セミナーレポート
327 ニュース

20200903
セミナーレポートiTHEMS MathPhys joint seminar was held on August 31 and September 1, 2020
The iTHEMS MathPhys 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, Sasadasan 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 adhoc analytic estimations. Moreover, they obtain a version of Varadhan’s decomposition in a very general setting. On Day 2, Bannaisan 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.

20200903
セミナーレポートBiology Short Talk by Dr. Ryosuke Iritani on September 2, 2020
On September 2, Ryosuke Iritani gave a lecture at iTHMES Biology Seminar. In this seminar, Ryo explained the principles of evolution in an easytounderstand 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.

20200827
セミナーレポートBiology Seminar by Dr. Gen Kurosawa on August 26, 2020
On August 26th, Gen Kurosawa gave a talk at the iTHEMS Biology seminar. The main topic of the talk was biological timing, and he introduced his work on mathematical modelling of circadian rhythm and hibernation. In addition, he also talked about his current effort in trying to apply theories developed in biology to understand the transaction network between companies. He clearly made a lot of effort to make the seminar accessible and enjoyable to people without background knowledge, and I'm sure many people appreciated that.

20200822
セミナーレポートiTHEMS Theoretical Physics Seminar by Dr. Takuya Shimazaki on August 21, 2020
On August 21st (Fri.), Takuya Shimazaki (The University of Tokyo) gave an iTHEMSphys seminar on an application of the Lefschetz thimble method to the Schwinger mechanism, or a particle production problem caused by strong electric fields. In the seminar, he has demonstrated a new formulation to estimate the particle production rate. The new formulation gives a good result even in some regimes where one cannot use the Dykhne–Davis–Pechukas (DDP) formula (a commonly used approximation in a twolevel quantum system equivalent to the Schwinger mechanism). There were a lot of lively discussions, and the audience looked enjoying the seminar.

20200805
セミナーレポートBiology Seminar by Dr. Lukasz Kusmierz on August 5, 2020
On 5th August, Ph.D. Lukasz Kusmierz ( RIKEN Center for Brain Science ) gave a talk at the iTHEMS Biology Seminar. Dr. Kusmierz introduced us to his work that modeling of heavy tails in the distribution of synaptic weights in the brain. His modeling, called "Cauchy network" which is based on the Cauchy distribution, has been successful in recreating biologically distributions. It could serve as a useful framework for checking the effects of synaptic heavy tails in various scenarios. His research will be a major step forward in the future of neuroscience. Thank you very much, Lukasz!

20200805
セミナーレポートMath Seminar by Dr. Tadahiro Miyao
The iTHEMS Math seminar entitled "Stability of ferromagnetism in manyelectron systems”, by Dr. Tadahiro Miyao, was held on 31 July. In the first part, the speaker reviewed basic properties of electron and introduced the Hubbard model, which describes interacting electrons. In addition, he constructed a model independent framework describing stabilities of ferromagnetism in strongly correlated electron systems. Especially, he reinterpreted the famous MarshallLiebMattis theorem and Lieb’s theorem. Then he showed that Lieb’s theorem still holds true even if the electronphonon and electronphoton interactions are taken into account. As examples, he explained the HolsteinHubbard model and the Kondo lattice model. Finally, he also mentioned other stability classes and open problems. In the second part, the speaker introduced order preserving operator inequalities and many mathematical tools, such as the PerronFrobeniusFaris theorem, abstract reflection positivity, the holeparticle transformation, and so on. He also explained how these inequalities are applied to the mathematical study of ferromagnetism. Then Lieb's theorem of the Hubbard model and its stabilities were discussed in terms of the inequalities.

20200731
セミナーレポートBiology Seminar by Dr. Takashi Okada on July 29, 2020
On 29th July, Takashi Okada gave us a talk on his work on population genetics theory. He first explained that the classical WrightFisher demography cannot inherently consider the realistic situation in which the offspringnumber distribution is skewed. Second, he talked about what if we extend the WrightFisher demography to a skewed offspring number (power low distribution), showing us that the powerlow distribution can dramatically change the timescale of evolution (e.g., sojourn time of fixation of a neutral mutant) as well as large population size limits. We learned that even the classic theory arising from Sewall Wright and Ronald A Fisher entails mathematical expansion. Thank you so much, Takashi, for the great talk!

20200727
セミナーレポートSpecial DMWG seminar : The latest results from the XENON1T experiment
XENON1T collaboration has reported interesting results in June, which could be the signature of the physics beyond the standard model. We held a special DMWG seminar on July 22, inviting Prof. Yamashita, who is a specialist in the XENON1T data analysis, from Nagoya University. Many people from various research fields have registered and participated in this online seminar. The number of registrants is more than 180 while the participants than 100. We first would like to apologize to our guests, especially to whom could not attend the seminar although they have registered due to our trouble with the webinar system. XENON1T is an experiment aiming to detect the scattering between dark matter (DM) and a xenon nucleus. Xenon is one of the best targets material for WIMP (Weakly Interacting Massive Particle) because of its stability and the large atomic number. By setting the detector deep underground, the cosmicray scattering event, which is the main source of the background, is efficiently removed. The original experiment was started in 2005 (XENON10) and after several upgrades, XENON1T has completed its first observing run in 2018. The signature of the socalled nuclear recoil event is searched to detect WIMP. There is another type of event referred to as the electronic recoil event, which is also useful to detect other DM signatures, and this seminar focuses on such a kind of event. The target region of the DM parameter space is different between these two event types. The 285 electronic recoil events over the expected 217247 from the background are observed in the recoil energy range of 17keV during the 1st observing run of the XENON1T experiment. In this talk, Prof. Yamashita has explained the details of the analysis and the possible interpretation of the signature. Starting from the introductions about the possible background considered in the traditional analysis, the statistical treatments, and also the model fitting results are provided. There are several possibilities for explaining the excess: (i) tritium background, (ii) solar axion, (iii) anomalous neutrino magnetic moment, and (iv) bosonic DM. If the excess is explained by tritium (i), it means that we have detected the first tritium background events while others indicate the detection of the signatures of the new physics. Solar axion (ii) could fit the recoil spectrum beautifully, however, there may not be consistent with the results from astrophysical observations. The neutrino scenario (iii) is another possibility with less significance, and the significance of the bosonic DM scenario (iv) could not over the 3.0 sigma. The excess itself is convincing while it is difficult to conclude its origin. Abobementioned possibilities are planned to be tested with further upgrades of the XENON1T experiment, XENONnT. We should be excited about the results in the near future. Stay tuned!

20200720
セミナーレポートMath seminar by Dr. Yuichi Ike on July 15, 2020
We have all heard that "data is the new oil". But just like any fossil resource, data also has to be worked with to use it effectively. In his talk, titled "Topological data analysis from a practical and mathematical perspective", Dr. Yuichi Ike from Fujitsu highlighted several mathematical aspects of data processing as well as relevant applications in the health sector. In the first part of the talk, the audience was introduced to basic concepts of topological data analysis. The goal of this technique is to infer the shape of data  i.e. topological quantities such as the number of connected components, loops, cavities, etc.  from the input data points. While the shape is represented by the homology group in the continuous case, the discrete case calls for different methodology. One possible technique is the creation of persistence diagrams to identify critical components. In a general application workflow, these approaches appear as follows. From the input data, its persistent homology is computed, visualized via a persistence diagram, and finally passed on to experts for evaluation. This has applications in material sciences and time series analysis as well as medical settings. Here, a recent work of the speaker was able to reduce misclassifications in a diagnosis setting by up to 70%. The second part of the talk was devoted to the mathematical foundations of the presented work, namely on persistencelike distance on the sheaf category and displacement energy. Starting from elements in symplectic geometry, via a Morse theory for sheaves, the speaker integrated several mathematical fields. Finally, after introducing the nondisplacement theorem, the audience learned about several proofs in the field. Thus, the talk nicely tied current relevant applications to deep results in theoretical mathematics.

20200716
セミナーレポートBiology Seminar about "Application of geometry to protein structure analysis" on July 15, 2020
In Biology Seminar on 15th July, a graduate student Haru OonoNegami (Engineering department, University of Tokyo) talked about a general overview of the interdisciplinary topic between geometry and protein biology, as well as her own work on the proteinclassification algorithms based on topological properties. Understanding and predicting the function of structurally "similar" proteins is of pivotal importance to any field of biology. Her work extends previous studies that classify the topological structure of proteins in a computationally reasonable time still with a good accuracy. We audience, after her talk, excitedly discussed extensions and background problems behind her talk. Thank you so much for the great talk, Harusan!  Ryosuke Iritani

20200716
セミナーレポートDMWG seminar on July 13 by Dr. Michimura
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 highintensity 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 axionlike particle, ALP) coupled to photon exists, the velocity of the right and lefthanded polarized waves should be different. Hence by setting the "bowtie" cavity to realize different pathlength for the right and lefthanded 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 microeV. Furthermore, this new search can be done during the gravitationalwave observations and do not affect such observations. He also has shown the expected sensitivity for scalar and vector DM picking up wellmotivated examples and told us another idea for the experiment. Such new ideas should open new ways to access the nature of dark matter!

20200708
セミナーレポートBiology Seminar by Dr. Yui Uchida on July 8, 2020
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.

20200702
セミナーレポートBiology Seminar by Dr. Shingo Gibo on July 1, 2020
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

20200701
セミナーレポートMath seminar by Dr. Ryusuke Hamazaki on Jun 24, 2020
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 constraineddynamics in generic gapped quantum systems. He introduced his result about a universal and rigorous error bound for a constraineddynamics approximation in generic gapped quantum systems. Then, he gave the outline of the proof of the error bound. The proof uses the SchriefferWolf 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.

20200625
セミナーレポートDark Matter Working Group Seminar on June 22, 2020
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(100)TeV, i.e., the range where it is difficult to probe with onEarth 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 Cooperpair braking & formation are considered. But another important process socalled 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. 
20200623
セミナーレポートMath seminar by professor Tasuku Soma
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 eprojection, 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 eprojection.

20200619
セミナーレポートReport on iTHEMS Intensive Course by Dr. Yoh Iwasa  Sex expression and sex allocation of marine organisms
This month, we hold 4day intensive course of mathematical biology. This is especially for nonexpert. 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

20200615
セミナーレポートBiology Seminar by Dr. Martin Skrodzki on June 10, 2020
On 10th June, Martin Skrodzki talked about Turing models. Historically, Turing's models have been very successful to describe various patternformations 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

20200615
セミナーレポート”Field theoretical approach to relativistic hydrodynamics" on June 12, 2020.
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 lowenergy effective theory of a conserved charge density, which describes a longdistance and longtime behavior of manybody systems. It is applicable not only to a nonrelativistic weaklyinteracting dilute gas but also a relativistic stronglyinteracting dense liquid like a quarkgluon plasma. The main purpose of this seminar is to explain how we can derive the hydrodynamic equation from the underlying fieldtheoretical description of systems [13]. The derivation is based on the recent development of nonequilibrium statistical mechanics, and they show that the procedure to derive hydrodynamic equations is similar to the socalled renormalized/optimized perturbation theory. Also, to describe transport phenomena in local thermal equilibrium, they give a pathintegral formula for a thermodynamic functional, which results in the emergence of thermally induced curved spacetime [2]. These results enable us to derive hydrodynamic equation based on quantum field theories.

20200615
セミナーレポートDark Matter Working Group Seminar on June 12, 2020
Among the numbers of dark matter (DM) scenarios, Weakly Interacting Massive Particle (WIMP) is one of the beststudied 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 freezeout. 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 crosssection (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 nonequilibrium between them around the freezeout epoch. Such a situation is referred to as the kinetic decoupling. The kinetic decoupling before the freezeout 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 freezeout process in detail and showed that the scattering crosssection, 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 nearfuture experiments. We should carefully work on the synergy between different types of experiments in this highprecision era of DM search.

20200605
セミナーレポートBiology Seminar by Dr. Hiroshi Yokota on June 3, 2020
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

20200601
セミナーレポートQFTcore Seminar by Dr. Ryusuke Hamazaki on May 29, 2020
The second QFTcore seminar entitled “Localization and universality in nonHermitian manybody systems” given by Dr. Ryusuke Hamazaki (RIKEN Hakubi/iTHEMS) was held on May 29. NonHermitian physics is now one of the topics studied actively, and he is one of the worldleading physicists of this topic. In the seminar, first, he introduced the basic ideas of thermalization of the isolated quantum systems and nonHermitian physics with simple examples. After that, some cuttingedge progress of nonHermitian manybody localization, and universality of nonHermitian 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.

20200601
セミナーレポートBiology Seminar on May 27, 2020
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 dopaminerelated 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 generalpurpose practical science and improve their research motivation.

20200529
セミナーレポートMath Seminar by Dr. Masaki Taniguchi
The iTHEMS Math seminar entitled "Knotted 2spheres in the 4space and YangMills 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 1knots up to equivalent. As an example, he introduced a knot invariant coming from 3colorings. For two dimensional knot theory, he explained the problem of how we write diagrams of 2knots 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 YangMills gauge theory for 4manifolds obtained by the surgery of 2knots.

20200525
セミナーレポートQFTcore Seminar “Gradient Flow Equation and Its Applications” on May 15, 2020
The QFTcore 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 nonrenormalization 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.

20200520
セミナーレポートFirst virtual Math Seminar on May 1, 2020
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.

20200515
セミナーレポートMath Seminar by Dr. Yukimi Goto
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 ThomasFermi theory and see TF functional appears as a leading term of grand state energy for large atom. She introduced HartreeFock 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.

20200513
セミナーレポートBiology Seminar by Dr. Catherine Beauchemin on May 13, 2020
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 COVID19 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

20200512
セミナーレポートTotani’s Equation: Abiogenesis probability in an inflationary universe
Abiogenesis is the natural process by which life has arisen from nonliving 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 lightyear 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.

20200508
セミナーレポートThird virtual Biology Seminar on May 7, 2020
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 threedimensional structures of DNA and proteins in cells, We felt that Dr. Sano's research could be applied to various structural problems in molecular biology.

20200507
セミナーレポートSecond iTHEMS Biology Seminar on April 30, 2020
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 largescale 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 nonbiologists 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

20200430
セミナーレポートNerd Night Tokyo: public talk by Don Warren
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!

20200430
セミナーレポートFrontier Science Lecture by iTHEMS Researchers
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.

20200428
セミナーレポートSearching the signature of the ultralight axions using gravitational waves
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 gravitationalwave physics. Axions and axionlike 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 socalled 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/axionlike particle, this scattering leads to the multiple particle production hence they form a cloudlike structure around the BH, which resembles the electron cloud of the atom. Such a BHaxion cloud object can be the source of the continuous gravitational wave since axions in the cloud are converted to gravitons when they pairannihilate. 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 cloudformation 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 1001000 continuous gravitationalwave signals generated in the axion clouds. We can probe the axion/axionlike particle of which mass is 0.11 picoeV using this method. The sensitivity with the LIGOVirgo facilities peaks at ~0.5 picoeV. We could see the signatures of the new physics and/or the hint of dark matter by conducting intensive analyses.

20200423
セミナーレポートFirst virtual Biology Seminar on April 22, 2020
Though this fiscal year started with the confusion for COVID19, 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 virusvirus 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)

20200403
セミナーレポートMath Seminar Talk by Dr. Mikio Furuta, February 25, 2020.
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 WilsonDirac 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 WilsonDirac operator, which is defied on a discrete lattice. This equality is given in a suitable Kgroup, 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.

20200217
セミナーレポートBoosting the lensing study for DM properties with machine learning techniques
Strong lensing of the galaxy, which can be seen as arclike features, is a powerful probe of the smallscale DM halos. The populations of smallscale 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 stronglensing image data using likelihood ratio test. The machinelearning 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 largesized lensing image data. In the near future, we should probe the parameters of the subhalo mass function hence the DM properties from galaxygalaxy lensing. Furthermore, the method is so flexible that encourages us to consider much wider applications in DM search.

20200213
セミナーレポートBiology Talk by Dr. Yasuo Yasui, February 5, 2020.
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 nonmajor 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 nonbiologists, and many nonbiologists from iTHEMS were able to join and ask many questions.

20200212
セミナーレポートMath Seminar Talk by Dr. Martin Skrodzki, February 7, 2020.
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 kd 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.

20200131
セミナーレポートABBLiTHEMS Joint Seminar by Dr. Hajime Sotani
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 lowmass 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 socalled 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 lowmass neutron stars constructed with various EOSs up to twice the saturation density, the suitable combination of K0 and L for expressing well the lowmass 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.

20200124
セミナーレポートMath seminar by Dr. Shu Nakamura
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.

20200117
セミナーレポートMath Seminar by Prof. Syuji Yamamoto
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.

20191218
セミナーレポートMath seminar talk by Dr. Wahei Hara
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.

20191212
セミナーレポートDMWG Seminar by Dr. Chiaki Hikage
2nd IPMUiTHEMS DMWG seminar was held on Dec. 12 at IPMU. Dr. Hikage gave a talk about the weak lensing cosmology by Subaru Hyper SuprimeCam(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 linesofsight, 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 1030% 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.

20191120
セミナーレポートMath Seminar talks by Dr. Atsushi Ito
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.

20191113
セミナーレポートiTHEMS Public Lectures at RIKEN Kobe Open Campus 2019
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 twobody systems, and how to overcome the difficulty by computational approach. Both lectures were pedagogical enough for nonscientists and stimulated interesting questions from the audience.

20191101
セミナーレポートMath Seminar talks by Dr. Ken Shiozaki
The iTHEMS Math seminar was held on 24 Oct., inviting Ken Shiozaki from Kyoto university. The title of the talk was "AtiyahHirzebruch spectral sequence in band theory". The main subject of the talk was topological Ktheory, a branch of topology in mathematics, from the viewpoint of physics. In the theory of condensed matter physics, it is wellunderstood that a classification of topological phases is given by topological (twisted equivariant) Ktheory. Conversely, some physical intuitions help us understanding (or even calculating) Ktheory. In the talk, the speaker illustrated "physical meanings" of basic mathematical notions such as the axioms of cohomology theory, the MayerVietoris exact sequence and the Bott periodicity.

20191030
セミナーレポートMath Seminar talks by Professor Masaki Tsukamoto
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, 15:3016:30, 16:4017:40, 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 (minimax) variational principle to the dynamical rate distortion. His talks on October 22 and 23, 13:3014:30 at the room 435437 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.

20191024
セミナーレポートDMWG Seminar by Dr. Toyokazu Sekiguchi
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 splitSUSY 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 socalled freezeout 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 freezeout mechanism to determine the DM relic density. However, the WIMP and the SM particle are still kinetically coupled even after the thermal freezeout. 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(1e7) 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 smallscale halos resides in the larger halo increases. The enhancement in the number of smallscale halos leads to a higher flux for gammaray annihilations in presentday halos. We have an increased possibility of detecting DM signatures in the ongoing and planned astrophysical observations.

20191009
セミナーレポートiTHEMS Colloquium given by Professor Yasuyuki Kawahigashi
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 quasiparticles. 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 LanWangWen about the mathematical formulation of gapped domain wall, which is rejected by a knowledge in subfactor theory. The second is alphainduction 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 8090's. Because the talk was organized coherently, we can enjoy a lot of topics in 90 minutes.
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