セミナー

Several identities related to the degenerate Bernoulli polynomials and numbers

2018年2月24日(土) 16:00 - 17:00

Takao Komatsu (Professor, Wuhan University, China)

In this talk we demonstrate some relations in degenerate Bernoulli polynomials, which may be expressed as a general convolution identity. We also show some properties of hypergeometric degenerate Bernoulli polynomials and numbers.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Diophantine Frobenius Problems — counting theory, generating function and zeta functions

2018年2月23日(金) 16:00 - 17:00

Takao Komatsu (Professor, Wuhan University, China)

When a_1, ...,a_m are relatively prime positive integers, the number of solutions of the linear Diophantine equation a_1 x_1 + … + a_m x_m = b in non-negative integers x_1, ...,x_m, for any integer b, is our concern. We show several formulas to give the largest integer b without solution. Then we discuss the generating function of the number of solutions. Finally, we derive an explicit expression for an inverse power series over the gaps values of numerical semigroups generated by two integers. It implies a set of new identities for the Hurwitz zeta function.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Statistical mechanics of tissue homeostasis

2018年1月22日(月) 14:00 - 15:00

川口 喬吾 (東京大学)

Adult tissues undergo rapid turnover as mature cells are continuously lost and new cells arise through cell division. The balance between the gain and loss of cells must be finely orchestrated to maintain tissues, but how this balance is achieved remains largely unknown. Previous works [1] have used universal scaling laws to claim that the fate choice of stem cells (division or differentiation) are made strictly cell-autonomously. However, we recently recorded every stem cell fate choice within the mouse skin epidermal regions over one week and found that, far from being cell-autonomous, stem cell loss by differentiation is compensated by direct neighboring division [2]. In this talk, I will describe a model of tissue homeostasis using a macroscopic nonequilibrium setup, and explain how the coarse-graining of this model will lead to the effective dynamics of the voter model (DP2). I will show how we can use the property of dynamical crossover in the model -from the cell-autonomous regime (critical birth-death model) to the fate-coordinated regime (voter model)- to measure the length and time scales of stem cell coordination. I will then explain the pitfall in two-dimensions of using scaling relations for the clonal fate trace of cells, and present the workaround we used in the data analysis to definitively show the existence of cell-to-cell fate correlation.

会場: コモンルーム (246-248号室)

イベント公式言語: 英語

高密度天体現象と状態方程式

2017年12月28日(木) 10:30 - 11:30

古澤 峻 (数理創造プログラム 基礎科学特別研究員)

会場: SUURI-COOL (Kyoto)

イベント公式言語: 英語

体内時計の普遍性と種特異性に関する数理的研究

2017年12月27日(水) 16:00 - 17:00

黒澤 元 (数理創造プログラム 研究員 / 理化学研究所 望月理論生物学研究室 研究員)

会場: SUURI-COOL (Kyoto)

イベント公式言語: 英語

網膜細胞モザイクパターン形成の数理モデリング

2017年12月27日(水) 13:30 - 14:30

小川 軌明 (理化学研究所 理論科学連携研究推進グループ (iTHES) 特別研究員)

会場: SUURI-COOL (Kyoto)

イベント公式言語: 英語

作用素のトポロジーとトポロジカル絶縁体

2017年12月27日(水) 10:30 - 11:30

窪田 陽介 (数理創造プログラム 研究員)

会場: SUURI-COOL (Kyoto)

イベント公式言語: 英語

Chiral Phases in Frustrated 2D Antiferromagnets and Fractional Chern Insulators

2017年12月21日(木) 11:00 - 12:00

Eduardo Fradkin (University of Illinois, USA)

会場: 研究本館 5階 535-537号室

イベント公式言語: 英語

Baryon Asymmetry of the Universe generated by Helical Hypermagnetic fields through chiral anomaly

2017年12月20日(水) 11:00 - 12:00

Kohei Kamada (Center for Theoretical Physics of the Universe, Institute for Basic Science, Republic of Korea)

Recent observations of TeV blazars by Fermi identified deficits of secondary GeV cascade photons.These observations can be explained by intergalactic magnetic fields, which may have a primordial origin.If the magnetic fields are helical and generated before the electroweak symmetry breaking,nontrivial interaction between (hyper)magnetic fields and other particles can cause some interestingand non negligible phenomena in the early Universe. In this talk, I will show that the baryon asymmetry can be generated by the chiral anomaly and this mechanism might be responsible for the present baryon asymmetry of the Universe. The intergalactic magnetic fields are its smoking-gun. If this mechanism is responsible for the present Universe,the BSM physics is needed for the generation of (hyper)magnetic fields but not for the baryogenesis.

会場: セミナー室 (160号室)

イベント公式言語: 英語

A New Look at Matrix Models for QCD3

2017年11月24日(金) 16:30 - 18:00

金澤 拓也

Non-chiral random matrix models for QCD in 2+1 dimensions and their new generalizations will be discussed.

会場: セミナー室 (160号室)

イベント公式言語: 英語

The Riemann-Roch theorem

2017年9月26日(火) 14:00 - 15:00

窪田 陽介 (数理創造プログラム 研究員)

In the mid- 19th century, B. Riemann introduced the notion of Riemann surface in his Ph.D thesis on complex analysis. Together with non-Euclidean geometry, the theory of Riemann surface is a germination of modern geometry in both algebraic and analytic sense. In this talk, I will give an introduction of the theory of Riemann surface centering around the Riemann-Roch theorem. It is an important prototype of the Atiyah-Singer index theorem, the starting point of my research field.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Connections of Pair Correlations to Equidistribution and Additive Energy

2017年8月31日(木) 13:30 - 15:00

Thomas Lachmann (Graz University of Technology, Austria)

会場: コモンルーム (246-248号室)

イベント公式言語: 英語

Pulsar Winds: Ultimate Relativistic Outflows

2017年8月29日(火) 13:30 - 14:30

Dmitry Khangulyan (立教大学)

A highest density body that features the strongest magnetic field launches, no surprise, an ultimate outflow -- pulsar wind. Despite their relativistic nature and complexity, a few simple analogies can help us to understand the essence of pulsar physics. I will present several links connecting basic mechanics and electrodynamics, every-day thermodynamics and hydrodynamics to the processes taking place in the vicinity of pulsars. These fundamental relations not only provide a simple mental image for the pulsar physics but also have their imprint in high-energy data obtained from pulsars and pulsar wind nebulae.

会場: 研究本館 433号室

イベント公式言語: 英語

Joint Seminar with Condensed Matter Theory Laboratory

2017年7月20日(木) 13:30 - 15:00

笠 真生 (Associate Professor, Department of Physics and the College, The University of Chicago, USA)

会場: 研究本館 435-437号室

イベント公式言語: 英語

数論への誘い

2017年7月10日(月) 13:30 - 14:30

宮﨑 弘安

The goal of number theory is to reveal the mystery of natural numbers 1,2,3…. It has a long history, and it is still developing by exchanging ideas with many other branches of mathematics. In the long history, number theory had been thought of as a pure mathematics with no direct application outside mathematics. However, the rapid development of computer science changed the situation: the theory of prime numbers has been applied to code theory, cryptography, random number generation etc. It seems that there are several researches in physics and biology using the method of number theory, too. The aim of this talk is to give a beginner-friendly introduction to number theory. Among many topics, I will focus on very fundamental and important concepts: the “p-adic numbers” and the “finite fields.” I hope that this talk will motivate you to relate your research to number theory.

会場: セミナー室 (160号室)

イベント公式言語: 英語

組ひもと位相的混合

2017年6月26日(月) 14:00 - 15:00

金 英子 (大阪大学)

In mathematics, the braids are important tools for the knot theory, hyperbolic geometry, and dynamical systems etc. In the last ten years, the braids have been used to study mixing in fluids. Various simple mixing devices (e.g. taffy machines) have been developed. These devices utilize a particular type of braid, so-called a pseudo-Anosov type. The notion of pseudo-Anosov braids comes from the Nielsen-Thurston theory on the surface automorphisms, and the theory says that the devices using pseudo-Anosov braids are "efficient" in some sense. In this lecture, I will give a quick introduction of the Nielsen-Thurston theory and the classification of braids. I will give a picture of the "complexity" forced by pseudo-Anosov braids. In particular, I will explain why pseudo-Anosov braids are useful and why they can be used to build interesting mixing devices. Cosponsored by RIKEN iTHEMS and AIP Mathematical Science Team

会場: 理化学研究所 東京連絡事務所

イベント公式言語: 英語

Homological algebra, Renormalization and Transversality

2017年6月26日(月) 10:30 - 11:30

深谷 賢治 (Permanent Member, Simons Center for Geometry and Physics, Stony Brook University, New York, USA)

Transversality is a basic concept of differential topology and theory of manifold. Homological algebra may be regarded as a method to approximate `spaces' by an algebra and is a basic concept in agebraic topology. I would like to explain in this talk how they are related to some basic problem of quantum field theory such as renormalization. Cosponsored by RIKEN iTHEMS and AIP Mathematical Science Team

会場: 理化学研究所 東京連絡事務所

イベント公式言語: 英語

Galois representations and the Langlands correspondence

2017年6月8日(木) 13:30 - 14:30

時本 一樹 (京都大学)

The Langlands correspondence relates number-theoretic objects to completely different objects. While still largely conjectural, it has attracted interests of many mathematicians over the years. It is known that the local Langlands correspondence in a special case can be constructed in a geometric way (the non-abelian Lubin-Tate theory). In this talk, I will explain some basic concepts in mathematics (such as groups, representations and Galois groups) and then try to convey some flavor of my result related to the non-abelian Lubin-Tate theory.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Atypicality of most few-body observables

2017年5月29日(月) 13:30 - 14:30

濱崎 立資 (東京大学)

Understanding how isolated quantum systems thermalize has recently gathered renewed interest among theorists, thanks to the experimental realizations of such systems. The eigenstate thermalization hypothesis (ETH) is particularly investigated as a sufficient condition for the approach to thermal equilibrium. It states that diagonal matrix elements of an observable for the energy eigenstates are almost the same within a small energy shell. The ETH is justified for an observable and a Hamiltonian whose respective eigenbases are typically oriented to each other; i.e., for almost all unitary transformations of these two eigenbases with respect to the uniform Haar measure. In this seminar, we consider a Hamiltonian with few-body interactions and random observables without assuming the uniform Haar measure. These observables are chosen in an operational manner as random linear combinations of the operator basis of spins. We show that most few-body observables have atypical matrix elements when the energy width is not exponentially small with the system size. Namely, the maximum fluctuation for diagonal matrix elements is larger than that predicted by the uniform Haar measure.

会場: 研究本館 433号室

イベント公式言語: 英語

Guiding principles to develop tough polymer materials: An exactly solvable model

2017年5月25日(木) 10:30 - 11:30

作道 直幸 (お茶の水女子大学 ソフトマター教育研究センター 特任助教)

Needs to impart appropriate elasticity and high toughness to viscoelastic polymer materials are ubiquitous in industries such as concerning automobiles and medical devices. One of the major problems to overcome for toughening is catastrophic failure linked to a velocity jump [1-3], i.e., a sharp transition in the velocity of crack propagation occurred in a narrow range of the applied load. However, its physical origin has remained an enigma despite previous studies [4] over 35 years. Here, we propose an exactly solvable model that exhibits the velocity jump incorporating linear viscoelasticity with a cutoff length for a continuum description [5]. With the exact solution, we elucidate the physical origin of the velocity jump: it emerges from a dynamic glass transition in the vicinity of the propagating crack tip. We further quantify the velocity jump together with slow- and fast-velocity regimes of crack propagation, which would stimulate the development of tough polymer materials.

会場: セミナー室 (160号室)

イベント公式言語: 英語