過去の記録

過去の記録 ~11/14本日 11/15 | 今後の予定 11/16~

2018年03月09日(金)

講演会

13:30-14:30   数理科学研究科棟(駒場) 056号室
Luc Illusie 氏 (パリ南大学名誉教授)
Sliced nearby cycles and duality, after W. Zheng (ENGLISH)
[ 講演概要 ]
In the early 1980's Gabber proved duality for nearby cycles and, by a different method, Beilinson proved duality for vanishing cycles in the strictly local case (up to a twist of the inertia action on the tame part). Recently W. Zheng found a simple proof of a result, conjectured by Deligne, which implies them both, and extended it over finite dimensional excellent bases. I will explain the main ideas of his work, which relies on new developments, due to him, of Deligne's theory of fibered and oriented products.

2018年03月02日(金)

統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 270号室
Arnaud Gloter 氏 (Université d'Evry Val d'Essonne)
"Estimating functions for SDE driven by stable Lévy processes"
Joint work with Emmanuelle Clément (Ecole Centrale)
[ 講演概要 ]
In this talk we will discuss about parametric inference for a stochastic differential equation driven by a pure-jump Lévy process, based on high frequency observations on a fixed time period. Assuming that the Lévy measure of the driving process behaves like that of an α-stable process around zero, we propose an estimating functions based method which leads to asymptotically efficient estimators for any value of α ∈ (0, 2).

2018年02月23日(金)

談話会・数理科学講演会

15:30-16:30   数理科学研究科棟(駒場) 002号室
田中公 氏 (東大数理)
正標数における極小モデル理論について (JAPANESE)
[ 講演概要 ]
極小モデル理論は代数多様体の分類理論である。20世紀の初頭に確立された代数
曲面論に端を発し、1980年代に爆発的に進展した。特に、標数ゼロの三次元代数
多様体に対する極小モデル理論がこの頃に完成し、近年では正標数の世界におい
ても大きく進展している。本講演では、極小モデル理論について概説した後、時
間が許せば正標数特有の問題等についても触れたい。

FMSPレクチャーズ

13:30-15:00   数理科学研究科棟(駒場) 002号室
全3回講演の(3)
Etienne Ghys 氏 (ENS de Lyon)
The topology of singular points of real analytic curves (ENGLISH)
[ 講演概要 ]
In the neighborhood of a singular point, a germ of real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram : an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this mini course is to give an complete description of those ‘’analytic ? chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory and operads.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ghys.pdf

2018年02月22日(木)

FMSPレクチャーズ

15:00-16:30   数理科学研究科棟(駒場) 117号室
全3回講演の(2)
Etienne Ghys 氏 (ENS de Lyon)
The topology of singular points of real analytic curves (ENGLISH)
[ 講演概要 ]
In the neighborhood of a singular point, a germ of real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram : an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this mini course is to give an complete description of those ‘’analytic ? chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory and operads.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ghys.pdf

2018年02月21日(水)

FMSPレクチャーズ

15:00-16:30   数理科学研究科棟(駒場) 117号室
全3回講演の(1)
Etienne Ghys 氏 (ENS de Lyon)
The topology of singular points of real analytic curves (ENGLISH)
[ 講演概要 ]
In the neighborhood of a singular point, a germ of real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram : an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this mini course is to give an complete description of those ‘’analytic ? chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory and operads.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ghys.pdf

トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 122号室
Tea: Common Room 16:30-17:00
Gwénaël Massuyeau 氏 (Université de Bourgogne)
The category of bottom tangles in handlebodies, and the Kontsevich integral (ENGLISH)
[ 講演概要 ]
Habiro introduced the category B of « bottom tangles in handlebodies », which encapsulates the set of knots in the 3-sphere as well as the mapping class groups of 3-dimensional handlebodies. There is a natural filtration on the category B defined using an appropriate generalization of Vassiliev invariants. In this talk, we will show that the completion of B with respect to the Vassiliev filtration is isomorphic to a certain category A which can be defined either in a combinatorial way using « Jacobi diagrams », or by a universal property via the notion of « Casimir Hopf algebra ». Such an isomorphism will be obtained by extending the Kontsevich integral (originally defined as a knot invariant) to a functor Z from B to A. This functor Z can be regarded as a refinement of the TQFT-like functor derived from the LMO invariant and, if time allows, we will evoke the topological interpretation of the « tree-level » of Z. (This is based on joint works with Kazuo Habiro.)

2018年02月19日(月)

数値解析セミナー

15:00-16:00   数理科学研究科棟(駒場) 056号室
Michael Plum 氏 (Karlsruhe Insitute of Technology)
Existence, multiplicity, and orbital stability for travelling waves in a nonlinearly supported beam (English)
[ 講演概要 ]
For a nonlinear beam equation with exponential nonlinearity, we prove existence of at least 36 travelling wave solutions for the specific wave speed c=1.3. Our proof makes heavy use of computer assistance: starting from numerical approximations, we use a fixed point argument to prove existence of solutions "close to" the approximate ones. Furthermore we investigate the orbital stability of these solutions by making use of both analytical and computer-assisted techniques.

数値解析セミナー

16:15-17:15   数理科学研究科棟(駒場) 056号室
長藤かおり 氏 (Karlsruhe Insitute of Technology)
An approach to computer-assisted existence proofs for nonlinear space-time fractional parabolic problems (English)
[ 講演概要 ]
We consider an initial boundary value problem for a space-time fractional parabolic equation, which includes the fractional Laplacian, i.e. a nonlocal operator. We treat a corresponding local problem which is obtained by the Caffarelli-Silvestre extension technique, and show how to enclose a solution of the extended problem by computer-assisted means.

2018年02月14日(水)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 126号室
Valerio Proietti 氏 (Copenhagen Univ.)
Index theory on the Mishchenko bundle (English)

2018年02月06日(火)

東京無限可積分系セミナー

15:00-17:30   数理科学研究科棟(駒場) 002号室
桂 法称 氏 (東大理物) 15:00-16:00
1次元量子臨界系のサイン二乗変形 (ENGLISH)
[ 講演概要 ]
サイン二乗変形(SSD)とは、量子系のハミルトニアンの局所的エネルギースケールを、サイン二乗関数にしたがって空間的方向に変調させる変形操作である。SSDにより、一様周期境界条件を課した系のハミルトニアンは、開放境界条件を課した空間的に非一様なハミルトニアンへと変形される。しかしながら、空間次元1次元で系が臨界的な場合には、この変形後のハミルトニアンの基底状態は、変形前の一様周期的な基底状態からほとんど変化しないということが、現在までに明らかにされている。特に講演者は、臨界的なXYスピン鎖や横磁場Ising模型においては、両者の基底状態が厳密に一致することを示している
[1,2,3]。また、ディラック・フェルミオン系や一般の(1+1)次元の共形場理論についても、適切にSSDを定義すれば、やはり一様周期系とSSD系の基底状態が一致するという結果を紹介する。時間が許せば、その他の最近の結果
[4,5] や、SSD系の励起状態についての結果についても紹介する。

[1] H. Katsura, J. Phys. A: Math. Theor. 44, 252001 (2011).
[2] H. Katsura, J. Phys. A: Math. Theor. 45, 115003 (2012).
[3] I. Maruyama, H. Katsura, T. Hikihara, Phys. Rev. B 84, 165132 (2011).
[4] K. Okunishi and H. Katsura, J. Phys. A: Math. Theor. 48, 445208 (2015).
[5] S. Tamura and H. Katsura, Prog. Theor. Exp. Phys 2017, 113A01 (2017).
佐藤 僚 氏 (東大数理) 16:30-17:30
モジュラー不変性をもつ $N=2$ 頂点作用素超代数の表現に
ついて (ENGLISH)
[ 講演概要 ]
よいクラスの頂点作用素超代数の表現の指標はモジュラー不変性という顕著な性質を示す.この性質の応用として,中心電荷が$c_{p,1}=3(1-2/p)$である$N=2$頂点作用素超代数のフュージョン則は,モジュラー$S$行列から Verlinde公式によって計算されることが知られている(脇本実氏とD. Adamovic氏の結果による).本セミナーでは,互いに素な$2$以上の整数組$(p,p')$を用いて中心電荷が$c_{p,p'}:=3(1-2p'/p)$と表わされる場合に,然るべき意味でモジュラー不変性を示す新たな$N=2$頂点作用素超代数の表現族を紹介する.また,Creutzig--Ridoutによって提案されたVerlinde公式の一般化を踏まえて,フュージョン則の計算への応用を議論する.

2018年02月04日(日)

統計数学セミナー

12:00-18:00   数理科学研究科棟(駒場) 118号室
Yukai Yang 氏 (Uppsala University) 12:30-15:00
Nonlinear Economic Time Series Models

[ 講演概要 ]
The lecture goes through several chapters in the book “Modelling Nonlinear Economic Time Series” by Teräsvirta, Tjøstheim and Granger in 2010. The lecture serves as an introduction for the students and researchers who are interested in this area. It introduces a number of examples of families of nonlinear time series parametric models in economic theory. It also talks about testing linearity against parametric alternatives with the presence of a characterization of the identification problem in many situations. Different ways of solving the identification problem are presented and their merits and disadvantages are discussed.
Yuliia Mishura 氏 (The Taras Shevchenko National University of Kiev ) 15:30-18:00
Analytic, representation and statistical aspects related to fractional Gaussian processes.

[ 講演概要 ]
We consider the properties of fractional Gaussian processes whose covariance function is situated between two self-similarities, or, in other words, these processes belong to the generalized quasi-helix, according to geometric terminology of Kahane. For such processes we consider the two-sided bounds for maximal functionals and the representation results. We consider stochastic differential equations involving fractional Brownian motion and present also several results on statistical estimations for them.

2018年02月02日(金)

統計数学セミナー

13:30-14:40   数理科学研究科棟(駒場) 052号室
Ioane Muni Toke 氏 (Centrale Supelec Paris)
Estimation of ratios of intensities in a Cox-type model of limit order books
[ 講演概要 ]
We introduce a Cox-type model for relative intensities of orders flows in a limit order book. The Cox-like intensities of the counting processes of events are assumed to share an unobserved and unspecified baseline intensity, which in finance can be identified to a global market activity affecting all events. The model is formulated in terms of relative responses of the intensities to covariates, and relative parameters can be estimated by quasi likelihood maximization. Consistency and asymptotic normality of the estimators are proven. Computationally intensive inferences are run on large samples of tick-by-tick data (35+ stocks and 220+ trading days, adding to more than one billion events). Penalization methods are also investigated. Results of the model are interpreted in terms of probability of occurrence of events. Excellent agreement with empirical data is found. Estimated model reproduces known empirical facts on imbalance, spread and queue sizes, and helps identifying trading signals of interests on a given stock.

Joint work with N.Yoshida.

博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 118号室
林 拓磨 氏 (東京大学大学院数理科学研究科)
A study on (g,K)- modules over commutative rings
(可換環上の(g,K)加群の研究)
(JAPANESE)

博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 122号室
野崎 雄太 氏 (東京大学大学院数理科学研究科)
An invariant of 3-manifolds via homology cobordisms and knots in lens spaces
(ホモロジーコボルディズムを用いた3次元多様体の不変量とレンズ空間内の結び目)
(JAPANESE)

博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 122号室
谷村 慈則 氏 (東京大学大学院数理科学研究科)
An Application of the F-method to Duflo-Corwin-Greenleaf's Polynomial Conjecture
(Duflo-Corwin-Greenleafの多項式予想に対するF-methodの適用)
(JAPANESE)

博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 118号室
釼持 智哉 氏 (東京大学大学院数理科学研究科)
Numerical analysis for evolution equations
(発展方程式に対する数値解析)
(JAPANESE)

博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 122号室
東條 広一 氏 (東京大学大学院数理科学研究科)
Continuous Analogue of the Existence Problem of Compact Clifford-Klein Forms
(コンパクトClifford-Klein形の存在問題の連続類似)
(JAPANESE)

博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 122号室
賀 卓豊 氏 (東京大学大学院数理科学研究科)
Actions on noncommutative tori and classification of the crossed products
(非可換トーラス上の作用と接合積の分類)
(JAPANESE)

2018年02月01日(木)

博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 122号室
川島 夢人 氏 (東京大学大学院数理科学研究科)
A new relationship between the dilatation of pseudo-Anosov braids and fixed point theory
(擬アノソフ組みひもの拡張率と固定点理論との新たな関係)
(JAPANESE)

博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 122号室
Jimenez Pascual, Adrian 氏 (東京大学大学院数理科学研究科)
On wrapping number, adequacy and the crossing number of satellite knots
(ラッピング数、充足性とサテライト結び目の最小交点数について)
(JAPANESE)

博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 126号室
細野 元気 氏
On L2-extension theorems and singularities of plurisubharmonic functions in complex analysis and geometry
(複素解析・複素幾何におけるL2拡張定理と多重劣調和関数の特異性について)
(JAPANESE)

博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 118号室
長町 一平 氏 (東京大学大学院数理科学研究科)
Criteria for good reduction of hyperbolic polycurves
(多重双曲的曲線の良還元判定条件)
(JAPANESE)

博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 122号室
中川 淳一 氏
Creation of mathematical methods for the social cooperation:
solutions of problems in the steel industry, environments and the traffic flow
(社会連携における数学的手法の創造:製鉄業、環境ならびに交通流についての課題の解決)
(JAPANESE)

博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 118号室
松原 宰栄 氏 (東京大学大学院数理科学研究科)
Studies on integral representations of GKZ hypergeometric functions
(GKZ超幾何函数の積分表示に関する研究)
(JAPANESE)

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