セミナー

Geometric Perspective for the Theory of Hydrodynamic Limits

2020年8月31日(月) - 9月1日(火)

佐々田 槙子
坂内 健一 (慶應義塾大学 理工学部 数理科学科 教授)

This is a series of lectures on "Geometric Perspectives for Fluid Dynamic Limit Theory" by the following speakers: [DAY 1: Aug 31] Dr. Makiko Sasada (University of Tokyo) [DAY 2: Sept 1] Prof. Kenichi Bannai (Keio University) Abstract: One of the fundamental problems in the natural and social sciences is to explain macroscopic phenomena that we can observe from the rules governing the microscopic system giving rise to the phenomena. Hydrodynamic limit provides a rigorous mathematical method to derive the deterministic partial differential equations describing the time evolution of macroscopic parameters, from the stochastic dynamics of a microscopic large scale interacting system. In the article "Topological Structures of Large Scale Interacting Systems via Uniform Locality" joint with Yukio Kametani, we introduce a general framework encompassing a wide variety of interacting systems in order to systematically investigate various microscopic stochastic large scale interacting systems in a unified fashion. In particular, we introduced a new cohomology theory called the uniformly local cohomology to investigate the underlying geometry of the interacting system. Our theory gives a new interpretation of the macroscopic parameters, the role played by the group action on the microscopic system, and the origin of the diffusion matrix associated to the macroscopic deterministic partial differential equation obtained via the space-time scaling limit of the microscopic system. The purpose of the series of lectures is to introduce to the audience the theory of hydrodynamic limits, especially the relation between the macroscopic observables and the microscopic interacting system. We then explain our new perspective of how geometry comes into play in investigating the interacting system, and introduce the ideas and results of our article. *Detailed information about the seminar refer to the email.

会場: via Zoom

イベント公式言語: 英語

Modeling biological timing

2020年8月26日(水) 10:00 - 11:00

黒澤 元 (数理創造プログラム 専任研究員)

Under stay-at-home situation, some of you may suffer from sleep disorder. Efficacy of a drug often depends on the timing of its prescription. We know this fact about our "timing", but we don't know why. This time, I wish to introduce two big mysteries in regard to biological timing. First is our internal daily clock. In general, biochemical process is believed to accelerate with temperature. In contrast, the period of our daily clock, made up of biochemical reactions is somehow stable to temperature. The prediction from simpler biochemical mathematical model, and its experimental verification will be presented. Second is hibernation. During winter, some birds and mammals decrease drastically their body temperature possibly to decrease their energy expenditure. Many studies about hibernation have been conducted for many years. However, basic mechanisms of hibernation (e.g. how the duration of hibernation is determined?) are largely unknown. Recently, we started to investigate body temperature time-series of hibernating hamsters over 100 days in the collaboration with experimental biologists. Preliminary results will be presented.

会場: via Zoom

イベント公式言語: 英語

Lefschetz-thimble inspired analysis of the Dykhne–Davis–Pechukas method and an application for the Schwinger Mechanism

2020年8月21日(金) 13:00 - 14:30

島崎 拓哉 (東京大学 ハドロン理論グループ 研究生)

Dykhne–Davis–Pechukas (DDP) method is a common approximation scheme for the transition probability in two-level quantum systems, as realized in the Landau–Zener effect, leading to an exponentially damping form comparable to the Schwinger pair production rate. We analyze the foundation of the DDP method using a modern complex technique inspired by the Lefschetz-thimble method. We derive an alternative and more adaptive formula that is useful even when the DDP method is inapplicable. As a benchmark, we study the modified Landau–Zener model and compare results from the DDP and our methods. We then revisit a derivation of the Schwinger Mechanism of particle production under electric fields using the DDP and our methods. We find that the DDP method gets worse for the Sauter type of short-lived electric pulse, while our method is still a reasonable approximation. We also study the Dynamically Assisted Schwinger Mechanism in two methods.

会場: via Zoom

イベント公式言語: 英語

Nambu-Goldstone fermion in a Bose-Fermi mixture with an explicitly broken supersymmetry

2020年8月7日(金) 13:00 - 14:30

田島 裕之 (高知大学 自然科学系理工学部門 特任助教)

Supersymmetry, which is a symmetry associated with interchange between bosons and fermions, is one of the most important symmetries in high-energy physics but its evidence has never been observed yet. Apart from whether supersymmetric partners such as squark exist or not in our world, it is an interesting problem to explore the consequences of the supersymmetry in an ultracold atomic gas. In this study, we address the Nambu-Goldstone mode called Goldstino associated with the spontaneous supersymmetry breaking in a Bose-Fermi mixture. While the explicit supersymmetry breaking is unavoidable even in cold atomic systems, the energy gap in Goldstino spectra can be measured in such atomic systems. By comparing the energy gaps obtained from the Gell-Mann-Oakes-Renner relation and the random phase approximation, we elucidate how the Goldstino acquires the energy gap due to the explicit breakings. We also show effects of Goldstino pole on the fermionic single-particle spectral functions, which can be measured in the recent experiments.

会場: via Zoom

イベント公式言語: 英語

Heavy tails in the brain

2020年8月5日(水) 10:00 - 11:00

Lukasz Kusmierz (理化学研究所 脳神経科学研究センター (CBS) 研究員)

In my talk I will discuss the relation between two seemingly unrelated measures in the brain that exhibit heavy tails: neuronal avalanches, i.e. bursts of activity with power-law distributions of sizes and lifetimes, and synaptic weights that are believed to be distributed according to the log-normal distribution. Many current models of neuronal avalanches do not rely on heavy-tailed synaptic weight distributions, suggesting that heavy tails of these two quantities may not be related. However, our recent theoretical considerations indicate that this independence no longer holds if two biologically relevant constraints are introduced, i.e., that neurons (1) receive many incoming connections and (2) do not spike if the membrane potential is below some positive threshold, e.g., in the absence of inputs. Under these assumptions we have shown that heavy tails of synaptic weights are necessary to generate biologically plausible low activity levels and associated neuronal avalanches. Our results suggest that the observed distributions of synaptic weights may play important functional roles in the brain.

会場: via Zoom

イベント公式言語: 英語

Stability of ferromagnetism in many-electron systems

2020年7月31日(金) 16:00 - 18:10

宮尾 忠宏 (北海道大学 理学部数学科 准教授)

First part Title: Stability of ferromagnetism in many-electron systems Abstract: I construct a model-independent framework describing stabilities of ferromagnetism in strongly correlated electron systems. Within the new framework, I reinterpret the Marshall-Lieb-Mattis theorem and Lieb’s theorem; in addition, from the new perspective, I prove that Lieb’s theorem still holds true even if the electron-phonon and electron-photon interactions are taken into account. I also examine the NagaokaThouless theorem and its stability. These examples verify the effectiveness of the new viewpoint. Second part Title: Order preserving operator inequalities in many-electron systems Abstract: In this talk, I will introduce order preserving operator inequalities and explain how these inequalities are applied to the mathematical study of ferromagnetism. As examples of applications, Lieb's theorem of the Hubbard model and its stabilities will be discussed in terms of the inequalities.

会場: via Zoom

イベント公式言語: 英語

Time-dependent bias emerges in population models with broad offspring number distributions

2020年7月29日(水) 10:00 - 11:00

岡田 崇 (数理創造プログラム 上級研究員)

It has been increasingly recognized that natural populations exhibit broad offspring number distributions, either because offspring numbers are strongly variable (e.g. marine organisms) or because range expansion processes generate jackpot events. In this talk, I will review the basic concepts of theoretical population genetics and then discuss how broad offspring number distributions affect the evolutionary dynamics.

会場: via Zoom

イベント公式言語: 英語

DMWG special seminar : “The result of the XENON1T experiment and its implications”

2020年7月22日(水) 15:30 - 17:00

山下 雅樹 (名古屋大学 宇宙地球環境研究所 宇宙線研究部 特任准教授)

会場: via Zoom

イベント公式言語: 日本語

Human Time vs. Mouse Time in Embryonic Development

2020年7月17日(金) 16:00 - 17:00

戎家 美紀 (Group Leader, European Molecular Biology Laboratory, Barcelona, Spain)

Different species have different tempos of development: larger animals tend to grow more slowly than smaller animals. My group has been trying to understand the molecular basis of this interspecies difference in developmental time, using the segmentation clock as a model system. The segmentation clock is the oscillatory gene expressions that regulate the timing of body segment formation during early embryogenesis. We have recently succeeded in recapitulating the segmentation clock from both human and mouse pluripotent stem cells, detecting oscillations and traveling waves in vitro. Interestingly, the oscillation period of human segmentation clock was 5-6 hours while that of mouse was 2-3 hours. Taking advantage of our in vitro system and simple mathematical models, we have been comparing the genome sequences and molecular processes of the segmentation clock between human and mouse to explain the interspecies difference in the oscillation period.

会場: via Zoom

イベント公式言語: 英語

Topological data analysis from a practical and mathematical perspective

2020年7月15日(水) 16:00 - 18:10

池 祐一 (株式会社富士通研究所 人工知能研究所 研究員)

1. Topological data analysis and its applications In this talk, I will explain some methods in topological data analysis (TDA) and their applications. First I recall persistent homology, which is a central tool to analyze the "shape" of a point cloud set. Then I show several applications to material science and time-series analysis. I also talk about our collaborative research with Inria on noise-robust persistent homology and an automated vectorization method of persistence diagrams. 2. Persistence-like distance on sheaf category and displacement energy In this talk, I will talk about relation among sheaf theory, persistence modules, and symplectic geometry. We introduce a persistence-like distance on Tamarkin sheaf category and prove a stability result with respect to Hamiltonian deformation of sheaves. Based on this result, we propose a new sheaf-theoretic method to give a lower bound of the displacement energy of compact subsets of a cotangent bundle. This is a joint work with Tomohiro Asano.

会場: via Zoom

イベント公式言語: 英語

Application of geometry to protein structure analysis

2020年7月15日(水) 14:00 - 15:00

根上 春 (東京大学 工学系研究科先端学際工学専攻 博士課程)

Geometry is applied in various fields as a method for revealing the structure of data. In this seminar, I will introduce the topological method, fatgraph model, to classify protein structures. I will also introduce another related geometric model and its application to viral glycoprotein analysis. This method provides an a priori prediction of structural rearrangement of proteins.

会場: via Zoom

イベント公式言語: 英語

Search for ultralight dark matter with laser interferometric gravitational wave detectors

2020年7月13日(月) 10:00 - 11:00

道村 唯太 (東京大学 大学院理学系研究科 物理学専攻 助教)

会場: via Zoom

イベント公式言語: 英語

Complex Langevin study of an attractively interacting two-component Fermi gas in 1D with population imbalance

2020年7月10日(金) 13:30 - 14:30

筒井 翔一朗 (理化学研究所 仁科加速器科学研究センター (RNC) 量子ハドロン物理学研究室 基礎科学特別研究員)

We investigate an attractively interacting two-component Fermi gas in 1D described by the Gaudin-Yang model with population imbalance. While the Gaudin-Yang model is known as a solvable model based on the thermodynamic Bethe ansatz, the binding energy and mass of poralon at finite temperature and moderate impurity density are still unknown. Moreover, in such a system, quantum Monte Carlo simulation suffers from the sign problem because the population imbalance makes the fermion determinant non-positive definite. In this study, we apply complex Langevin method, a holomorphic extension of the stochastic quantization to overcome the sign problem. We first confirm our numerical results satisfy a criteria for correct convergence [1], and present how the polaron energy depends on temperature and density of impurity. We also compare our results with a recent study based on a diagrammatic approach [2].

会場: via Zoom

イベント公式言語: 英語

Constrained evolution of animal embryogenesis

2020年7月8日(水) 10:00 - 11:00

内田 唯 (理化学研究所 生命機能科学研究センター (BDR) 多階層生命動態研究チーム 基礎科学特別研究員)

Animals have developed a great variety of morphologies during the course of evolution. Despite this, phylogeny-specific features have sometimes been maintained for hundreds of millions of years, suggesting that there are constraints to morphological evolution. In my talk, I will introduce some of general motivations behind the EvoDevo study and talk particularly about the blank space in morphospaces (Each axis of a morphospace corresponds to a variable describing morphological features). It remains to be seen if these blank areas are caused by impossible developmental pathways. However, computer simulations of embryogenesis, which has been proposed in recent years, may provide a clue to a solution. Finally, I’m going to talk about my research plan based on this.

会場: via Zoom

イベント公式言語: 英語

Waveform Analysis of Biological Rhythms

2020年7月1日(水) 10:00 - 11:00

儀保 伸吾 (数理創造プログラム 特別研究員)

Nonlinear oscillatory phenomena often emerge in various systems, for example circadian rhythms in biological systems and acoustic vibrations in engineering. Analysis and control of these oscillatory phenomena are one of the big problems in science and technology. My main research field is biological oscillations, especially circadian clocks. The circadian clocks are based on gene-activity rhythms with approximately 24-hour period, and its temporal waveforms are of various shapes. Recently, we theoretically showed that the period of circadian clocks is proportional to the waveform distortion from sinusoidal waves. Interestingly, we found the waveform is important for periods not only in biological oscillations but also in several other types of nonlinear oscillator models.

会場: via Zoom

イベント公式言語: 英語

Universal Error Bound for Constrained Quantum Dynamics

2020年6月24日(水) 16:00 - 18:10

濱崎 立資 (数理創造プログラム 上級研究員 / 理化学研究所 開拓研究本部 (CPR) 濱崎非平衡量子統計力学理研白眉研究チーム 理研白眉研究チームリーダー)

In quantum mechanics, the existence of large energy gaps allows us to trace out the degrees of freedom of irrelevant energy scale. Consequently, we can treat a system within a constrained subspace obtained by the projection of the total Hilbert space. While this statement has widely been used to approximate quantum dynamics in various contexts, a general and quantitative justification stays lacking. In this talk, we show a universal and rigorous error bound for such a constrained-dynamics approximation in generic gapped quantum systems [1,2]. This universal bound is a linear function of time that only involves the energy gap and coupling strength, provided that the latter is much smaller than the former. If time allows, I will briefly talk about generalizations of our result to e.g., quantum many-body systems and open quantum systems.

会場: via Zoom

イベント公式言語: 英語

Dark Matter Heating vs. Rotochemical Heating in Old Neutron Stars

2020年6月22日(月) 16:00 - 17:00

濱口 幸一 (東京大学 大学院理学系研究科 准教授)

*Detailed information about the seminar refer to the email

会場: via Zoom

イベント公式言語: 英語

Information geometry of operator scaling

2020年6月17日(水) 16:00 - 18:10

相馬 輔 (東京大学 大学院情報理工学系研究科 助教)

Matrix scaling is a classical problem with a wide range of applications. It is known that the Sinkhorn algorithm for matrix scaling is interpreted as alternating e-projections from the viewpoint of classical information geometry. Recently, a generalization of matrix scaling to completely positive maps called operator scaling has been found to appear in various fields of mathematics and computer science, and the Sinkhorn algorithm has been extended to operator scaling. In this study, the operator Sinkhorn algorithm is studied from the viewpoint of quantum information geometry through the Choi representation of completely positive maps. The operator Sinkhorn algorithm is shown to coincide with alternating e-projections with respect to the symmetric logarithmic derivative metric, which is a Riemannian metric on the space of quantum states relevant to quantum estimation theory. This talk is based on joint work with Takeru Matsuda.

会場: via Zoom

イベント公式言語: 英語

Field theoretical approach to relativistic hydrodynamics

2020年6月12日(金) 13:00 - 14:30

本郷 優 (数理創造プログラム 客員研究員 / Postdoctoral Research Associate, Physics Department, The University of Illinois at Chicago (UIC), USA)

Hydrodynamics is a low-energy effective theory of a conserved charge density, which describes a long-distance and long-time behavior of many-body systems. It is applicable not only to a non-relativistic weakly-interacting dilute gas but also a relativistic strongly-interacting dense liquid like a quark-gluon plasma. The main purpose of this seminar is to explain how we can derive the hydrodynamic equation from the underlying field-theoretical description of systems [1-3]. Our derivation is based on the recent development of non-equilibrium statistical mechanics, and we show that the procedure to derive hydrodynamic equations is similar to the so-called renormalized/optimized perturbation theory. Also, to describe transport phenomena in local thermal equilibrium, we give a path-integral 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.

イベント公式言語: 英語

The effect of the early kinetic decoupling in a fermionic dark matter model

2020年6月12日(金) 10:00 - 11:00

阿部 智広 (名古屋大学 素粒子宇宙起源研究所 (KMI) 特任助教)

*Detailed information about the seminar refer to the email

会場: via Zoom

イベント公式言語: 英語