セミナー

Introduction to Singularity Theory in Algebraic Geometry

2019年5月16日(木) 16:00 - 18:10

佐藤 謙太 (数理創造プログラム 基礎科学特別研究員)

Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. In this talk, I will explain for all scientists how singularities are studied in algebraic geometry. In algebraic geometry, we study algebraic varieties, which are figures defined as the zero sets of polynomial equations. To study an algebraic variety, we often expect that the variety is smooth, that is, the variety locally resembles Euclidian spaces. However, even if we start from smooth varieties, we sometimes encounter non-smooth varieties. This is one of the reasons why we need to study singularities. Part I: In the first one hour, I will explain how singularities are studied. I will introduce two invariants of singularities by which we can compare singularities numerically. One invariant is defined in terms of resolution of singularities and the other is defined in terms of positive characteristic methods. I also explain a surprising relation of these invariants. Part II: In the second one hour, I will explain how singularity theory is used to study smooth projective varieties. I will introduce Minimal Model Program and explain the relation with singularity theory.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Three quantizations of conformal field theory

2019年5月1日(水) 15:40 - 17:30

多田 司 (数理創造プログラム コーディネーター / 理化学研究所 仁科加速器科学研究センター (RNC) 量子ハドロン物理学研究室 副主任研究員)

Needless to say, conformal field theory is elemental in the study of string theory, statistical quantum systems, and various quantum field theories. Two-dimensional conformal field theory is usually quantized by the so-called radial quantization. However, this is not the only way. As a matter of fact, there are two other distinctive choices for the time foliation, or equivalently, the Hamiltonian. One of these choices yields the continuous Virasoro algebra, while the other choice leads to the Virasoro algebra on a torus. The former case corresponds to the recently found (and perhaps less known) phenomenon, sine-square deformation. The latter yields the well-known entanglement entropy. I will present a comprehensive treatment of these three quantizations and discuss its physical implications.

会場: Old LeConte Hall 402, UC Berkeley

イベント公式言語: 英語

Gauge theory and symmetries of 4-dimensional spaces

2019年4月26日(金) 16:00 - 18:10

今野 北斗 (数理創造プログラム 基礎科学特別研究員)

Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Although the term "gauge theory" is usually used in physical contexts, in the early 1980's, mathematicians found that gauge theory has many striking applications to purely mathematical problems. Most of typical applications are related to topology of 4-dimensional spaces. As a recent development in this direction, I used gauge theory to study "the shape of the space of all symmetris of a 4-dimensional space". In the first one hour, I will explain a notion of mathematical spaces, called manifolds, and try to describe the idea: how mathematicians make use of gauge theory to study the topology of a 4-dimensional manifold. In the second one hour, I will explain what the space of symmetries of a manifold means, and which type of theorems about the space of symmetries can be obtained using gauge theory.

会場: セミナー室 (160号室)

イベント公式言語: 英語

Introduction to Galois Theory and Class Field Theory

2019年4月18日(木) 16:00 - 18:00

宮﨑 弘安 (数理創造プログラム 基礎科学特別研究員)

Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half. Part I: Galois theory is one of the most important theories in mathematics. Speaking in one phrase, it explains the correspondence between “extensions of numbers” and “subgroups of Galois group”. Basically, finding subgroups of a finite group is much easier than finding extensions of numbers. As a result, Galois theory has incredibly strong applications. For example, we can prove polynomial equations of degree greater than 4 are not always solvable by radicals, which is a celebrated result by Abel and Galois. In the first part of the talk, I will introduce Galois theory in an accessible way for all scientists. Part II: Class Field Theory (CFT) is a monumental work in number theory. Given Galois theory, which is explained in Part I, classifying “extension of numbers” is reduced to classifying “subgroups of Galois group”. So, the next thing to do would be to analyze the structure of Galois groups. CFT enables us to describe the Galois group of a number field K by using only the language of K, i.e., not by using its extensions. In the second part of the talk, I will explain CFT in an as accessible way as possible for all scientists (in particular, also for mathematicians). If time permits, I would like to explain a geometric interpretation of Galois theory, and higher dimensional CFT.

会場: セミナー室 (160号室)

イベント公式言語: 英語

ABBL, iTHEMS, r-EMU Joint Seminar: Impacts of New Carbon Fusion Cross Sections on Type Ia Supernovae

2019年4月12日(金) 15:00 - 16:00

森 寛治

会場: セミナー室 (132号室)

イベント公式言語: 英語

iTHEMS Seminar+discussion on "non-equilibrium physics of living matter"

2019年4月8日(月) 14:00 - 15:30

川口 喬吾 (東京大学 / 理化学研究所 生命機能科学研究センター (BDR) 生体非平衡物理学理研白眉研究チーム 理研白眉研究チームリーダー)
足立 景亮 (理化学研究所 生命機能科学研究センター (BDR) 生体非平衡物理学理研白眉研究チーム 研究員)

14:00-14:50 (40 min. talk + 10 min discussion) "Physical" problems in multicellular dynamics and cell differentiation Kyogo Kawaguchi (RIKEN Hakubi Research Group) 14:50-15:30 (30 min. talk + 10 min. discussion) Phase transition in a chromatin model with epigenetic modification Kyosuke Adachi (Kawaguchi Lab.) 15:30- Informal discussions

会場: セミナー室 (160号室)

イベント公式言語: 英語

Lifting low dimensional local systems

2019年4月3日(水) 15:45 - 16:45

De Clercq Charles (Université Paris 13, Sorbonne, France)

The content of this seminar is basically for mathematicians (sorry). If you are interested in how a professional math seminar works, please feel free to join! A long-standing conjecture predicts the existence of lifts for Galois representations with F_p coefficients to p-adic coefficients. The case 2-dimensional representations of the absolute Galois group of Q is closely related to Serre's modularity conjecture, proved by Khare and Witenberger. After some recollection on the state of the art about this problem, i will develop the machinery underneath the notion of smooth profinite groups. We will then show how this machinery allows to prove some lifting theorems for low dimensional Galois representations and local systems, getting out of the classical arithmetic world usually considered for this conjecture.

会場: セミナー室 (160号室)

イベント公式言語: 英語

The Origin of the X-ray Clumpy Ejecta in Type Ia Supernova Remnants

2019年4月3日(水) 14:00 - 15:00

佐藤 寿紀 (理化学研究所 開拓研究本部 (CPR) 玉川高エネルギー宇宙物理研究室 基礎特別研究員)

X-ray-emitting clumpy structures are generally observed in young Type Ia supernova remnants although the origin is still obscure. There are two candidates for explaining the formation of clumps; initial clumpiness in ejecta at the explosion (i.e., clumpy ejecta model) or hydrodynamic instabilities made from smooth ejecta profile (i.e., smooth ejecta model). This information should reflect the initial ejecta structure of SNe Ia, so it is important for understanding the Type Ia explosion itself. Our preliminary investigations into constraining the structure of SN Ia remnants using Fourier and wavelet-transform analyses did not turn out to be sufficiently powerful at discriminating the two hydro models and the observed Tycho image from each other. This led us to investigate an approach that would be more sensitive to patterns in the distribution of clumps and holes in the images, such as the "genus statistic.” In this study, for the first time, the genus statistics have been applied to a famous type Ia remnant, Tycho (SN 1572) to understand the formation of the clumps by comparing with hydrodynamical models (Sato et al. 2019, arXiv: 1903.00764). We found the genus curve from Tycho's supernova remnant strongly indicates a skewed non-Gaussian distribution of the ejecta clumps, which is similar to that of a hydrodynamical model for the clumpy ejecta model. In contrast, a hydrodynamical model for the smooth ejecta model has a genus curve that is similar to that of a random Gaussian distribution. Thus, our results support the initial clumpiness in the Type Ia ejecta is more reasonable for the origin of the clumps and demonstrate usefulness of the genus statistics for this field. In addition, we will also discuss the origin of “Fe-rich” ejecta clumps in Type Ia SNRs in this seminar.

会場: 研究本館 433号室

イベント公式言語: 英語

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 (数理創造プログラム 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