セミナー

Tensor Berry connections and their topological invariants

2019年4月2日(火) 14:00 - 15:00

ジャンドミニコ・パルンボ (Researcher, Université Libre de Bruxelles, Belgium)

The Berry connection plays a central role in our description of the geometric phase and topological phenomena. In condensed matter, it describes the parallel transport of Bloch states and acts as an effective "electromagnetic" vector potential defined in momentum space. Inspired by developments in high-energy physics, where higher-form Kalb-Ramond gauge fields were introduced, I hereby explore the existence of "tensor Berry connections" in quantum matter. My approach consists in a general construction of effective gauge fields, which I ultimately relate to the components of Bloch states. I apply this formalism to various models of topological matter, and I investigate the topological invariants that result from generalized Berry connections. I introduce the 2D Zak phase of a tensor Berry connection, which I then relate to the more conventional first Chern number; I also reinterpret the winding number characterizing 3D topological insulators to a Dixmier-Douady invariant, which is associated with the curvature of a tensor connection. Besides, my approach identifies the Berry connection of tensor monopoles, which are found in 4D Weyl-type systems in ultracold atoms.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Machine Learning for Intelligent Multiscale Modeling of Platelet Dynamics

2019年3月19日(火) 15:00 - 17:00

Yuefan Deng (Professor, Applied Mathematics Department, Stony Brook University, USA)

Multiscale modeling in biomedical engineering is gaining momentum because of progress in supercomputing, applied mathematics, and quantitative biomedical engineering. For example, scientists in various disciplines have been advancing, slowly but steadily, the simulation of blood including its Olowing and the physiological properties of such components as red blood cells, white blood cells, and platelets. Platelet activation and aggregation stimulate blood clotting that results in heart attacks and strokes causing nearly 20 million deaths each year. To reduce such deaths, we must discover new drugs. To discover new drugs, we must understand the mechanism of platelet activation and aggregation. To model platelets’ dynamics involves setting the basic space and time discretization in huge ranges of 5-6 orders of magnitudes, resulting from the relevant fundamental interactions at atomic, to molecular, to cell, to Oluid scales. To achieve the desired accuracy at the minimal computational costs, we must select the correct physiological parameters in the force Oields such as the Morse potential and Hooke’s law as well as the spatial and temporal discretization, by machine learning. We demonstrate our preliminary results of speeding up a multiscale two-platelet aggregation simulation, while maintaining sufOicient accuracy, by nearly one order of magnitude, compared with traditional algorithm that uses the smallest of all temporal and spatial scales in order to capture the Oinest details of the dynamics. We present our analyses of the accuracies and efOiciencies of the representative modeling. We will also outline the general methodologies of multiscale modeling of cells at atomic resolutions.

会場: 研究本館224-226室

イベント公式言語: 英語

On special values of the multiple zeta functions of Arakawa-Kaneko type

2019年3月16日(土) 15:00 - 17:30

大野 泰生 (東北大学 理学部数学科 教授)
鈴木 雄太 (名古屋大学 大学院多元数理科学研究科 学振特別研究員)

15:00~16:00: Yasuo Ohno (Tohoku University) "On special values of the multiple zeta functions of Arakawa-Kaneko type" Arakawa-Kaneko's zeta function is a kind of generalization of the Riemann zeta function by using polylogarithms. I am planning to introduce two topics on combinatorics around its values at positive or negative integral points. This talk is based on joint work with N. Kawasaki. 16:20~17:20: Yuta Suzuki (Nagoya University) "On relatively prime amicable pairs" A famous Greek mathematician, Pythagoras tried to find symbolical meanings in numbers. One famous example of such symbolism in numbers is amicable pair, which was introduced as a symbol of friendship. A pair of positive integers $(M,N)$ is called an amicable pair if the sum of all divisors of $M$ except $M$ itself is equal to $N$ and the sum of all divisors of $M$ except $N$ itself is also equal to $M$. The smallest example is $(220,284)$. Even amicable numbers are introduced more than 20 centuries ago, most of their properties are still unknown. For example, the infinitude of amicable pairs has not yet been proven. In this talk, we pick up a conjecture of Gmelin (1917), which claims that there is no relatively prime amicable pairs, and try to introduce some atmosphere of "modern elementary number theory". In particular, we improve Pollack's partial result (2015) on Gmelin's conjecture.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Joint value distribution of quadratic L-functions (joint work with Hirofumi Nagoshi)

2019年2月25日(月) 16:20 - 17:20

Hidehiko Mishou (東京電機大学)

In 1975, Voronin established the universality theorem for the Riemann zeta function. Roughly speaking this theorem asserts that any holomorphic function on 1/2

会場: セミナー室 (160号室)

イベント公式言語: 英語

Symmetric Tornheim double zeta functions

2019年2月25日(月) 15:00 - 16:00

中村 隆 (東京理科大学)

Let $s,t,u \in {\mathbb{C}}$ and $T(s,t,u)$ be the Tornheim double zeta function. We investigate some properties of symmetric Tornheim double zeta functions. As a corollary, we give explicit evaluation formulas for $T(s,t,u)$ in terms of series of the gamma function and Riemann zeta function.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Biology Seminar

2018年12月13日(木) 14:00 - 16:00

風間 裕介 (理化学研究所 仁科加速器科学研究センター (RNC) 植物ゲノム進化研究チーム チームリーダー)
ジェフリ・フォーセット (理化学研究所 数理創造プログラム (iTHEMS) 上級研究員)

Speaker: Jeffrey Fawcett (iTHEMS) Title: Introduction to Genomics Abstract: The genetic information, or the genome, of almost all species are determined by the order (i.e. the "sequence") of millions of nucleotides represented by A, G, C, and T. I will first outline what we already know about the genome, how they differ across species and individuals, and how we can study them. I will then briefly introduce "3D Genomics", a topic that is becoming quite hot in biology now: the genome is not only a one dimensional "sequence" information but the chromosomes must be folded up to fit into the cell nuclei, and this 3D structure of the chromosome and the spatial positioning of the genes might be important for the biology of each species. Speaker: Yusuke Kazama (Nishina Center) Title: 大きな玉ほど大きく壊す：シロイヌナズナを用いて明らかにした重イオンビーム変異の特徴 Abstract: 重イオンビームはγ線やX線よりも線エネルギー付与（LET)が高いことで知られ、核種やビームの速度を選択することによりLETを調節して照射することもできる。私たちは、モデル植物シロイヌナズナを用いてLETが変異誘発に与える影響を調べ、変異率が最大となるLET＝30.0 keV/μm(LETmax)を発見した。突然変異体の全ゲノム解析を行ない、LETmaxでは塩基置換や小さい欠失が多いのに対し、LET=290 keV/μmでは大きな欠失や染色体再編成の頻度が高いことを明らかにした。目的や材料に合わせて「高効率で1遺伝子を破壊するにはLETmax照射」を、「2遺伝子以上の破壊や染色体再編成の誘発には高LET照射」を行うオンデマンド照射技術を確立した。今後は、染色体再編成が植物の形質に与える影響を、3Dゲノム構造の変化、クロマチン構造の変化、遺伝子発現の変化に注目して研究していきたい。

会場: セミナー室 (160号室)

イベント公式言語: 英語

Cosmic-ray air showers: new arrays for searching origins and link to the collider physics

2018年12月7日(金) 14:00 - 15:00

﨏 隆志 (東京大学 宇宙線研究所 (ICRR))

会場: セミナー室 (160号室)

イベント公式言語: 英語

Probability density functions attached to zeta functions

2018年12月6日(木) 16:00 - 17:00

Masahiro Mine (東京工業大学)

The study of the value-distribution of the Riemann zeta function is a classical topic in analytic number theory. In 1930s, Bohr and Jessen proved the existence of a certain limit value regarded as the probability that values of the Riemann zeta function belong to a given region in the complex plane. After Bohr and Jessen, similar results were proved for many other zeta functions. In this talk, I'll talk about density functions of such probabilities attached to the value-distributions of zeta functions. The density functions, which were named M-functions'' by Ihara, are connected with mean values of zeta functions, distributions of zeros of zeta functions, and so on.

会場: セミナー室 (160号室)

イベント公式言語: 英語

On A_2-liftings of sum formulas and Bowman-Bradley type formulas for finite multiple zeta values

2018年11月22日(木) 11:40 - 12:40

関 真一朗 (東北大学)

Both the sum formula and Bowman-Bradley's theorem for multiple zeta values are well known. Recently, Saito and Wakabayashi proved counterparts of these two formulas for A-finite multiple zeta values. In this talk, I will explain that A_2-liftings of some parts of Saito-Wakabayashi's results have simple forms using Seki-Bernoulli numbers. The first part of this talk is a joint work with Shuji Yamamoto. The second part is a joint work with Hideki Murahara and Tomokazu Onozuka.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Generating functions of CM & RM values

2018年11月22日(木) 10:30 - 11:30

松坂 俊輝 (九州大学)

The special values of the elliptic modular j function j(z) at imaginary quadratic points are known as singular moduli (CM values), and play important roles in algebraic number theory. As a real quadratic analogue, Kaneko (2009) defined the `values’ of j(z) at real quadratic points (RM values). In 2011, Duke-Imamoglu-Toth showed that the generating function of the traces of these CM & RM values becomes a harmonic Maass form of weight 1/2. In this talk, I shall introduce a new class called polyharmonic weak Maass forms, inspired by works of Lagarias-Rhoades on the Kronecker limit formula, and give a generalization of Duke-Imamoglu-Toth’s work for any polyharmonic weak Maass form.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Study of density dependent nuclear symmetry energy by using heavy RI collisions at RIKEN-RIBF

2018年11月16日(金) 14:00 - 16:00

磯部 忠昭 (理化学研究所 仁科加速器科学研究センター (RNC) RI物理研究室 専任研究員)

The nuclear Equation of State (EoS) is a fundamental property of nuclear matter. An international collaboration, named SPiRIT, to study the density dependence of asymmetry term in nuclear EoS has been formed since 2009. The main aim of this collaboration is to make the constraint on the asymmetry term of nuclear EoS for higher dense region($\rho>\rho_0$). In this talk, the conceptual idea of the project will be given in addition to some result of data analysis for the physics run performed at 2016 spring.

会場: セミナー室 (160号室)

イベント公式言語: 英語

非慣性系のスピン輸送理論

2018年11月15日(木) 13:00 - 18:00

松尾 衛 (University of Chinese Academy of Sciences, China)

会場: セミナー室 (160号室)

イベント公式言語: 日本語

New Venues in Formation and Detection of Primordial Black Hole Dark Matter

2018年11月12日(月) 14:00 - 15:00

Volodymyr Takhistov

Abstract: Primordial black holes (PBH) provide an attractive non-particle dark matter (DM) candidate. I will discuss a novel PBH production mechanism that can appear generically in models with scalar fields. Recent re-evaluations of PBH constraints suggest that the open parameter space for PBHs to constitute all of dark matter is appreciably larger than previously thought. I will show how compact stars can serve as laboratories for probing it. The variety of resulting novel astrophysical signals are of particular interest to the vibrant field of multi-messenger astronomy. More-so, PBH-star interactions suggest an elegant resolution to some of the most puzzling questions in astrophysics, such as the origin of gold and other heavy elements.

会場: セミナー室 (160号室)

イベント公式言語: 英語

第28回 QCD Club

2018年11月9日(金) 15:00 - 17:00

タイトル： Application of a gradient flow method to thermodynamics of QCD with dynamical quarks 講師： 金谷 和至 氏 (筑波大) 概要： グラジエントフロー法を応用してくりこまれた物理量を格子上で評価する新しい方法が九州大学の鈴木博さんらにより提案されました。この方法を用いれば、格子化により陽に壊される対称性に関係する物理量でも直接評価可能で、並進対称性やカラル対称性、超対称性など、これまで複雑な処理や膨大な計算コストを要求したり、そもそも格子上でどう定義すればいいかわからなかった物理量を議論する可能性を開きました。我々は、これを動的なクォークを含む2+1フレーバーQCDに応用して、QCD熱力学の系統的な研究を試みています。 QCDの熱力学量は、スタガード型クォークを用いた研究により、物理点での連続極限での値が得られていますが、スタガード型クォークで連続極限が正しくQCDになるかという原理的問題が残されたままになっています。連続極限が保証されているウイルソン型クォークではカイラル対称性の扱いで複雑なくりこみが要求され、カイラル対称性を保つ格子カイラルフェルミオンでは膨大な計算時間が要求され、いずれも物理的予言を行える段階には至っていませんでした。 グラジエントフロー法により、ウイルソン型クォークでもカイラル対称性に関わる物理量を直接評価できる可能性が開かれました。 ウイルソン型クォークを用いたフルQCD計算の進行状況と実情について報告します。 言語：日本語または英語

イベント公式言語: 英語

Population genetics of duplicated genes

2018年11月1日(木) 15:30 - 18:00

印南 秀樹 (総合研究大学院大学)

会場: セミナー室 (160号室)

イベント公式言語: 英語

Assembly rules and a theory for invasion and extinction in minimal food webs

2018年10月29日(月) 15:00 - 18:00

御手洗 菜美子 (Associate Professor, Niels Bohr Institute, University of Copenhagen, Denmark)

We propose a theory of the evolution of a minimal food web by sequential invasion of new species [1]. Our theory is based on the standard generalized Lotka-Volterra equations, where basal species compete through resource depletion [2]. The considered food webs are “minimal”, as each species only feeds on a single resource, leading to a hierarchical, tree-like food web [1,3]. We prove that at each invasion step there is one uniquely determined outcome: either the invader peacefully coexists with the residents and resources are re-distributed; the invader is eliminated; or one or several of the resident species are removed in a uniquely defined extinction cascade. At the end of either of these processes the resulting food web relaxes to a globally stable (and feasible) steady state. We break down the essence of our theory in the conceptual “invasion extinction model” (IEM), which allows us to analytically compute the persistence time and the extinction size distribution.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Relations between fractal dimensions and arithmetic progressions

2018年10月23日(火) 11:35 - 12:35

Kota Saito (名古屋大学)

In this talk we give estimates for the dimensions of sets in real numbers which uniformly avoid finite arithmetic progressions. More precisely, we say that $F$ uniformly avoids arithmetic progressions of length $k\geq 3$ if there is an $\epsilon>0$ such that one cannot find an arithmetic progression of length $k$ and gap length $\Delta>0$ inside the $\epsilon\Delta$ neighbourhood of $F$. Our main result is an explicit upper bound for the Assouad (and thus Hausdorff) dimension of such sets in terms of $k$ and $\epsilon$. In the other direction, we give examples of sets which uniformly avoid arithmetic progressions of a given length. We also consider higher dimensional analogues of these problems, where arithmetic progressions are replaced with arithmetic patches lying in a hyperplane. As a consequence, we obtain a discretised version of a `reverse Kakeya problem': we show that if the dimension of a set in $\mathbb{R}^d$ is sufficiently large, then it closely approximates arithmetic progressions in every direction. The above is a joint work with Fraser and Yu. Finally we show that the converse of `reverse Kakeya problem' does not hold. This is a single-author work.

会場: 統合支援施設（第一食堂） 2階 大会議室

イベント公式言語: 英語

Generalized Erdös and Obláth theorem for polynomial-factorial Diophantine equations

2018年10月23日(火) 10:30 - 11:30

武田 渉 (名古屋大学)

Diophantine equations are equations where only integer solutions are accepted. There are many types of Diophantine equations and many results are known. Our Diophantine equation is of the form x^n+y^n=m!. Erdös and Obláth showed that the Diophantine equation x^2+y^2=m! has only two positive integer solutions (x,y,m)=(1,1,2),(12,24,6). In this talk, the factorial function m! is replaced with a generalized factorial function Π(m) over number fields. Then whether there are infinitely many solutions or not depends on the number field. We give necessary and sufficient condition for existence of infinitely many solutions of x^2+y^2=Π(m). More generally, we introduce an observation for higher degree equation x^n+y^n=Π(m).

会場: 統合支援施設（第一食堂） 2階 大会議室

イベント公式言語: 英語

励起子ポラリトンのボーズ・アインシュタイン凝縮から半導体レーザーへの非エルミート相転移

2018年9月28日(金) 13:30 - 17:00

花井 亮 (大阪大学)

超伝導や超流動などの巨視的スケールで自発的にコヒーレンスが現れる現象は、現代物性物理学の中心的トピックのひとつに数えられる。ボーズアインシュタイン凝縮(BEC)は、熱化により巨視的な数の粒子が単一エネルギーレベルに占有する現象で、液体ヘリウム、冷却原子気体、マグノン、そして最近では光子に至るまでの様々な系で観測されている。また、光子レーザーは媒質中の反転分布がもたらす光学利得により光の巨視的コヒーレンスが現れる、非平衡凝縮現象である。 励起子ポラリトン系では、ポンプ強度の強弱によって、これら２種類の凝縮現象（ポラリトンBECとVertical cavity surface emitting laser, VCSEL)を単一デバイス中で実現することが可能で、両者の類似性・相違性が盛んに研究されている。興味深いことに、BECからレーザーへと系を変化させると、放射エネルギーに飛びが見られ、両者の間に相境界が存在することが多くの実験で示されている。しかし、どちらも凝縮相にあり 、系の対称性が同一であるため、このような相境界が現れる積極的な理由は一見見当たらず、実際、既存の理論は（我々の知る限り）すべて、クロスオーバーを予言する。 本講演では、このような凝縮相内で現れる相転移が、非エルミート性により引き起こされている、というシナリオを提案する。励起子ポラリトン系の最近の発展について簡単なレビューを行なった後、流入と流出のある量子多体系の理論的な枠組みを説明する。そこで得られる運動方程式の構造から、電子正孔光子凝縮体の非平衡定常解は必ず2種類に分類できることを示し、非エルミート性が相転移をもたらしうることを示す。特に、2種類の解が「合体する」点（例外点）が 、気液相転移の臨界点と同様、相転移線の終端点になることを示す。以上の結果から、予想される相図を提案する。 本講演で提案するシナリオは、非エルミート性のみが本質的であるため、流入と流出のある二成分凝縮体に一般に適用可能である。

会場: セミナー室 (160号室)

イベント公式言語: 日本語

Number Theory Seminar: 3 Talks

2018年7月24日(火) 10:00 - 12:35

小野 雅隆 (慶應義塾大学)
杉山 真吾 (日本大学)
平川 義之輔 (慶應義塾大学)

This seminar is aimed at scientists in general, not only to mathematicians. 10:00-10:45 Title: Multiple zeta functions associated with 2-colored rooted trees Speaker: Dr. Masataka Ono (Keio University) Abstract: In our recent work, we introduced a combinatorial object and finite sum associated with them which we call finite multiple zeta values associated with 2-colored rooted trees and gave a unified interpretation to some types of finite multiple zeta values. In this talk, we introduce multiple zeta function associated with 2-colored rooted tree and discuss its analytic properties, for example, the possible singularities and functional equations. 10:55-11:40 Title: Modular forms and trace formulas with applications to equidistributions of their Fourier coefficients Speaker: Dr. Shingo Sugiyama (Nihon University) Abstract: Modular forms are interesting objects in number theory as they are related to arithmetic problems. Trace formulas of Hecke operators acting on modular forms are very useful tools to study arithmetic invariants: Fourier coefficients, special values of L-functions, Hurwitz class numbers. We will start fundamental notions on modular forms and trace formulas of Hecke operators for non-experts, and introduce our results on a generalization of Serre’s vertical Sato-Tate law. Some results in this talk are based on a joint work with Masao Tsuzuki (Sophia University). 11:50-12:35 Title: On a generalization of Dobinski's formula Speaker: Yoshinosuke Hirakawa (Keio University) Abstract: Dobinski's formula is a very classical formula, which expresses the Bell number as an infinite series. Here, the Bell number is the number of partitions of a finite set. Such a "combinatorial-analytic" formula should lead us to more beautiful number theory. In this talk, we introduce a generalization of Dobinski's formula by means of a certain multiple generalization of the exponential function.

会場: セミナー室 (160号室)

イベント公式言語: 英語