The Unreasonable Effectiveness of Quantum Theory in Mathematics

2020年11月26日(木) 10:00 - 11:30

Robbert Dijkgraaf (Director, Institute for Advanced Study in Princeton, USA)

November 26 at 10:00-11:30, 2020 (JST) November 25 at 20:00-21:30, 2020 (EST) The physical concepts of quantum theory, in particular of quantum gravity and string theory, have proven to be extremely powerful in addressing deep problems in pure mathematics, from knot invariants to algebraic geometry. Is there such a thing as “quantum mathematics”? Should we add Feynman diagrams, strings, branes and black holes to the language of mathematics?

会場: via Zoom

イベント公式言語: 英語

Symmetry and conservation laws in neural networks

2020年11月20日(金) 10:00 - 11:00

Hidenori Tanaka (Group Leader & Senior Scientist, Physics & Informatics Laboratories, NTT Research, Inc., USA / Visiting Scholar, Stanford University, USA)

Symmetry is the central guiding principle in the exploration of the physical world but has been underutilized in understanding and engineering neural networks. We first identify simple yet powerful geometrical properties imposed by symmetry. Then, we apply the theory to answer a series of following important questions: (i) What, if anything, can we quantitatively predict about the complex learning dynamics of real-world deep learning models driven by real-world datasets? (ii) How can we make deep learning models more efficient by removing parameters without disconnecting information flow? (iii) How can we distill experimentally testable neuroscientific hypotheses by reducing the complexity of deep learning models mimicking the brain? Overall, our approach demonstrates how we can harness the principles of symmetry and conservation laws to reduce deep learning models' complexity and make advances in the science and engineering of biological and artificial neural networks.

会場: via Zoom

イベント公式言語: 英語

Representations of fundamental groups and 3-manifold topology

2020年11月16日(月) 16:00 - 18:10

北山 貴裕 (東京大学 大学院数理科学研究科 准教授)

In 3-dimensional topology the great progress during the last two decades revealed that various properties of 3-manifolds are well understood from their fundamental groups. I will give an introduction to the study of splittings of 3-manifolds along surfaces, with an emphasis on an application of group representations. A fundamental and difficult problem in general is to find surfaces essentially embedded in a given 3-manifold. I will explain how such surfaces are detected by deformations of representations of the fundamental group, and what information of detected surfaces is described in terms of topological invariants derived from representations.

会場: via Zoom

イベント公式言語: 英語

Efficient probabilistic assessment of building performance: sequential Monte Carlo and decomposition methods

2020年11月13日(金) 16:00 - 18:10

ティエンフォン・ホウ (数理創造プログラム 特別研究員 / 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 / 理化学研究所 計算科学研究センター (R-CCS) データ同化研究チーム 特別研究員)

The use of numerical simulations for complex systems is common. However, significant uncertainties may exist for many of the involved variables, and in order to ensure the reliability of our simulation results and the safety of such complex systems, a stochastic approach providing statistics of the probability distribution of the results is of crucial importance. However, when a highly accurate result is required, the conventional Monte Carlo based probabilistic methodology inherently requires many repetitions of the deterministic analysis and in cases where that deterministic simulation is (relatively) time consuming, such probabilistic assessment can easily become computationally intractable. Hence, to reduce the computational expense of such probabilistic assessments as much as possible, the targets of this seminar are twofold: (1), to exploit an efficient sampling strategy to minimize the number of needed simulations of Monte Carlo based probabilistic analysis; (2), to investigate a surrogate model to reduce the computational expense of single deterministic simulation. This seminar contains two parts and will be accompanied by a set of illustrative building physical case studies (analysis of the heat and moisture transfer through building components). The first part of this seminar focusses on the use of quasi-Monte Carlo based probabilistic assessment for building performance, since it has the potential to outperform the standard Monte Carlo method. More specifically, the quasi-Monte Carlo sampling strategies and related error estimation techniques will be introduced in detail. In addition, questions on under which conditions the quasi-Monte Carlo can outperform the standard Monte Carlo method will be answered by a set of analyses. The second part of this seminar targets the investigation of using model order reduction methods for optimizing the deterministic simulation, given that it generally allows a (large) reduction of the simulation time without losing the dynamic behavior of the conventional models (such as the transient finite element analysis). Particularly, the fundamental concepts of one common model order reduction method – proper orthogonal decomposition (POD) will be provided, and its potential use for simulating (building physical) problems with different levels of non-linearity and complexity will be illustrated.

会場: via Zoom

イベント公式言語: 英語

第13回 MACSコロキウム

2020年11月13日(金) 15:00 - 18:00

川口 真也 (京都大学 大学院理学研究科 生物科学専攻 生物物理学教室 高次情報形成学講座 教授)
杉田 有治 (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) 杉田理論分子科学研究室 主任研究員)

15:00- 川口 真也 博士「神経系のやわらかい情報処理」 16:15- 杉田 有治 博士「計算機シミュレーションで細胞の中を観る」 17:15- 継続討論会

会場: via Zoom

イベント公式言語: 日本語

Some idea on quantum tunneling via Lefschetz thimbles

2020年11月12日(木) 10:30 - 12:00

谷崎 佑弥 (理化学研究所 仁科加速器科学研究センター (RNC) 理論研究グループ 基礎科学特別研究員 / 京都大学 基礎物理学研究所 助教)

In this talk, I will explain my previous study with Takayuki Koike on a possible approach to quantum tunneling via Lefschetz thimbles. We classified all the complex saddle points for the real-time path integral for the symmetric double-well quantum mechanics. We looked at various properties of those complex solutions, which motivated us to conclude that the computation of tunneling amplitudes for the symmetric double well requires the interference of infinitely many Lefschetz thimbles. I would also like to talk about some speculations, admittingly being very optimistic.

会場: via Zoom

イベント公式言語: 英語

Mathematics of thermalization in isolated quantum systems

2020年11月10日(火) 16:00 - 18:10

白石 直人 (学習院大学 理学部 物理学科 助教)

If an isolated macroscopic quantum system is left at a nonequilibrium state, then this system will relax to the unique equilibrium state, which is called thermalization. Most of quantum many-body systems thermalize, while some many-body systems including integrable systems do not thermalize. What determines the presence/absence of thermalization and how to understand thermalization from microscopic quantum mechanics are profound long-standing problems. In the first part of my talk, I briefly review some established results of quantum thermalization. I first clarify the problem of thermalization in a mathematical manner, and then introduce several important results and insights: typicality of equilibrium states [1], relaxation caused by large effective dimension [2], and eigenstate thermalization hypothesis (ETH) [3,4] and weak-ETH [5]. In the second part of my talk, I explain some of my results. First, I introduce a model which is non-integrable and thermalizes but does not satisfy the ETH [6,7]. This finding disproves the conjectures that all nonintegrable systems satisfy the ETH and that the ETH is a necessary condition for thermalization. I also discuss the hardness of the problem of thermalization from the viewpoint of computational science [8]. Then, I move to an analytical approach to a concrete model, and prove that S=1/2 XYZ chain with a magnetic field is nonintegrable [9]. This is the first example of proof of nonintegrability in a concrete quantum many-body system, which will help a mathematical approach to thermalization.

会場: via Zoom

イベント公式言語: 英語

Mathematical aspects of quasi-Monte Carlo integration

2020年11月5日(木) 16:00 - 18:10

鈴木 航介 (広島大学 大学院先進理工系科学研究科 助教)

In this talk, I will introduce mathematical aspects of quasi-Monte Carlo (QMC) integration. We aim to approximate the integral of a function on the d-dimensional hypercube [0,1]^d. A useful approach is Monte-Carlo (MC) integration, which uses randomly chosen samples. A drawback of MC is the rate of convergence; the standard deviation of the estimator converges as 1/sqrt(n) asymptotically in n. To have a better rate of convergence as O(log^d N/N) or more, QMC uses deterministic, uniformly distributed points. In the first part, I will give an overview of QMC, such as star-discrepancy, Koksma-Hlawka inequality, and some explicit constructions as lattices and digital nets. In the second part, I will show that QMC using lattices and digital nets can achieve a higher rate of convergence for smooth integrands.

会場: via Zoom

イベント公式言語: 英語

Evolution of a peak of genetic divergence driven by local adaptation

2020年11月5日(木) 10:00 - 11:00

坂本 貴洋 (総合研究大学院大学 先導科学研究科 特別研究員)

In species that are distributed in various environments, each subpopulation adapts to the local environment. In general, when there is migration between subpopulations, genetic divergence does not proceed because the genomes are exchanged between subpopulations. However, around the loci involved in local adaptation, genetic divergence proceeds. This is because different genotypes are favored between subpopulations, so that the alleles of migrants are purged by natural selection and the exchange of genomes is suppressed. It has not been theoretically known how the degree of genetic differentiation evolves over time, making the interpretation of population genomic data difficult. In this study, we constructed and analyzed a model of population genetics to clarify the dynamics of genetic divergence.

会場: via Zoom

イベント公式言語: 英語

A physicist’s adventures in virology: Catherine Beauchemin live webcast

2020年11月5日(木) 9:00 - 10:00

カトゥリン・ボシゥメン (数理創造プログラム 副プログラムディレクター / Professor, Department of Physics, Ryerson University, Canada)

In her public lecture webcast, physicist Catherine Beauchemin will draw on contemporary examples from COVID-19 and influenza to explain eroding public trust in health research and why physics might be the answer. To watch the webcast, visit the page at the relevant link on November 4 at 7 pm ET (November 5 at 9 am JST).

会場: via Online

イベント公式言語: 英語

日本数学会 異分野・異業種研究交流会2020

2020年10月31日(土) 10:00 - 17:00

「数学・数理科学専攻若手研究者のための異分野・異業種研究交流会（研究交流会）」は、 数学・数理科学専攻の博士課程学生をはじめとする若手研究者と産業界を含む異分野の方々 との「双方向の交流の場」として2014年から開催しております。若手研究者の皆様に、諸科学や産業への応用展開のような数学の思わぬ力を発見してもらう ことや、産業界を含む様々な分野で活躍できる場の存在を認識してもらうことが主たる目的 です。高等学校、大学を含む教育・研究機関の教職員や企業関係者の皆様にも、産業界における数学 ・数理科学やその知識を有する人材のニーズを把握してもらうことも目的の一つです。 詳しくは関連リンクから、社会連携協議会内の研究交流会ホームページをご参照ください。

会場: via Online

イベント公式言語: 日本語

Basics of population genomic data analysis

2020年10月29日(木) 10:00 - 11:00

ジェフリ・フォーセット (数理創造プログラム 上級研究員)

In recent years, it has become possible to obtain the DNA sequence data of a large number of individuals of the same species. This data set is basically a M (number of samples) x N (number of genomic positions) matrix where each data point is 0 or 1. Using this data set, we try to understand, for example, the relationship between each sample or group of samples, and the population process that has generated the data set. In this talk, I will introduce the basic concepts behind the approaches we use to analyze such data sets.

会場: via Zoom

イベント公式言語: 英語

Toward simulating Superstring/M-theory on a Quantum Computer

2020年10月23日(金) 17:00 - 18:00

花田 政範 (Department of Mathematics, University of Surrey, UK)

We 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 we 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. We show the procedures are conceptually rather simple and efficient quantum algorithms can be applied. In addition, as a (kind of) byproduct, we provide a new formulation of pure Yang-Mills on quantum computer. If you would like to participate, please register using the form below.

会場: via Zoom

イベント公式言語: 英語

Realistic shell model and chiral three-body force

2020年10月22日(木) 13:30 - 15:00

福井 徳朗 (京都大学 基礎物理学研究所 研究員)

We show an evolution to derive the effective Hamiltonian in the shell-model framework starting from two- and three-body interactions based on the chiral effective field theory. A new way to calculate three-body matrix elements of the chiral interaction with the nonlocal regulator is proposed. We apply our framework to the p-shell nuclei and perform benchmark calculations to compare our results with those by an ab initio no-core shell-model. We report that our results are satisfactory and the contribution of the three-body force is essential to explain experimental low-lying spectra of the p-shell nuclei. We discuss the contribution of the three-body force on the effective single-particle energy extracted from the monopole interaction. Next, we investigate the shell evolution on the pf-shell nuclei. We show that the monopole component of the shell-model effective Hamiltonian induced by the three-body force plays an essential role to account for the experimental shell evolution. Moreover, we present our latest results on the investigation of the possible neutron dripline of the Ca isotopes. Finally, we discuss very neutron-rich systems, namely, the oxygen isotopes at the dripline and beyond, where the interplay between the three-body force and continuum states plays an important role. If you would like to participate, please register using the form below.

会場: via Zoom

イベント公式言語: 英語

代官山 音楽大学 講座 Vol.1「音楽×数学～音楽は感性の数学、数学は理性の音楽～」

2020年10月21日(水) 20:00 - 21:00

坪井 俊 (数理創造プログラム 副プログラムディレクター / 武蔵野大学)

iTHEMS副プログラムディレクターの坪井俊理学博士が、山岸ルツ子氏のピアノ演奏とともに、数学の美しさと調和を解説します。

会場: via Online

イベント公式言語: 日本語

Bayesian nonparametric estimation of Random Dynamical Systems

2020年10月21日(水) 14:00 - 15:00

Christos Merkatas (Postdoctoral Researcher, Aalto University, Finland)

In this talk, a Bayesian nonparametric framework for the estimation and prediction, from observed time series data, of discretized random dynamical systems is presented [1]. The size of the observed time series can be small and the additive noise may not be Gaussian distributed. We show that as the dynamical noise departs from normality, simple Markov Chain Monte Carlo method (MCMC) models are inefficient. The proposed models assume an unknown error process in the form of a countable mixture of zero mean normals, where a–priori the number of the countable normal components and their variances is unknown. Our method infers the number of unknown components and their variances, i.e., infers the density of the error process directly from the observed data. An extension for the joint estimation and prediction of multiple discrete time random dynamical systems based on multiple time-series observations contaminated by additive dynamical noise is presented [2]. In this case the model assumes an unknown joint error process with a pairwise dependence in the sense that to each pair of unknown dynamical error processes, we assign a– priori an independent Geometric Stick-Breaking process mixture of normals with zero mean. These mixtures a–posteriori will capture common characteristics, if there are any, among the pairs of noise processes. We show numerically that when the unknown error processes share common characteristics, it is possible under suitable prior specification to induce a borrowing of strength relationship among the dynamical error pairs. Then time-series with an inadequate sample size for an independent Bayesian reconstruction can benefit in terms of model estimation accuracy. Finally, possible directions for future research will be discussed.

会場: via Zoom

イベント公式言語: 英語

甘利俊一名誉教授文化勲章受章記念シンポジウム 開催のお知らせ

2020年10月21日(水) 13:00 - 18:00

甘利俊一名誉教授（東京大学大学院工学系研究科・工学部）の2019年度の文化勲章受章を記念して、シンポジウムを開催いたします。 13:00　合原 一幸（東京大学）開会の挨拶 13:05　豊泉 太郎（理研・東京大学）「桃李の下で脳の数理に志す」 13:50　村田 昇（早稲田大）「90年代の機械学習」 14:35　休憩 14:50　駒木 文保（東京大学）「多次元ポアソンモデルの情報幾何とベイズ統計」 15:35　藤原 彰夫（大阪大学）「ふるさとは遠きにありて思ふもの？」 16:20　休憩 16:30　甘利 俊一（理研）「深層学習の統計神経力学およびWasserstein統計学」 18:00　閉会 詳細およびイベントの予約は、関連リンクよりご参照ください。

会場: via Online

イベント公式言語: 日本語

Composite Dark matter and gravitational waves

2020年10月20日(火) 10:00 - 11:00

リナルディ エンリコ (数理創造プログラム 客員研究員 / AI Researcher/Engineer, Arithmer Inc.)

With non-perturbative lattice calculations we investigate the finite-temperature confinement transition of a composite dark matter model. We focus on the regime in which this early-universe transition is first order and would generate a stochastic background of gravitational waves. Future searches for stochastic gravitational waves will provide a new way to discover or constrain composite dark matter, in addition to direct-detection and collider experiments. As a first step to enabling this phenomenology, we determine how heavy the dark fermions need to be in order to produce a first-order stealth dark matter confinement transition.

会場: via Zoom

イベント公式言語: 英語

2020年度 武蔵野大学 数理工学シンポジウム MCME SYMPOSIUM 2020

2020年10月15日(木) - 16日(金)

初田 哲男 (数理創造プログラム プログラムディレクター)
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)

武蔵野大学数理工学センターで、「武蔵野大学数理工学シンポジウム」を開催いたします。 プログラム一部抜粋 10月16日（金） 13:30-14:40　濱崎 立資 「孤立量子系における熱力学第0 法則の普遍性」 14:50-16:00　初田 哲男 「格子ゲージ理論とその応用ー湯川秀樹から富岳コンピュータまで」 詳細およびシンポジウムの申し込みは、関連リンクよりご参照ください。

会場: via Online

イベント公式言語: 日本語

A PDE model for the localization and spread of flu in the human respiratory tract

2020年10月14日(水) 10:00 - 11:00

クリスチアン・キルエットゥ (Ph.D. Student, Department of Medical Physics, Ryerson University, Canada)

Within the human respiratory tract (HRT), virus diffuses through the periciliary fluid (PCF) bathing the epithelium. But it also undergoes advection: as the mucus layer sitting atop the PCF is pushed along by the ciliated cell's beating cilia, the PCF and its virus contents are also pushed along, upwards towards the nose and mouth. Our PDE model represents the HRT as a one-dimensional track extending from the nose down to the lower HRT, wherein stationary cells interact with virus which moves within (diffusion) and along with (advection) the PCF. In the PDE model, diffusion is negligible in the presence of advection which effectively sweeps away virus, preventing infection from spreading below the depth of deposition. Higher virus production rates (10-fold) are required at higher advection speeds (40 micron/s) to maintain equivalent infection severity and timing. Because virus is entrained upwards, upper parts of the HRT located downstream of the advection flow see more virus than lower parts, and so infection grows, peaks, and resolves later in the lower HRT. Clinically, the infection would appear to progress from the upper towards the lower HRT, as reported in mice. When the PDE model is expanded to include cellular regeneration and an immune response, it reproduces tissue damage levels reported in patients. This new PDE model offers a convenient and unique platform from which to study the localization and spread of respiratory viruses (flu, RSV, COVID-19) within the HRT during an infection.

会場: via Zoom

イベント公式言語: 英語