses to a classical black hole. Hawking derived that the black hole evaporates slowly by emitting radiations due to the quantum properties of the vacuum. Then, where has the information of the matter gone after the evaporation? The information seems to disappear because the matter is trapped inside the horizon while the black hole evaporates. Any information must be preserved in quantum theory, but the mechanism is not clear in the black hole evaporation. As he said, one scenario is that some remnant is formed instead of complete evaporation. He first explained that, due to quantum fluctuation of the vacuum, the region near the would-be horizon is modified to obtain a “neck” structure without a horizon. The (proper) volume inside the neck is larger than the usual volume of the 3-dimensional sphere with the radius of the neck (because of negative energy). This is like a SF apartment: when you enter a room, it has a larger space than you expected from the outside. This is one possibility of quantum black holes. He also discussed dynamics of the neck black hole. As it evaporates, the neck would shrink and the information inside the neck would be left as a remnant, but this seems to be not a good solution to the information problem because the information would be isolated from the exterior world forever. Finally, he introduced his recent progress: when a trapping horizon (a local and dynamical notion of horizons) becomes timelike, negative energy occurs and the black-hole mass decreases (not by Hawking radiation). It is a non-perturbative effect w.r.t. Planck constant, which could not exist in the classical limit. This result implies that the four factors are closely related: dynamics near quantum black hole, appropriate energy condition including quantum effects, a more proper description beyond the semi-classical one, and the mechanism of information recovery. His entertaining talk showed that a black hole is not just a hole but a window to a new world. It is time to ask again “What is black hole?”
Hiroki Kodama had a seminar talk in the iTHEMS math seminar on 20 June. The topic was the foundation of metric space and its generalizations. Metric space is one of the most primitive setting of geometry. This notion is defined in an abstract way by metric function satisfying 3 axioms. Not only the Euclidean metric, which is familiar for all of us, many ideas arising all over the science (e.g. the distance of two DNAs) are formulated as a kind of metric. A main interest of this seminar was a generalization of metric space, which is less popular even for mathematicians. A function satisfying the axioms of metric space except for the symmetry axiom d(x,y)=d(y,x) is called an asymmetric metric (a typical example is the cost for a ship on a river to move from one point to another). In the first half of the talk, Kodama introduced the basic notion of (asymmetric) metric spaces with various examples. In the second half, he introduced an interest of asymmetric metric space by showing rich information it includes.