Mathematics of Post-Quantum Cryptography

2022年11月18日(金) 14:00 - 16:30

相川 勇輔 (三菱電機株式会社 情報技術総合研究所 研究員)

Cryptography keeps our everyday information communications secure. Cryptography based on key sharing have been used mainly for military purposes since ancient times in human history, but with the advent of the Internet, cryptography that does not require key sharing has become necessary. In 1976, Diffie and Hellman proposed the concept of public key cryptography, which does not require key sharing among communicators. Since then, research on public key cryptography has progressed, involving not only computer science but also mathematics, and has become an essential technology for the society we live in. The security of public key cryptography is supported by computational hardness of problems derived from mathematics. For example, the integer factoring problem is a basis for the security of RSA cryptography, and the discrete logarithm problem is for elliptic curve cryptography. However, in 1994, Shor proposed an efficient quantum algorithm that solves these problems. This means that emergence of large-scale quantum computers will break RSA and elliptic curve cryptography we use today. For this reason, research on next-generation cryptography, so-called Post-Quantum Cryptography (PQC for short), is currently underway to prepare for a future in which quantum computers will emerge. In this talk, without assuming any knowledge of cryptography, I will give a brief overview of cryptography and the progress of PQC. The first half of the talk will mainly outline the relationship between mathematics and cryptography, while the second half will discuss isogeny-based cryptography, one of the promising PQC, with our recent results.

会場: コモンルーム 246-248号室 とZoomのハイブリッド開催

イベント公式言語: 英語

Emergence of growth and dormancy from a kinetic model of the Escherichia coli central carbon metabolism

2022年11月17日(木) 18:00 - 19:00

姫岡 優介 (東京大学 生物普遍性研究機構 助教)

Physiological states of bacterial cells exhibit a wide spectrum of timescale. Under nutrient-rich conditions, most of the cells in an isogenic bacterial population grow at certain rates, while a small subpopulation sometimes stays in a dormant state where the growth rates slow down by orders of magnitude. For revealing the origins of such heterogeneity of timescales, we studied the kinetic model of Escherichia coli central carbon metabolism. We found that the model robustly exhibits both the growing- and the dormant state. Performing the model reduction, we have revealed the necessary conditions for the distinct behaviour, namely, the depletion of energy due to the futile cycle and its non-uniform impact on the kinetics because of the coexistence of the energy currency-coupled and uncoupled reactions as well as branching of the network.

会場: via Zoom

イベント公式言語: 英語

2022年度 武蔵野大学 数理工学シンポジウム MCME SYMPOSIUM 2022

2022年11月16日(水) - 17日(木)

三好 建正 (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 チームリーダー)
田屋 英俊 (数理創造プログラム 基礎科学特別研究員)
西森 秀稔 (東京工業大学 特任教授)

武蔵野大学数理工学センターでは、今年も「武蔵野大学数理工学シンポジウム」を開催いたします。なお、本シンポジウムは参加費無料で、どなたでもご参加いただけます。 iTHEMSの関係者も講演予定です。以下、プログラムより一部抜粋します。 11月16日（水）13：30 - 14：40「ビッグデータ同化：ゲリラ豪雨予測から予測科学へ」 三好 建正 11月17日（木）10：00 - 11：10「「無」から「有」をつくる： 素粒子物理学の視点から」田屋 英俊 11月17日（木）14：50 - 16：00「量子アニーリングによる量子シミュレーション」西森 秀稔 参加登録は11月14日まで。下記、関連リンクよりお申し込みください。 主催：武蔵野大学数理工学センター（MCME） 共催：理化学研究所数理創造プログラム（iTHEMS）

会場: 武蔵野大学有明キャンパス5号館301教室とZoomのハイブリッド開催

Merger and post-merger of binary neutron stars with a quark-hadron crossover equation of state

2022年11月15日(火) 15:00 - 17:01

黄 永嘉 (Ph.D. Student, University of Science and Technology of China, China)

The state of the ultra-dense matter remains one of the long-standing open questions. Neutron star (NS), as it cools down the eons ahead after the birth in the supernova explosion, provides an astrophysical laboratory to investigate the dense, strongly interacting nuclear matter at zero temperature. On the other hand, the most intense gravitational wave(GW) radiation is produced in regions of the strong gravitational field by coherent movements of masses with large compactness. Therefore, GW from binary neutron star(BNS) merger naturally contains the information from the ultra-dense matter. In this talk, I will introduce our recent work, "Merger and post-merger of binary neutron stars with a quark-hadron crossover equation of state ."Quark-hadron crossover(QHC) is one way of hadron-quark transition, which generally predicts a peak in sound speed vs. density, and so releases more pressure during the hadron-quark transition. I will first briefly summarize the features of QHC EOS and the BNS merger. I will then focus on how information on the hadron-quark transition shows in the GW and its spectrum during the BNS merger.

会場: via Zoom

イベント公式言語: 英語

Expanding Edges of Quantum Hall Systems in a Cosmology Language - Hawking Radiation from de Sitter Horizon in Edge Modes

2022年11月11日(金) 16:00 - 17:30

堀田 昌寛 (東北大学 大学院理学研究科物理学専攻 助教)

Expanding edge experiments are promising to open new physics windows of quantum Hall systems. In a static edge, the edge excitation, which is described by free fields decoupled with the bulk dynamics, is gapless, and the dynamics preserve conformal symmetry. When the edge expands, such properties need not be preserved. We formulate a quantum field theory in 1+1 dimensional curved spacetimes to analyze the edge dynamics. We propose methods to address the following questions using edge waveforms from the expanding region: Does the conformal symmetry survive? Is the nonlinear interaction of the edge excitations induced by edge expansion? Do the edge excitations interact with the bulk excitations? We additionally show that the expanding edges can be regarded as expanding universe simulators of two-dimensional dilaton-gravity models, including the Jackiw-Teitelboim gravity model. As an application, we point out that our theoretical setup might simulate emission of analog Hawking radiation with the Gibbons-Hawking temperature from the future de Sitter horizon formed in the expanding edge region.

会場: 研究本館 3階 345−347号室 (メイン会場) / via Zoom

イベント公式言語: 英語

Arithmetic dynamics on algebraic varieties

2022年11月11日(金) 14:00 - 16:30

松澤 陽介 (大阪公立大学 大学院理学研究科 数学専攻 准教授)

The study of self-maps of algebraic varieties is a relatively new and active area in mathematics. Such a self-map can be considered as a discrete dynamical system, and we can study the asymptotic properties of such systems from various points of views, including number theoretic viewpoint. I will introduce several problems in arithmetic dynamics and some of my results in this area.

会場: コモンルーム 246-248号室 とZoomのハイブリッド開催

イベント公式言語: 英語

Sociogenesis: motivations and first steps

2022年11月10日(木) 16:00 - 17:00

Cédric Ho Thanh (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)

Sociogenesis is a project that aims to study emergent social behaviors of multi-agent systems. In its simplest form, and agent simply seeks to survive by consuming food and maximizing some happiness score. In this presentation, I will discuss some motivations and inspirations of this project, as well as the challenges to get an agent to survive on its own. I will then showcase some methods to evaluate the quality of agents and their underlying architecture beyond simply looking at their lifespan. I will then conclude with some potential applications. No prior knowledge in reinforcement/deep learning is required to attend this presentation. This work is still mostly at an exploratory stage, so discussions and inputs from the audience are more than welcome!

会場: via Zoom

イベント公式言語: 英語

An Introduction to Quantum Measurement Theory for Physicists

2022年11月10日(木) - 12日(土)

堀田 昌寛 (東北大学 大学院理学研究科物理学専攻 助教)

In this lecture, basic concepts in quantum measurement theory are introduced, including measurement operators and POVM's. The related topics are also picked up. Lecture 1: Nov. 10, 10:30 - 12:00 Lecture 2: Nov. 10, 13:30 - 15:00 Lecture 3: Nov. 10, 15:30 - 17:00 Lecture 4: Nov. 11, 10:30 - 12:00 Lecture 5: Nov. 11, 13:30 - 15:00 Lecture 6: Nov. 12, 10:30 - 12:00

会場: 研究本館 3階 345−347号室 (メイン会場) / via Zoom

イベント公式言語: 英語

Tensor renormalization group approach to quantum fields on a lattice

2022年11月8日(火) 13:30 - 15:00

秋山 進一郎 (東京大学 量子ソフトウェア寄付講座 特任助教)

Tensor renormalization group (TRG) approach is a variant of the real-space renormalization group to evaluate the path integral defined on the thermodynamic lattice, without resorting to any probabilistic interpretation for the given Boltzmann weight. Moreover, since the TRG can directly deal with the Grassmann variables, this approach can be formulated in the same manner for the systems with bosons, fermions, or both. These advantages of the TRG approach have been confirmed by the earlier studies of various lattice theories, which suggest that the TRG enables us to investigate the parameter regimes where it is difficult to access with the standard stochastic numerical methods, such as the Monte Carlo simulation. In this talk, explaining our recent applications of the TRG approach to several lattice models, we demonstrate the efficiency of the TRG as a tool to investigate lattice theories particularly in higher dimensions and future perspective.

会場: コモンルーム 246-248号室 とZoomのハイブリッド開催

イベント公式言語: 英語

UHECR anisotropy: effects of the Galactic magnetic field on the UHECR correlation studies

2022年11月4日(金) 14:00 - 15:00

樋口 諒 (理化学研究所 開拓研究本部 (CPR) 長瀧天体ビッグバン研究室 基礎科学特別研究員)

Telescope Array (TA) and Auger experiments reported anisotropies in the arrival direction of ultra-high-energy cosmic rays (UHECRs). In the current correlation studies between UHECRs and source candidates, the Auger experiment reported a correlation between the flux model of assumed sources and UHECR events and suggested a 10% contribution of starburst galaxies (SBGs) to the anisotropy of UHECRs. However, they do not consider the effect of coherent deflection by the galactic magnetic field (GMF), and they should significantly affect the results of the correlation studies. In this talk, we introduce a current study of UHECR anisotropy and the effect of GMF on them.

会場: via Zoom

イベント公式言語: 英語

Gamma-ray emission from the Sagittarius Dwarf Spheroidal galaxy due to millisecond pulsars

2022年10月28日(金) 17:00 - 18:00

Oscar Macias (Faculty of Science, University of Amsterdam, Netherlands)

The Fermi Bubbles are giant, gamma-ray emitting lobes emanating from the nucleus of the Milky Way discovered in ~1-100 GeV data collected by the Fermi Gamma-Ray Space Telescope. Previous work has revealed substructure within the Fermi Bubbles that has been interpreted as a signature of collimated outflows from the Galaxy's super-massive black hole. In this talk, I will show that much of the gamma-ray emission associated to the brightest region of substructure -- the so-called cocoon -- is likely due to the Sagittarius dwarf spheroidal (Sgr dSph) galaxy. This large Milky Way satellite is viewed through the Fermi Bubbles from the position of the Solar System. As a tidally and ram-pressure stripped remnant, the Sgr dSph has no on-going star formation, but I will demonstrate that the dwarf's millisecond pulsar (MSP) population can plausibly supply the observed gamma-ray signal. This finding plausibly suggests that MSPs produce significant gamma-ray emission amongst old stellar populations, potentially confounding indirect dark matter searches in regions such as the Galactic Centre, the Andromeda galaxy, and other massive Milky Way dwarf spheroidals.

会場: via Zoom

イベント公式言語: 英語

Measuring diversity: species similarity

2022年10月28日(金) 16:00 - 17:00

トム・レンスター (Professor, University of Edinburgh, UK)

Traditional measures of the diversity of an ecological community depend only on how abundant the species are, not the similarities or differences between them. To better reflect biological reality, species similarity should be incorporated. Mathematically, this corresponds to moving from probability distributions on sets to probability distributions on metric spaces. I will explain how to do this and how it can change ecological judgements. Finally, I will describe a surprising theorem on maximum diversity (joint with Meckes and Roff), which reveals close connections between maximum diversity and invariants of geometric measure.

会場: via Zoom

イベント公式言語: 英語

Migration dynamics and model of cells crawling on a matrix with cell-scale stiffness heterogeneity

2022年10月27日(木) 16:00 - 17:00

江端 宏之 (九州大学 大学院理学研究院 助教)

In living tissues where cells migrate, spatial distribution of mechanical properties, especially matrix stiffness, are generally heterogenous with cell-scales ranging from 10 to 1000 μm. Since the cell migration in our body plays critical role in morphogenesis, wound healing, and cancer metastasis, it is essential to understand the migratory dynamics on the matrix with cell-scale stiffness heterogeneity. However, while cellular responses to homogeneous matrix have been extensively explored, studies of the cell motility with stiffness heterogeneity have been limited to the directional movement (durotaxis) driven by a simple stiffness gradient. Thus, we need to elucidate how cell migration is determined through the interaction among cell-scale stiffness heterogeneity and cellular responses such as dynamics of the cell-matrix adhesion site, the intracellular prestress, and cell shape. In this talk, we introduce our experiments on cell motility, shaping, adhesion, and traction forces at long time scales using microelastically patterned hydrogels that enable us to systematically control the cell-scale heterogeneity of the matrix-stiffness. Using microelastically patterned hydrogels, we showed that the cell exhibited a general mode of durotaxis depending on the shape and size of the stiff domains, which was coincided with the extraordinarily large fluctuation of the traction force. We proposed a cell migration model based on equations of a deformable self-propelled particle adopting an amoeboid swimmer-like velocity-shape relationship. By considering the cellular response to stiffness gradients, the model can reproduce general durotaxis driven by cell-scale heterogeneity of the matrix-stiffness.

会場: via Zoom

イベント公式言語: 英語

Measuring diversity: the axiomatic approach

2022年10月21日(金) 16:00 - 17:00

トム・レンスター (Professor, University of Edinburgh, UK)

Ecologists have been debating the best way to measure diversity for more than 50 years. The concept of diversity is relevant not only in ecology, but also in other fields such as genetics and economics, as well as being closely related to entropy. The question of how best to quantify diversity has surprising mathematical depth. I will argue that the best approach is axiomatic: to enable us to reason logically about diversity, the measures we use must satisfy certain mathematical conditions, and those conditions dramatically limit the choice of measures. This point will be illustrated with a theorem: using a simple model of ecosystems, the only diversity measures that behave logically are the Hill numbers, which are very closely related to the Rényi entropies of information theory.

会場: via Zoom

イベント公式言語: 英語

How can interspecific pollen transfer affect coexistence and evolution of sex ratio of two closely related plant species?

2022年10月20日(木) 16:00 - 17:00

森田 慶一 (総合研究大学院大学 先導科学研究科 生命共生体進化学専攻 博士課程)

In co-flowering species with shared pollinators, interspecific pollen transfer (IPT) may occur, in which pollen grains are transferred between different species. Yet, it is unclear how the costs of IPT in reduced pollen grains (i.e., costs for males) and seed set (i.e., costs for females) can affect coexistence and evolution of sex ratio. We investigated the conditions for which two closely related plants can coexist and of evolution in sex ratio, by constructing a theoretical model that incorporates the dynamics of population, pollen export, pollen reception on an ovule, and seed production in two closely related plants with resource competition and IPT. The model analysis revealed that coexistence is likely with infrequent IPT, α, and weak interspecific resource competition, β, and high production rates of pollen, Am, and ovules, Af. Also, we found a trade-off where too low value of either Am or Af makes both species go extinct. Furthermore, even when α and β were small enough, too low Am and Af made extinction of both species likely, because of the Allee effect due to resource competition and interspecific pollen competition for a small number of ovules. Adaptive dynamics, analysis of evolutionary dynamics showed that sex ratio evolve to 1:1 as the optimum allocation of resource to produce pollen grains and ovules.

会場: via Zoom

イベント公式言語: 英語

Quantum nucleation of topological solitons

2022年10月20日(木) 13:30 - 15:00

衛藤 稔 (山形大学 理学部 教授)

The chiral soliton lattice is an array of topological solitons realized as ground states of QCD at finite density under strong magnetic fields or rapid rotation, and chiral magnets with an easy-plane anisotropy. In such cases, topological solitons have negative energy due to topological terms originating from the chiral magnetic or vortical effect and the Dzyaloshinskii-Moriya interaction, respectively. We study quantum nucleation of topological solitons in the vacuum through quantum tunneling in 2+1 and 3+1 dimensions, by using a complex ϕ4 (or the axion) model with a topological term proportional to an external field, which is a simplification of low-energy theories of the above systems. In 2+1 dimensions, a pair of a vortex and an anti-vortex is connected by a linear soliton, while in 3+1 dimensions, a vortex is string-like, a soliton is wall-like, and a disk of a soliton wall is bounded by a string loop. Since the tension of solitons can be effectively negative due to the topological term, such a composite configuration of a finite size is created by quantum tunneling and subsequently grows rapidly. We estimate the nucleation probability analytically in the thin-defect approximation and fully calculate it numerically using the relaxation (gradient flow) method. The nucleation probability is maximized when the direction of the soliton is perpendicular to the external field.

会場: via Zoom

イベント公式言語: 英語

An Introduction to Rough Geometry (with a view to Euclidean Gravity)

2022年10月14日(金) 14:00 - 16:30

クリスティ・コウジ・ケリー (数理創造プログラム 基礎科学特別研究員)

The mathematical formulation of Einstein gravity typically utilises differentiable manifolds as models of smooth spacetimes. In many scenarios, however, it is desirable to have coarser models of spacetime and a correspondingly rough theory of geometry applicable to these coarser spacetime structures. In 2D Euclidean quantum gravity, for instance, the use of Regge calculus allows one to treat triangulations as regularisations of smooth spacetimes. There has been much recent progress in the mathematical (rigorous) understanding of this theory which we briefly review. We also introduce a rich alternative framework for the study coarse Euclidean geometry in the form of metric geometry augmented by optimal transport theory. In particular we introduce several optimal transport theoretic curvatures and demonstrate that these recover the familiar smooth notions under suitable limits.

会場: コモンルーム 246-248号室 とZoomのハイブリッド開催

イベント公式言語: 英語

Introduction to cepstrum analysis and its applications

2022年10月13日(木) 16:00 - 17:00

儀保 伸吾 (数理創造プログラム 特別研究員)

Recent advances in experimental technique enable us to obtain many time-series data of biological oscillatory systems. These time-series are of various shapes, which means that the envelop of spectrum are also various. Cepstrum analysis is well-known method for evaluating the spectrum shapes in acoustic engineering. In this talk, I will introduce cepstrum analysis and its applications for analyzing biological oscillations.

会場: via Zoom

イベント公式言語: 英語

Ultra-Light Axion Dark Matter: Bose-Einstein condensates and superfluids in the sky

2022年10月11日(火) 13:30 - 15:00

エリザ・フェレイラ (東京大学 カブリ数物連携宇宙研究機構 (Kavli IPMU) 特任助教)

The nature of dark matter (DM) is one of the biggest mysteries in cosmology. There are many different models to explain the nature of this elusive component. In this talk I will present a class of dark matter models: ultra-light dark matter (ULDM) or ultra-light axions (ULA). I will show the different models present in the literature and classify them according to the way they behave on small scales. One of the most interesting features of this class of DM models is that it might condense in the interior of the halos of galaxies forming a Bose-Einstein condensate (BEC) or superfluid. This interesting quantum phenomena on macroscopic scales, and the wave nature of ULDM leads to different and interesting astrophysical consequences that can be probed on small scales. I will quickly review first the fuzzy dark matter model, one of the most well studied ULA models, where I will present its description, predictions and current bounds. Then I will introduce the DM superfluid model, where, upon condensation in the interior of galaxies, DM dynamics represents that of MOdified Newtonian Dynamics (MOND) on galactic scales. This behaviour can address some of the curiosities of the behaviour of DM on small scales. I plan to show the theoretical description of this model and its interesting phenomenology.

会場: コモンルーム 246-248号室 とZoomのハイブリッド開催

イベント公式言語: 英語

Isometric tensor networks in two dimension

2022年10月11日(火) 10:30 - 12:00

ヤンタオ・ウー (数理創造プログラム 特別研究員)

In this talk, I would like to explain the ansatz of isometric tensor network states (isoTNS) as candidate wavefunctions in two-dimensional condensed matter systems. I will explain how the isometric structure in 2D helps generalize many 1D tensor network algorithms, like the density matrix renormalization group and the time-evolution block decimation methods, to two dimensions. Both bosons and fermions; ground states and dynamics will be discussed. I will also explain why it is a friendly trial wavefunction in the context of variational Monte Carlo, where the sampling correlation time vanishes. I will also explain its relation to quantum error correction and how it provides an interesting playground of quantum information. If time permits, I would like to discuss some open questions about its representability of topological phases.

会場: コモンルーム (246-248号室) (メイン会場) / via Zoom

イベント公式言語: 英語