セミナー

TQFT, integrable lattice model, and quiver gauge theories

2020年10月2日(金) 16:00 - 18:00

太田 敏博 (数理創造プログラム 研修生 / 大阪大学 大学院理学研究科 博士課程)

1st part (math): In physics literature, “lattice models” appear quite often as mathematical models of physical systems, e.g. Ising model, vertex models, lattice gauge theory. The aim of the 1st part is to introduce ‘what is (T)QFT,’ ‘what is lattice model,’ and ‘what does integrability mean’ in the language of mathematics. In turn, they will play a crucial role in the 2nd part of my talk. I also hope that this will lead to a good exchange among us, especially between physicists and mathematicians. 2nd part (physics): In the 2nd part, I would like to explain where an integrable lattice model may come from, especially for people in the physics background. I will show a certain class of integrable lattice models is realized by Wilson-’t Hooft lines in 4d quiver gauge theories. I will also explain a bit how these gauge theories are constructed from brane configurations in string theory. String dualities allow us to relate the original 4d setups to 4d partially topological Chern-Simons theory, which is a partial TQFT and generates integrable lattice models. Please contact Keita Mikami's mail address to get access to the Zoom meeting room.

会場: via Zoom

イベント公式言語: 英語

The Uchuu Simulations: Data Release 1 and Dark Matter Halo Concentrations

2020年10月1日(木) 14:00 - 15:00

石山 智明 (千葉大学統合情報センター 准教授)

We introduce the Uchuu suite of large high-resolution cosmological N-body simulations. The largest simulation, named Uchuu, consists of 2.1 trillion dark matter particles in a box of 2.0 Gpc/h. The highest resolution simulation, called Shin-Uchuu, consists of 262 billion particles in a box of 140 Mpc/h. Combining these simulations we can follow the evolution of dark matter haloes (and subhaloes) spanning from dwarf galaxies to massive galaxy cluster hosts. We present basic statistics, dark matter power spectra and halo (subhalo) mass function, to demonstrate the huge dynamic range and superb statistics of the Uchuu simulations. From the analysis of the evolution of the power spectra we conclude that our simulations are accurate enough from the Baryon Acoustic Oscillations up to very small scales. We also provide parameters of a mass-concentration model, which describes the evolution of halo concentrations, that reproduces our simulation data within 5% error for haloes with masses spanning nearly eight orders of magnitude at redshift 0

会場: via Zoom

イベント公式言語: 英語

Math Seminars by Dr. Genki Ouchi and Dr. Kenta Sato

2020年9月24日(木) 16:00 - 18:10

大内 元気 (数理創造プログラム 基礎科学特別研究員)
佐藤 謙太 (数理創造プログラム 基礎科学特別研究員)

[Talk 1] (16:00 - 17:00) Dr. Genki Ouchi Automorphism groups of cubic fourfolds and K3 categories In this talk, I would like to talk about symmetries of algebraic varieties, especially cubic fourfolds and K3 surfaces. It is known that symmetries of cubic fourfolds and K3 surfaces are related to sporadic finite groups as Mathieu groups and Conway groups in both algebraic geometry and string theory. Relations between cubic fourfolds and K3 surfaces are studied in the context of derived categories, Hodge theory and so on. I would like to explain the direct relation among symmetries of cubic fourfolds and K3 surfaces via their derived categories. [Talk 2] (17:10 - 18:10) Dr. Kenta Sato An algebraic approach to the four color theorem The four color theorem states that, given any separation of a plane into contiguous regions, no more than four colors are required to color the regions. Although this theorem was already proved about 40 years ago, another proof without using a computer is not found still now. In this talk, I will introduce an algebraic approach to this theorem, which states that a conjecture about singularities of algebraic varieties implies the four color theorem. In particular, I would like to focus on the connection of three different fields in mathematics: graph theory, convex geometry and algebraic geometry. *Detailed information about the seminar refer to the email.

会場: via Zoom

イベント公式言語: 英語

Phase Transitions in Biological Systems

2020年9月23日(水) 10:00 - 11:00

足立 景亮 (数理創造プログラム 基礎科学特別研究員 / 理化学研究所 生命機能科学研究センター (BDR) 生体非平衡物理学理研白眉研究チーム 基礎科学特別研究員)

Biological systems are built hierarchically by DNA, proteins, cells, tissues, organs, individuals, etc. Recent experiments have clarified the existence of interesting mesoscale phenomena inside cells, where the concept of condensed matter physics such as phase transition can be useful in its understanding. For example, interacting nucleosomes in a chromatin chain can cause the mega-base scale structural change, and sub-micron scale dense droplets of proteins/mRNAs can appear through phase separation. In this talk, I will discuss our recent topics: (i) structural transition of a chromatin with epigenetic marks, (ii) intracellular wetting of phase-separated droplets, and (iii) spontaneous aggregation of self-propelled individuals.

会場: via Zoom

イベント公式言語: 英語

Eco-evolutionary dynamics with novel mutations

2020年9月16日(水) 10:00 - 11:00

Hye Jin Park (Junior Research Group Leader, Statistical physics of ecology and evolution group, Asia Pacific Center for Theoretical Physics, Republic of Korea)

Evolution is driven by individual birth and death that are determined by interactions between individuals. Hence studying interactions is crucial to understand the population evolution. However, traditional approaches dealt with those interaction structures are given while spontaneous random mutations can generate new interactors. We considered “mutant interactors,” which lead to new interactions between the residents and invading mutants that can drive the population away from the previous equilibrium and lead to changes in the population composition. Thus, first, we investigated the changes in the population size induced by mutant interactors[1]. And then, we applied this approach to answer the question about relationships between species[2]: Why is cyclic dominance so rare?

会場: via Zoom

イベント公式言語: 英語

Singular point implies coexistence in adaptive dynamics

2020年9月9日(水) 10:00 - 11:00

立川 正志 (数理創造プログラム 客員研究員 / 京都大学 ウイルス･再⽣医学研究所 ⽣命システム研究部⾨ 准教授)

Adaptive dynamics is a relatively new mathematical framework for studying evolution(~1990s). Under the influence of the mathematical ecology and the game theory, adaptive dynamics considers the effect of resident populations on the fitness landscape. As a result, it explains a possible mechanism of evolutionary branching. In this talk, I introduce adaptive dynamics and Pairwise Invasibility Plot (PIP) analysis, a standard method for understanding the adaptive dynamics. Then, I propose a new approach to analyze the adaptive dynamics which enable us to understand higher dimensional systems than PIP does.

会場: via Zoom

イベント公式言語: 英語

Maximal Regularity and Partial Differential Equations

2020年9月8日(火) 16:00 - 18:10

古川 賢 (理化学研究所 開拓研究本部 (CPR) 三好予測科学研究室 特別研究員)

The theory of maximal regularity is a powerful tool to get solutions having the best regularity to linear partial differential equations (PDEs) of parabolic type. The theory is also applicable to show well-posedness of various non-linear PDEs. In the first part, We introduce the history of the development of the theory of maximal regularity and the way to apply non-linear PDEs. In the second part, We give some applications to PDEs, e. g. the primitive equations, the Navier-Stokes equations, and elliptic equations with dynamic boundary conditions. *Please contact Keita Mikami's mail address to get access to the Zoom meeting room.

会場: via Zoom

イベント公式言語: 英語

Potential Toolkit to Attack Nonperturbative Aspects of QFT －Resurgence and related topics－

2020年9月7日(月) - 25日(金)

Aleksey Cherman (University of Minnesota, USA)
Gerald Dunne (University of Connecticut, USA)
Mithat Unsal (North Carolina State University, USA)
藤森 俊明 (慶應義塾大学)
初田 泰之 (立教大学)
本多 正純 (京都大学 基礎物理学研究所 助教)
森川 億人 (九州大学 博士課程)
居石 直久 (名古屋大学)
山崎 雅人 (東京大学 カブリ数物連携宇宙研究機構 (Kavli IPMU))

Recently, there have been significant developments in theoretical techniques/frameworks to tackle non-perturbative aspects of quantum field theory (QFT) such as the resurgence theory, the Lefschetz thimble method, ’t Hooft anomaly matching, and novel lattice setups. Such developments are still growing very rapidly and making fruitful connections not only among physicists involved in fields with broad energy scales but also with mathematicians. These developments would enable us to unveil rich and exciting physics of QFT in the non-perturbative regime. It is of primary importance to hold a workshop for researchers in various fields related to the topics to get together and overview/share the recent progresses, to discuss future directions, and to seek for possible new collaborations bridging various fields of physics/mathematics. For more information, please see on the related link.

会場: YITP (Kyoto University), Zoom, and Mozilla hubs

イベント公式言語: 英語

The hitch-hiker’s guide to 
the concept of 
adaptive dynamics

2020年9月2日(水) 10:00 - 10:30

入谷 亮介 (数理創造プログラム 研究員)

Adaptation is of multi-causality, composed of mutation and selection processes. I will talk about how we model adaptation on the basis of the adaptive dynamics framework. This is a very quick, conceptual talk, rather than heavily mathematical, to draw attention from more people.

会場: via Zoom

イベント公式言語: 英語

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