セミナー

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

Chaos, Quark, Black Hole

2017年4月14日(金) 14:30 - 15:30

橋本 幸士 (大阪大学 大学院理学研究科 教授)

会場: セミナー室 (160号室)

イベント公式言語: 英語

HPC in precision medicine

2017年4月11日(火) 15:30 - 16:30

Tilo Wettig (Professor, Universität Regensburg, Germany)

In theoretical particle physics we have been using high-performance computing (HPC) for three decades to make scientific progress. Recent advances in next-generation sequencing, as well as the corresponding bioinformatics questions, generate an obvious need for HPC methods in the field of precision medicine. We have recently started to explore this field and believe that our HPC expertise can be used to speed up time-critical workflows, to better manage the large amount of data involved, and to lead to more cost- and energy-efficient solutions. I will discuss a few concrete examples, including interesting questions in single-cell sequencing.

会場: 研究本館 433号室

イベント公式言語: 英語

Geometry in condensed matter physics

2017年4月8日(土) 13:00 - 14:00

永長 直人 (理化学研究所 創発物性科学研究センター (CEMS) 強相関理論研究グループ 副センター長, グループディレクター / 東京大学 大学院工学系研究科 物理工学専攻 教授)

Quantum geometry plays essential roles current condensed matter physics. Aharonov-Bohm effect and Berry phase as its generalization are the key concepts in electronic systems in solids, which are described by the Bloch wavefunctions and electron correlation effects on top of them. In this talk, I will describe how the geometry determines the physical properties of materials focising on the gauge structure and electomagnetic responses.

会場: セミナー室 (160号室)

イベント公式言語: 英語

2次元整数格子上の単純ランダムウォークの局所時間と対応するガウス自由場

2017年4月6日(木) 10:30 - 11:30

岡田 いず海

本講演では、2次元 (整数格子上) の単純ランダムウォークの local time と対応するガウス自由場に関する極限定理を扱う。これらの確率過程は、様々な分野に応用されている重要な対象である。また、これまでこの2つの確率過程の関係性に関する様々な結果が示されており、講演者はさらなる詳細な解析を目指している。 その手始めとして、2次元の favorite point (単純ランダムウォークの local time が他点 と比べて極端に大きい点) などの特異点に対して研究を進めてきた。近年この分野の第一人者である A.Dembo, Y.Peres, O.Zeitouni, J.Rosen 氏らによって、 favorite point が local time の汎関数の極限定理と密接な関係を持つことが示されており、従って重要な研究対象と考えられる。

会場: セミナー室 (160号室)

イベント公式言語: 英語

Fatgraph models for RNA molecules

2017年3月23日(木) 10:30 - 11:30

藤 博之 (香川大学 教育学部 准教授)

Concepts of fatgraphs and partial chord diagrams occur in many branches of mathematics, including topology, geometry, and representation theory. During the last decade, some applications of these mathematical objects to the research of the molecular biology have been reported. Among them, in particular, a characterization by the genus in the fatgraph presentation of the RNA has been studied remarkably. In this talk, I will explain how the concepts of fatgraphs and partial chord diagrams are applied to the study of the secondary structure of the RNA with pseudoknots, and introduce the matrix model that is invented by basic techniques of the quantum field theory. If time permits, I shall discuss about the matrix model of the protein, and speculate about further developments.

会場: セミナー室 (160号室)

イベント公式言語: 英語

T-DUALITY AND SCATTERING OF STRINGY STATES

2016年12月12日(月) 15:00 - 16:00

Jnan Maharana

I shall first review the salient features of T-duality, paying special attentions to the worldsheet perspective. The construction of vertex operators for Moduli will be discussed. The KLT formalism will be applied to show that the S-matrix for scattering of massless state arising from toroidal compactification of closed bosonic string is T-duality invariant.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Non-perturabative quantum analysis based on resurgence theory

2016年11月11日(金) 10:30 - 11:30

三角 樹弘 (秋田大学 専任講師)

常微分方程式論においては，漸近展開に基づく形式的解から完全な解を構成するための理論体系「Resurgence理論」が確立されており，そこでは漸近級数ボレル和の総和として解が与えられる．一方，Resurgence理論を経路積分形式での量子論に適用することで，非摂動的に理論を解析する道が開ける．しかし，その際には「摂動級数の高次」と「古典作用の停留点」という2つの要素を手に入れる必要がある．実は，Resurgence理論は変数の複素化に伴う「ストークス現象」に基づくことから，ここでの停留点には実古典解だけでなく複素古典解も含まれる．したがって，Resurgence理論の量子論への応用においては，理論の複素古典解を求めその寄与を取り入れることが重要になる．このレクチャーでは，摂動級数と複素解に基づいた非摂動的解析法の理解を目標として，以下の順序で議論を進める．

会場: セミナー室 (160号室)

イベント公式言語: 日本語