Seminar Report
313 news
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2021-01-21
Seminar Report
Biology Seminar by Dr. Koichiro Uriu on January 7, 2021
On January 7th, Dr. Koichiro Uriu gave a talk on one of the most important pattern formation in our body. Koichiro was an active member of iTHES, and is currently an assistant professor at Kanazawa Univ. Rhythmic (ON and OFF) and also spatial gene activity pattern, termed the segmentation clock underlies our body axis segmentation (“Taisetsu" in Japanese). Thus, robust gene activity oscillation propagates from the backward to the forward domain by which the segment is formed sequentially. In the seminar, Koichiro discussed the recovery processes of the segment formation after the removal of the drug which blocks oscillator coupling in a fish, called zebrafish. Curiously, experiments show that intermingled segments can occur in the body of the fish especially when the drug is removed at early stage. To understand the pattern recovery, he developed a physical model incorporating mechanics and genetic oscillations. During and after the talk, there were numerous questions from the audience because his talk was very interesting and also very clear. Thank you and see you, Koichiro! - Gen Kurosawa
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2021-01-20
Seminar Report
Information Theory SG by Dr. Ryosuke Iritani on January 20, 2021
On January 20th, Dr. Ryosuke Iritani gave us a talk about his motivation to work with information theory. He first formulated the dynamics of species-site data in ecology as a Markov model. By reducing the model to a simpler one in an elegant way, he analytically obtained the evolution of the proportion of species. In addition, he discussed certain entropies that characterize the diversity of species and showed us the unique dynamics of the entropy in his model. His talk was clear as he explained mathematical concepts by using simple examples and illustrations, and there were questions and comments from several viewpoints. We are thankful to Ryosuke for the exciting talk! Kyosuke Adachi (BDR/iTHEMS)
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2021-01-19
Seminar Report
First Quantum Matter Seminar by Dr. Xueda Wen on January 18, 2021
We are happy to invite Dr. Xueda Wen from Harvard University to give a talk on January 18th. This talk is the first seminar of the quantum matter study group. The topic is time-dependent driven quantum critical systems in (1+1) dimensions, which connects condensed matter physics and high energy physics. Dr. Wen started with two different free-fermion lattice Hamiltonians. The system is driven periodically and alternatively with these two Hamiltonians. Interestingly, this driven system leads to two distinct two phases. This straightforward introduction smoothly brought us to the study of time-dependent driven conformal field theories. The driven CFTs show that the periodical driving systems can possess heating and non-heating phases, and the phase transition boundary separates these two phases. Dr. Wen further talked about the generalization of driving CFTs and several unsolved problems. This talk is informative as well as interactive. Drs. Tada, Hongo, and Takasan asked several key questions, and Dr. Wen answered those questions clearly and informatively. We thank Dr. Wen for the great talk. Reported by Ching-Kai Chiu
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2021-01-14
Seminar Report
Information Theory SG by Dr. Kyosuke Adachi on January 13, 2021
On January 13, Dr. Kyosuke Adachi gave a talk entitled “Accelerated equilibration in classical stochastic systems” at the journal club of information theory study group. First, he reviewed the concept of shortcuts to adiabaticity (STA) and discussed a two-level system as a concrete example. Then it was explained that STA are fast routes to the final states in quantum systems. Second, he introduced the engineered swift equilibration (ESE) in classical stochastic systems, which is a classical counterpart of STA. Indeed, he explained that the Fokker-Plank equation has a similar structure to the Schroedinger equation, and the fast routes from the initial equilibrium state to the final equilibrium state are ESE. As examples of ESE, compression of Brownian particles, and evolutionary systems were given. Finally, he mentioned some interesting questions. The talk had many stimulating discussions. We are grateful to Adachi-san for his excellent talk!
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2021-01-14
Seminar Report
Biology Seminar by Dr. Jeffrey Fawcett on January 14, 2021
In iTHEMS biology seminar on January 14, Jeffery Fawcett (RIKEN iTHEMS) gave us a talk on what genes are and how we can identify them. He started from the basics such as chromosomes, genes, and how proteins are produced from them. He then explained difficulties in defining a gene. This sounds very interesting because most of us (at least, I) naively think that we know what a gene is, even without knowing a precise definition of it. He also explained how we can predict the location of genes on the chromosomes. Jeff nicely presented keys ideas for non-experts, and all of us enjoyed his talk. I am also working on evolutionary biology, but I have never thought seriously about how genes are identified, and his talk became a nice introduction to this fascinating topic. Thank you very much, Jeff! - Takashi Okada
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2020-12-24
Seminar Report
Information Theory SG by Dr. Yukimi Goto on December 23, 2020
This week, Dr. Yukimi Goto gave us an introduction to the Lieb-Robinson bound. After reviewing several important preliminaries, such as Liouvillians for open quantum systems, she discussed the Lieb-Robinson bound, which is a theorem for the bound on speed of information propagation. She then explained two notable applications of the bound, i.e., correlation decay and the entanglement area law for a gapped ground state in isolated quantum systems. We thank Goto-san for her great talk!
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2020-12-23
Seminar Report
Biology Seminar by Dr. Shingo Iwami on December 22, 2020
In his seminar Dr. Iwami (Kyushu University) presented his mathematical model for coronavirus (新型コロナウイルス) in patients. The aim of the project was to determine why some papers disagreed on the efficacy of certain antiviral drugs to treat the coronavirus. Because the available data was limited, only a simple mathematical model was considered. The mathematical model only represents the fraction of cells remaining to be infected and the amount of virus. The curve for the virus in the model was fitted to the data of virus in the nasal swab of patients. From this analysis, Dr. Iwami's group could separate the patients into 3 types: with either slow, medium or fast decay of virus. He showed that in his model, only early treatment can be effective for all decay types. This can be one reason why two different clinical trials can find different results: if one trial includes late treatment then it can appear that the treatment is not effective. From the mathematical model, he suggested some changes in the criteria for patient inclusion into clinical trials to improve the ability to detect statistically significant effects for the antiviral drug. The seminar was very well attended, with many questions and discussions. Thank you Dr. Iwami for your great talk! - Catherine Beauchemin (iTHEMS)
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2020-12-18
Seminar Report
Biology Seminar by Akane Hara on December 17, 2020
In today's biology seminar, we invited Akane Hara, a PhD student at Kyushu University, to have her talk about how pathogen infection can cause autoimmune diseases. Normally, the immune systems attack germs like viruses and bacteria to prevent their growth within the body. However, these germs may mimic themselves to our body system so that they can avoid the attack. As a result, the immune system is not able to tell the germs from our body parts, and so even after the removal of the germs, it harms our body mistakenly. Wondering why - or when - this is the case, she considered ordinary differential equations of the compartment models for virus, helper cells, and memory T cells, by explicitly considering cross immunity. She presented a mathematical condition for which autoimmune diseases may be present and/or severe. We discussed possible extensions of the mathematical models. Thank you so much for the great talk, Akane! Personally, I was a colleague with her at Kyushu University and so feel a bit emotional that she's completing her PhD very soon! -Ryosuke Iritani
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2020-12-18
Seminar Report
iTHEMS-phys seminar by Takeru Yokota on December 17, 2020
On December 17, the iTHEMS-phys seminar entitled "Classical liquids and functional renormalization group" given by Dr. Takeru Yokota (ISSP, U. Tokyo) was held. He has been working for the functional-renormalization-group-aided density functional theory (FRG-DFT) for several years. Recently, he is applying this method to classical liquid. As a benchmark calculation, he applied to a one-dimensional exactly solvable system. The exact solution was sucessfully reproduced by the method. The seminar was held via the Zoom online conference systems. More than 20 people, including outside from iTHEMS, attended the seminar. The discussion was quite lively, and it was continued several hours even after the seminar.
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2020-12-18
Seminar Report
Math-Phys Joint Seminar by Dr. Naotaka Kubo on December 14, 2020
His talk was on the test of non-perturbative dynamics of three-dimensional gauge theories from the perspective of brane dynamics in string theory. In the first half of his talk, he explained important ideas in quantum field theory at an elementary level, such as renormalization group (RG) flow, supersymmetry (SUSY), and world-volume theory on branes in string/M-theory. Combining these fundamental ideas, he moved on to the discussion of duality cascades in quantum gauge theories in four and three dimensions. Using branes in string theory, he demonstrated that the duality cascades in M2-brane world-volume theories can be understood from the brane dynamics in type IIB string theory, which is the so-called Hanany-Witten move/transition. In particular, he mentioned that after the sequence of the Hanany-Witten transitions, one may predict if the original gauge theories have SUSY breaking under the RG flow. Then he concluded that all the world-volume theories related by the Hanany-Witten transitions would flow to the same IR theory, and SUSY will be broken if anti-D3-branes are created. In the latter part of the talk, he argued the non-perturbative tests of duality cascades in three-dimensional supersymmetric gauge theories using partition functions of the theories. He first introduced the notion of partition functions of quantum field theories on S^3 and rephrased the conclusion given in the first part in the language of partition function. He then illustrated the general idea to exactly compute the partition function of supersymmetric gauge theories, which is an analogue of Duistermaat-Heckman formula and is called supersymmetric localization. He gave a dictionary between the viewpoint of brane configuration and the partition function of supersymmetric gauge theories. With such a dictionary, the Hanany-Witten transition of branes was rewritten by an equality between the partition functions. Moreover, one can directly check the duality cascades and SUSY breaking by calculating the partition functions. Finally, he showed the duality cascades and SUSY breaking in supersymmetric gauge theories by an explicit evaluation of partition functions, with comments on Fermi gas formalism and residue computation.
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2020-12-17
Seminar Report
Biology Seminar by Dr. Yuri Kominami on November 27, 2020
In iTHEMS Biology Seminar on November 27th, Dr. Yuri Kominami from University of Tokyo gave us a talk about her experimental study on population dynamics of rotifer. It is often difficult to understand population dynamics of animals because the population is reflected by complex environmental conditions. In her study, by using rotifer as a model organism, she has succeeded in measuring the laboratory population size, the birth rate, and the life span in a controlled condition. In this seminar, she showed some of nontrivial results of her experiment. Her discoveries were very exciting for theoretical biologists, and we enjoyed active discussion. Thank you so much, Kominami-san! -Shingo Gibo
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2020-12-16
Seminar Report
Information Theory SG by Dr. Ryusuke Hamazaki on December 16, 2020
In the journal club of Information Theory Study Group held on December 16th, Dr. Ryusuke Hamazaki (CPR/iTHEMS) gave us a talk about recent proposals of a quantum version of the Wasserstein distance. He first reviewed the commonly used quantities expressing the distance between probability distributions, i.e., the total variation distance and the relative entropy. After pointing out certain problems with these quantities, he introduced the classical Wasserstein distance of order 1 as a better definition of the distance and explained its representative properties like transportation inequality and tensorization property. Next, he introduced a quantum counterpart of the Wasserstein distance, which can apply to spin-1/2 quantum systems. In contrast to the total variation distance, the quantum Wasserstein distance has interesting properties like the invariance under permutation or local unitary transformation. Lastly, he explained an application of the quantum version of transportation inequality to the eigenvalue distribution. Reflecting the interdisciplinary subject of the talk, there were several questions and comments from both mathematical and physical viewpoints. We are grateful to Ryusuke for the great talk! Kyosuke Adachi (BDR/iTHEMS)
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2020-12-16
Seminar Report
Information Theory SG by Dr. Koichiro Yoshino on December 16, 2020
As the first seminar speaker of the Information Theory study group, we invited Koichiro Yoshino (Teamleader of Robotics Project, RIKEN) to give a talk on natural language processing. First, he explained the statistical language model's basis, e.g. language model, distributed representations, etc, and then discussed his own works: 1) attribute transfer in word embedding space, 2) modeling sentence structure. Natural language processing is one of the good applicants of information theory, and we enjoyed his clear talk and discussions. Akinori Tanaka (iTHEMS/AIP)
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2020-12-15
Seminar Report
Math Seminar by Dr. Hideki Inoue on December 7, 2020
On December 7, there was a math seminar by Dr. Hideki Inoue. His talk aims to introduce Levinson's Theorem and its recent progress. In the first part, he gave a brief survey talk on Levinson's theorem and its formulation. He then explained that Levinson's theorem, which can be proved analytically. He then introduced abstract scattering theory and operator algebras and how they applied to Levinson's theorem study. In the second part, he explained his recent results on Levinson's theorem. He showed a straightforward representation formula of the wave operator, a significant research target in the scattering theory. With this formula, he proved that one could prove Levinson's theorem by abstract theory. He also explained similar results on discrete operators.
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2020-12-10
Seminar Report
Biology Seminar by Dr. Euki Yazaki on December 10, 2020
In iTHEMS Biology Seminar on December 10th, Dr. Euki Yazaki (iTHEMS) talked about recent techniques and problems in obtaining the large-scale sequence data of eukaryotes. He first mentioned the importance of identifying and comparing the genome sequence in biology. Then, he illustrated the two representative sequencing methods, Sanger sequencing and next-generation sequencing (NGS). He clearly explained the features of these methods, highlighting the advantages of NGS in exploring large-scale or novel sequences. In the latter part, he introduced a method using the graph theory to reconstruct the large-scale genome data from the fragments of a sequence obtained by NGS. He lastly pointed out some problems in the current reconstruction method, and we discussed possible ideas to mitigate them after the talk. We are grateful to Euki for the stimulating talk! Kyosuke Adachi (BDR/iTHEMS)
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2020-12-09
Seminar Report
Math Seminar by Dr. Tianfeng Hou on November 13, 2020
On November 13, Tianfeng Hou, a new member of the team, gave a math seminar on the Monte Carlo study. In the first part, the speaker focuses on quasi-Monte Carlo method and its probabilistic assessments. In the second part, the speaker explained reduced-order models and how they work in the hygrothermal model. He first showed his model works efficiently in the linear scenario. On the other hand, he explained that his model is not so efficient in some nonlinear scenario.
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2020-12-08
Seminar Report
Information Theory SG by Dr. Akinori Tanaka on December 8, 2020 (Continuation of last week)
Continued from last week, Dr. Akinori Tanaka (Senior Research Scientist of iTHEMS and AIP) gave us a talk about the connection between the thermodynamic law and the algorithms of deep learning. He first reviewed the second law of thermodynamics in Langevin systems and the representation of stochastic gradient descent algorithms using Gaussian fluctuation. He then explained about Generative Adversarial Networks (GAN), which can be used in producing near realistic fake images. Based on mathematical correspondence, he discussed a possible application of the modified thermodynamic law to the algorithms of GAN. We are thankful to him for the exciting talk! Kyosuke Adachi (BDR/iTHEMS)
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2020-12-07
Seminar Report
First Information Theory SG by Dr. Akinori Tanaka on December 1, 2020
Kicking off the study group of information theory, Akinori Tanaka (Senior Research Scientist of iTHEMS and AIP) talked about the connection between Langevin equation and deep neural networks. He first showed that by analyzing Langevin equations one can derive the second law of thermodynamics which posits that the total entropy of the system should increase. He then delved into stochastic gradient descent (SDG) and showed how to apply it to train the neural network in general. We discussed too enthusiastically for him to finish his talk, and so we'll organize the second part next week (08 December 2020). We are all looking forward to discussing more, and thank you so much for the elegant talk! -Ryosuke Iritani (iTHEMS)
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2020-12-07
Seminar Report
Math Seminar by Dr. Martin Skrodzki on November 30, 2020
Our colleague Martin Skrodzki gave a farewell-talk in iTHEMS Math seminar on November 30. The title of the talk was “Flat and spherical surface approximations”. He talked about two approaches to approximate surfaces by using flat objects and spherical objects. In the first part, he explained the approximation using flat objects. Naively, there are two approaches to approximate surfaces. One is local and the other is global. In local approach, we need to get extremely many samples. In global approach, it will produce extreme torsion of surfaces. To remedy these problems, we should think of medium approach, i.e., patching of small simple flat objects (like covering of manifolds). This is called Variational Shape Approximation (VSA). The VSA has three steps: seeding, flooding and updating (and we iterate these recursively). This method gives us a very nice approximation of surfaces, but it still has some defects. Indeed, The recursive process does not always converge, the result depends on initial random choice of seeding, and it also depends on the artificial choice of the number of proxies we use. Therefore, Martin and his collaborators refined the VSA, by adding new steps called “splitting”, “Merging” and “Switching”. These steps avoids all defects above. In the second part, he explained his project on approximating surfaces using spheres. He shows some extreme examples of surfaces which are not relevant for spherical approximation: cone and toilet paper. If you imagine a needle-shaped cone, then its intersection with a ball will be very small. On the other hand, if you thing of rolled paper, then its intersection with a ball have too large area. However, if the surface we want to approximate satisfies a relevant condition, we can obtain a condition on the radius of the ball we use to approximate the surface. During the lecture, he proposed an interesting question on the maximum/minimal area of the intersection of the ball and the surface, and there was an exciting discussion including the audience.
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2020-12-07
Seminar Report
DMWG Seminar by Dr. Naka: Directional Direct Detection Experiments
Among the kinds of dark matter (DM) candidates, Weakly Interacting Massive Particle (WIMP) shows a strong model motivation. It achieves the current DM density naturally via the so-called thermal freeze-out mechanism. The strength of the interaction between WIMP and the standard model particles should be finite, and various direct detection experiments have already excluded a large part of the favored parameter space. We are now in the phase to consider the next strategy. There are several directions to proceed. For example, annual and/or diurnal modulation of the event rate of the DM-nucleon scattering. However, the expected modulation amplitude is so small that a few percent for annual modulation and less than 1% for the diurnal case. Kinds of on-going experiments intensively search the modulation signature now, however, it is still difficult to confirm. Another possibility is to make use of directional information. One important advantage of the directional search is its power for background rejection. The DM signal should be more frequently found in the direction corresponding to the Galactic Center while the backgrounds are in different directional distributions. These differences enable us to reduce the number of scattering events required for claiming the detection from O(1e4) to O(100), compared to the conventional direct detection cases. Furthermore, it could potentially provide us with information about the velocity distribution function, of which precise understanding is a key to any kinds of direct detection experiments, as well as the scenarios explaining the evolution of our Galaxy. Hence, the directional search is an attractive idea to probe the nature of DM. Recently, such projects are launched, and still some technical issues to solve remain. We have to achieve the O(1e-9)m scale resolution of the particle track, to confirm the scalability and stability, and to understand the ultra-low background. Many projects are now tackling these problems. The new era for direct DM search now begins!
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2020-11-30
Seminar Report
Biology Seminar by Dr. Hidenori Tanaka on November 20, 2020
In iTHEMS Biology Seminar on November 20th, Dr. Hidenori Tanaka (Physics & Informatics Laboratories, NTT Research) gave us an exciting talk about physics principles in neural networks. He first reviewed the basic scheme of deep learning using neural networks. Then, he presented three questions regarding both neural science and machine learning and explained his recent works which address these questions. He stressed how physics principles like symmetry and conservation laws are useful in extracting minimal features of biological circuit models, improving algorithms to simplify neural networks, and predicting learning dynamics of neural networks. As his talk was clear and kind to both specialists and non-specialists, there were various questions from the audience. Hidenori is a very active researcher, and I was happy to invite him as a guest speaker. Kyosuke Adachi (BDR/iTHEMS)
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2020-11-24
Seminar Report
Math Seminar by Dr. Takahiro Kitayama on November 16, 2020
On November 16, professor Takahiro Kitayama from University of Tokyo gave a talk entitled “Representations of fundamental groups and 3-manifold topology” at the iTHEMS math seminar. In the first part, he introduced a central motivation of 3-manifold topology: classify all 3-manifolds up to diffeomorphisms. As one of the important tools, he introduced the fundamental groups of spaces. He reviewed several known results of the fundamental groups of manifolds. Next, he focused on essential surfaces and introduced Haken 3-manifolds as an important class of 3-manifolds. In particular, he introduced several examples of Haken and non-Haken manifolds. At the end of the first talk, he explained SL(2,C)-representation spaces (character varieties) of the fundamental groups of 3-manifolds. He mentioned that the representation space has been used as a fundamental tool to classify knots and 3-manifolds. In the second part, he first mentioned Culler-Shalen, Morgan-Shalen’s theorem which says that an ideal point of the SL(2,C)-character variety of a given 3-manifold M gives an essential surface of M. Friedl, Hara, Kitayama, and Nagel developed C-S and M-S’s theory for the Lie group SL(n,C). He explained the main idea to obtain all essential surfaces from ideal points of SL(n,C)-character variety. In particular, he introduced the tautological representation depending on some affine curve of the SL(2,C)-character variety, and an action of the fundamental group on some contractible simplicial complex called the Bruhat-Tits building. Then by a standard argument of topology, he constructed some simplicial map f from the universal covering space of a given 3-manifold to the Bruhat-Tits building. By taking the inverse image of f(after ignoring trivial parts and dividing by the fundamental group of the 3-manifold), he finally constructed an essential surface. Next, he also told us about a relation between (homotopy types of) boundary loops of essential surfaces of knot complements and slopes of sides of the Newton polygon obtained from A-polynomials. He said an essential idea of the result, which can detect whether the boundary of an essential surface obtained from an ideal point is boundary parallel or not. At the end of the second talk, as the leading coefficients of torsion functions, he gave a function c_{M, ψ} on the SL(n, C)-character variety. After explaining Dunfield-Friedl-Jackson’s conjecture, he gave a partial solution of the conjecture which is related to the finiteness of c_{M, ψ} on the ideal points.
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2020-11-16
Seminar Report
Math-Phys joint Seminar by Dr. Naoto Shiraishi on November 10, 2020
On November 10, Dr. Naoto Shiraishi from Gakushuin University gave a talk entitled “Mathematics of thermalization in isolated quantum systems” at the iTHEMS Math-Phys joint seminar. In the first part, he reviewed some results and problems of quantum thermalization. Besides, he explained the typicality of equilibrium states, the relaxation caused by large effective dimensions, and the weak/strong eigenstate thermalization hypothesis mathematically. In the second part, the speaker discussed the difficulty of the thermalization problems and some of his results. Mainly, he showed the absence of local conserved quantities in the S=1/2 XYZ chain with a magnetic field. The talk had many participants from in and out iTHEMS and many stimulating discussions.
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2020-11-09
Seminar Report
Biology Seminar by Dr. Takahiro Sakamoto on November 5, 2020
On November 5th, Takahiro Sakamoto from SOKENDAI gave a talk at the iTHEMS Biology Seminar. First, he gave a very nice introduction about the basics of population genetics, and then, he talked about his theoretical study about how genetic divergence proceeds when there is migration between two locally adapted sub-populations. He did very well in explaining his research, which is actually quite complicated, to non-experts, and because of that there were many questions and fruitful discussions. Takahiro is a student from my previous lab and I had in mind to invite him at some point because I knew he is good at giving talks and that his research should be interesting to iTHEMS people. So I was pleasantly surprised that Okada-san invited him, and I was very glad to see that many people enjoyed his talk. Jeffrey Fawcett
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2020-11-09
Seminar Report
Biology Seminar by Dr. Jeffrey Fawcett on October 29, 2020
In iTHEMS biology seminar on October 29, Jeffery Fawcett (RIKEN iTHEMS) gave us a talk on genomic data analysis. He started from explaining basic concepts of evolution and explained a couple of important quantities in population genetics, such as nucleotide diversity and the site frequency spectrum, which can be used to infer an underlying evolutionary process from sampled DNA sequences. He also explained statistical methods to study population structures and illustrated one of the methods in a study of the history of Japanese populations, which was very interesting. He made a great effort into his presentation. His talk was very educational and informative, and both experts and non-experts enjoyed his talk. Besides, the next biology seminar on 11/5 was on theoretical population genetics (I was actually the host), and Jeff helped us to prepare for the next week's seminar. Thank you very much, Jeff! - Takashi Okada
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2020-10-30
Seminar Report
iTHEMS Theoretical Physics Seminar on October 23, 2020
The iTHEMS Theoretical Physics Seminar is held on October 23, 2020. The speaker is Dr. Masanori Hanada in Department of Mathematics, the University of Surrey. The title is ”Toward simulating Superstring/M-theory on a Quantum Computer”. He present a framework for simulating superstring/M-theory on a quantum computer, based on holographic duality. Because holographicduality maps superstring/M-theory to quantum field theories (QFTs), we can study superstring/M-theory if we can put such QFTs on a quantum computer --- but it still looks like a complicated problem, if we use a usual lattice regularization. Here he propose an alternative approach, which turns out to be rather simple: we map the QFT problems to matrix models, especially the supersymmetric matrix models such as the Berenstein-Maldacena-Nastase (BMN) matrix model. Supersymmetric matrix models have natural applications to superstring/M-theory and gravitational physics, in an appropriate limit of parameters. Furthermore, for certain states in the Berenstein-Maldacena-Nastase (BMN) matrix model, several supersymmetric quantum field theories dual to superstring/M-theory can be realized on a quantum device. It is straightforward to put the matrix models on a quantum computer, because they are just quantum mechanics of matrices, and the construction of QFTs is mapped to the preparation of certain states. He show the procedures are conceptually rather simple and efficient quantum algorithms can be applied. In addition, as a (kind of) byproduct, he provide a new formulation of pure Yang-Mills on quantum computer. The seminar was held via the Zoom online conference systems, and more than 15 people including outside of iTHEMS attended the seminar.
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2020-10-23
Seminar Report
iTHEMS Theoretical Physics Seminar by Dr. Tokuro Fukui on October 22, 2020
On October 22, the iTHEMS-phys seminar entitled "Realistic shell model and chiral three-body force” given by Dr. Tokuro Fukui (YITP, Kyoto U.) was held. He and his collaborators proposed the way to calculate matrix elements of the three-body nuclear force, and showed the importance and effects of the three-body nuclear force in medium-heavy nuclei, such as calcium and nickel isotopes, starting from the chiral nuclear force using the shell model calculation. During his seminar, he introduced their works from the introduction to state-of-art results. The seminar was held via the Zoom online conference systems, and more than 25 people including outside of iTHEMS attended the seminar.
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2020-10-22
Seminar Report
Biology Seminar by Dr. Christos Merkatas on October 21, 2020
On October 21st, Dr. Christos Merkatas from Aalto University in Finland gave a talk at the iTHEMS Biology Seminar. His talk was entitled, “Bayesian Nonparametric Estimation of Random Dynamical Systems”. Suppose that the observed time series is small, and the noise process is non-Gaussian. How can we reconstruct and predict the behavior of the system? Dr. Merkatas showed that the proposed Bayesian approach enables us to reconstruct and predict the system by inferring the number of unknown components and their variances. According to him, the method can be applied to the problems in physics, biology, and economy. Since some of the audiences including me were not familiar with his method, we asked many basic questions. The talk by Dr. Merkatas was great and also educative. Gen Kurosawa
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2020-10-21
Seminar Report
DMWG seminar by Dr. Rinaldi: Towards the cosmological signature of composite DM
There are lots of dark matter (DM) candidates of particles and/or non-particles. One important requirement is that DM should be massive. When we consider the main origin of the visible mass in the Universe, it is the proton, i.e. a composite of three-quarks bound by the strong interaction. Then we can realize the DM mass naturally if we introduce similar dynamics in the dark sector. The interaction between the dark and the standard model sector is different from that of DM self-interaction, hence it is also safe under the cosmological requirements. Among the varieties of composite DM models, the stealth DM scenario is a well-motivated one with minimal assumptions. It is different from other baryonic composite DM since it is developed for solving the problem of DM rather than for another mystery in the standard model. Let's consider the signatures in cosmological observations which we could expect for the stealth DM scenario. Since the structure of the stealth DM is similar to that of the standard model baryons, they should experience the confined-unconfined phase transition in the early Universe. If the phase transition is of the 1st order, numerous vacuum babbles are produced in the transition from the false- to the true vacuum. The collision of these bubbles sources the low-frequency gravitational waves (GWs) of a ~nHz-mHz range. However, it is difficult to calculate the physics around the phase transition. Indeed, it is not obvious whether the phase transition occurs in the 1st order or not. When it is of the 1st order, the gravitational wave spectrum is determined using the temperature of the Universe at the phase transition. Dr. Rinaldi and the members of the Lattice Strong Dynamics collaboration have investigated the phase transition in the stealth DM scenario by applying the sophisticated calculation techniques developed for the strongly-interacting sector in the standard model. They reveal that the lower bound of the 1st order phase transition temperature for the scenario, which is then directly converted to the lower bound on the frequency of the GW. The technique should enable us to study DM from multiple aspects as is shown in this talk. Furthermore, this is the beginning of a new interdisciplinary study in which DM becomes the portal to connect the strong dynamics and GW cosmology, which could further enhance our understanding of this world!
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2020-10-07
Seminar Report
Math-Phys Joint Seminar by Toshihiro Ota on October 2, 2020
On October 2, Toshihiro Ota gave a talk at the iTHEMS Math-Phys Joint Seminar. His whole talk was on the interrelation among integrable lattIce models, quiver gauge theories, and hidden TQFT structure. His first talk was a sort of lecture on TQFT and integrable lattice model at an elementary level. At the beginning of the first talk, he explained quantum mechanics (QM). Then as a variant of QM, he introduced an axiomatic definition of topological quantum field theory as a special class of quantum field theory. He also introduced lattice model which can be seen as a discrete version of quantum field theories. In particular, he mentioned the integrability of the 1-dimensional Ising model. In the second talk, he focused on the correspondence between Wilson-'t Hooft lines in a class of quantum gauge theories and transfer matrices in the corresponding integrable lattice models. At first, he gave an explanation of “classical integrability” and “quantum integrability” for field theories. In the case of 2-dimensional lattice model, he explained that the integrability is described by the Yang-Baxter equation. Then he moved on to the details of the correspondence. In the lattice model side of the correspondence, he described the transfer matrix in terms of n-copies of L-operators. Moreover, in order to compare to the gauge theory side, he took the trigonometric limit and rewrote the transfer matrix by “more fundamental” L-operators. The gauge theory side is in particular given by 4d N=2 n-node circular quiver theory. The theory is defined on a 4d twisted spacetime S^1 xε R^2 x R, and he gave an expression of the Wilson-'t Hooft line wrapping the circle S^1. As the main result of his joint work with Kazunobu Maruyoshi and Junya Yagi, he gave a relation between these Wilson-’t Hooft lines and transfer matrices. Finally, he gave several comments related to integrability from TQFT in extra dimension.
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2020-10-02
Seminar Report
DMWG seminar by Dr. Ishiyama: a spectacular cosmological N-body simulation
Visible components of our Universe, such as galaxies, show hierarchical structures. Such structures are always embedded in DM structures called "halos". In the early Universe, there exist small density fluctuations that eventually collapse to halos at some points by their self-gravity. Then, halos grow to form larger structures again by self-gravity and this is the origin of the structure of the current Universe. The large-scale structure of halos as well as their inner structures contain information about the nature of the DM particle. Cosmological N-body simulation is a powerful computational method to follow that structure formation, by solving multi-body problems numerically. A halo, which is a clump of elementary DM particles, is treated as one smooth particle in N-body simulation. Its prediction power is so strong that the calculation corresponding to the upcoming cosmological survey, for example, has long been awaited. However, its computational costs scale as the square of the particle number N (or N log N when some reduction methods are adopted) and it is almost impossible to cover everything we need. There are two strategies in the calculation: simulating a large volume with large particle mass, or a small volume with small particle mass. The former is suitable for studies that deal with the large-scale structure while the latter has advantages in studying the properties of each halo. His group has conducted a large high-resolution simulation project which enables us to study both of them. The Uchuu simulation, which uses the cubic of 12800 particles in a 2 Gpc-scale simulation box, enables us to study large-scale structures. The Shin-Uchuu simulation in the same project, which uses the cubic of 6400 particles in a 140 Mpc-scale box, is provided aiming to study the inner structure of DM halos. Analyzing the simulated structure and halo properties, the matter power spectrum covering from the largest to the non-linear regime is obtained. Also, the so-called mass-concentration relation in a wide halo mass range is now available thanks to the project. There is another good news for DM hunters: the results of the simulation are open to the public. This should boost the DM study from many aspects!
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2020-09-25
Seminar Report
Biology Seminar by Dr. Kyosuke Adachi on September 23, 2020
On September 23rd, Kyosuke Adachi gave a talk at the iTHEMS Biology Seminar on phase transitions in Biology. He first introduced the concept of phase transition and its possible application to understanding a number of biological phenomena. Then, he talked about his research on modelling the structural transition of chromatin states, and also about equilibrium and non-equilibrium dynamics. His research is really nice in how it engages both biologists and physicists, and many people seemed to enjoy his talk. In particular, the topic of chromatin dynamics is an area many molecular biologists are interested in at the moment, and we will be looking forward to hearing about his progress in the future.
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2020-09-18
Seminar Report
Biology Seminar by Dr. Hye Jin Park on September 16, 2020
On 16th September, Hye Jin Park (Asia Pacific Center for Theoretical Physics; APCTP) gave us a talk about her work on eco-evolutionary dynamics. She specifically looked at what if there are novel mutations that generate a nonexistent phenotype (temporal emergence of different phenotypes) and how it affects the evolution of cyclic dominance. She took advantage of introducing novel phenotypes to construct phylogenetic-alike trees, which contain some information for which types are similar or dissimilar. She found that similar types are unlikely to exhibit cyclic dominance. We discussed how we can apply the theory to real systems and what factors are important. Thank you so much, Hye Jin for the fantastic talk! -Ryosuke Iritani
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2020-09-11
Seminar Report
Math Seminar by Dr. Ken Furukawa on September 8, 2020
On September 8, there was a math seminar by Dr. Ken Furukawa. He gave a talk entitled Maximal Regularity and Partial Differential Equations. In the first part of his talk, the speaker explained the maximal regularity of parabolic partial differential equations and various sufficient conditions for the maximal regularity. Especially he introduced some functional calculus to obtain the analytic semigroup. In the second part, the speaker explained his recent collaboration work on the primitive equation and its relationship to the Navier-Stokes equation. He first shows that we can formally obtain primitive equations from the Navier-Stokes equation on the thin domain. He then explained his recent collaboration work which justifies this formal derivation of the primitive equation and how the sufficient conditions in the first talk work.
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2020-09-09
Seminar Report
Biology Seminar by Dr. Masashi Tachikawa on September 9, 2020
On 9th September, Masashi Tachikawa (Kyoto University) gave us a talk on adaptive dynamics as a framework for evolutionary dynamics. He first gave us a quick overview for modeling evolution, and then introduced adaptive dynamics toolbox and pairwise invasibility plots to visualize trait-substitution processes towards evolutionarily singular points. He finally talked about how to capture evolutionary branching (two morphs emerging) using envelope with a trait value being tuned as-if a parameter. We all excitedly learned a lot from this talk. Thank you, Masashi! -Ryosuke Iritani
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2020-09-04
Seminar Report
Biology Seminar by Dr. Miki Ebisuya on July 17, 2020
In 1638, Galileo Galilei proposed “the square-cube law”: the ratio of two volumes is greater than the ratio of their surfaces. This law enables us to understand why large animals like elephants need longer time to cool their body temperature than small ones like human. On July 17th, Miki Ebisuya at European Molecular Biology Laboratory (EMBL) explained why human needs longer time to develop her/his body than mouse, at the iTHEMS seminar. In fact, the speed of the segment formation ("taisetsu" in Japanese) of human is twice or three times as slow as that of mouse. By combining state-of-the-art experiments and a model with two variables, her group discovered that the difference of tempos is due to the difference of biochemical parameters. The talk was clear and enjoyable. And it was accessible to the diverse audience. As a mathematician asked during the talk, their discovery raises a new fundamental question about why reactions in human are slower than those in mouse. The question might be also answered by the collaboration between biology and mathematics in a future.
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2020-09-03
Seminar Report
iTHEMS Math-Phys joint seminar was held on August 31 and September 1, 2020
The iTHEMS Math-Phys joint seminar was held on August 31st and September 1st, inviting Makiko Sasada from University of Tokyo and Kenichi Bannai from Keio university / RIKEN AIP. This was a series of lectures entitled “Geometric Perspective for the Theory of Hydrodynamic Limits”. They explained to us their recent joint work with Yukio Kametani on hydrodynamic limits from algebraic/geometric view point. On Day 1, Sasada-san gave an introduction to hydrodynamic limits, and explained the motivation of the joint work and the key ideas. One of the goals of the theory of hydrodynamic limits is to derive macroscopic dynamics from microscopic evolution equations rigorously. There have been many results to this problem, but all of them depend on specific microscopic models. The long term goal of this joint work is to construct an abstract and universal theory of hydrodynamic limits. One of the most important ingredients of the theory of hydrodynamic limits is the “decomposition of closed forms”, which have been obtained by Varadhan and other people using very technical argument depending on models. One of the aims of this work is to give a more general and clear understanding of this type of decompositions. Their strategy is as follows: the microscopic data can be divided into topological (geometric) part and stochastic (analytic) part. For discrete models, the former one is modeled by a directed graph, the set of states at each vertex, and the interaction through edges. A typical analytic datum is the jump rate, i.e., the frequency of interaction. They observed that some important feature of hydrodynamic limits depends only on the geometric data, and as a consequence, they could avoid ad-hoc analytic estimations. Moreover, they obtain a version of Varadhan’s decomposition in a very general setting. On Day 2, Bannai-san gave a precise mathematical formulation of their main results and proofs. As explained above, the geometric part of microscopic model is given by a directed graph, a pointed set of states, and a function which represents the interaction through edges. From this set of data, we can form a configuration space, each point of which corresponds to a possible state on the graph (The interaction data induce the transition structure on the configuration space). On the configuration space, they consider a special type of functions / forms called “uniformly local functions / forms”, and construct a cohomology theory (uniformly local cohomology) associated to them. Surprisingly, the uniformly local cohomology captures all conserved quantities (macroscopic observables). Moreover, from this fact, they can derive a local form version of Varadhan’s decomposition. An important ingredient of the proof is the group cohomology, which is often used in the field of number theory. They assume the existence of a free group action on the graph (which is valid in many important examples), and apply a general theory of group cohomology. It is very surprising that a fundamental result in hydrodynamic limits is derived from an abstract algebraic theory, and it will provide us a new and clear understanding of this field.
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2020-09-03
Seminar Report
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 easy-to-understand way, using examples such as the diversification of pet dogs and cruciferous plants, and changes in the structure of the gecko's hands. Especially, the formulation of adaptive evolution using Fokker planck equarion was introduced. His seminar will be very useful as a basic knowledge of evolutionary biology and mathematical biology that will be covered in future seminars.
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2020-08-27
Seminar Report
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.
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2020-08-22
Seminar Report
iTHEMS Theoretical Physics Seminar by Dr. Takuya Shimazaki on August 21, 2020
On August 21st (Fri.), Takuya Shimazaki (The University of Tokyo) gave an iTHEMS-phys 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 two-level quantum system equivalent to the Schwinger mechanism). There were a lot of lively discussions, and the audience looked enjoying the seminar.
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2020-08-05
Seminar Report
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!
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2020-08-05
Seminar Report
Math Seminar by Dr. Tadahiro Miyao
The iTHEMS Math seminar entitled "Stability of ferromagnetism in many-electron 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 Marshall-Lieb-Mattis theorem and Lieb’s theorem. Then he showed that Lieb’s theorem still holds true even if the electron-phonon and electron-photon interactions are taken into account. As examples, he explained the Holstein-Hubbard 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 Perron-Frobenius-Faris theorem, abstract reflection positivity, the hole-particle 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.
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2020-07-31
Seminar Report
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 Wright-Fisher demography cannot inherently consider the realistic situation in which the offspring-number distribution is skewed. Second, he talked about what if we extend the Wright-Fisher demography to a skewed offspring number (power low distribution), showing us that the power-low 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!
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2020-07-27
Seminar Report
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 cosmic-ray 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 so-called 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 217-247 from the background are observed in the recoil energy range of 1-7keV 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. Abobe-mentioned 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!
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2020-07-20
Seminar Report
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 persistence-like 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 non-displacement theorem, the audience learned about several proofs in the field. Thus, the talk nicely tied current relevant applications to deep results in theoretical mathematics.
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2020-07-16
Seminar Report
Biology Seminar about "Application of geometry to protein structure analysis" on July 15, 2020
In Biology Seminar on 15th July, a graduate student Haru Oono-Negami (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 protein-classification 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, Haru-san! - Ryosuke Iritani
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2020-07-16
Seminar Report
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 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!
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2020-07-08
Seminar Report
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.
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2020-07-02
Seminar Report
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
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2020-07-01
Seminar Report
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 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.
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