過去の記録

過去の記録 ~08/21本日 08/22 | 今後の予定 08/23~

統計数学セミナー

11:30-12:20   数理科学研究科棟(駒場) 123号室
Nobuaki Naganuma 氏 (Osaka University)
Error analysis for approximations to one-dimensional SDEs via perturbation method
[ 講演概要 ]
We consider one-dimensional stochastic differential equations driven by fractional Brownian motions and adopt the Euler scheme, the Milstein type scheme and the Crank-Nicholson scheme to approximate solutions to the equations. We introduce perturbation method in order to analyze errors of the schemes. By using this method, we can express the errors in terms of directional derivatives of the solutions explicitly. We obtain asymptotic error distributions of the three schemes by combining the expression of the errors and the fourth moment theorem. This talk is based on a joint work with Prof. Shigeki Aida (Tohoku University).

統計数学セミナー

13:50-14:40   数理科学研究科棟(駒場) 123号室
Seiichiro Kusuoka 氏 (Okayama University)
Characterization of the convergence in total variation by Stein's method and Malliavin calculus
[ 講演概要 ]
Recently, convergence in distributions and estimates of distances between distributions are studied by means of Stein's equation and Malliavin calculus. However, in known results, the target distributions of the convergence were some specific distributions. In this talk, we extend the target distributions to invariant probability measures of diffusion processes. Precisely speaking, we prepare Stein's equation with respect to invariant measures of diffusion processes and consider the characterization of the convergence to the invariant measure in total variation by applying Malliavin calculus. This is a joint work with Ciprian Tudor.

統計数学セミナー

14:50-15:40   数理科学研究科棟(駒場) 123号室
Teppei Ogihara 氏 (The Institute of Statistical Mathematics, JST PRESTO, JST CREST)
Parameter estimation for diffusion processes with high-frequency observations
[ 講演概要 ]
We study statistical inference for security prices modeled by diffusion processes with high-frequency observations. In particular, we focus on two specific problems on analysis of high-frequency data, that is, nonsynchronous observations and the presence of observation noise called market microstructure noise. We construct a maximum-likelihood-type estimator of parameters, and study their asymptotic mixed normality. We also discuss on asymptotic efficiency of estimators.

統計数学セミナー

15:40-16:30   数理科学研究科棟(駒場) 123号室
Kengo Kamatani 氏 (Osaka University, JST CREST)
Markov chain Monte Carlo for high-dimensional target distribution
[ 講演概要 ]
The Markov chain Monte Carlo (MCMC) algorithms are widely used to evaluate complicated integrals in Bayesian Statistics. Since the method is not free from the curse of dimensionality, it is important to quantify the effect of the dimensionality and establish an optimal MCMC strategy in high-dimension. In this talk, I will review some high-dimensional asymptotics of MCMC initiated by Roberts et. al. 97, and explain some asymptotic properties of the MpCN algorithm. I will also mention some connection to Stein-Malliavin techniques.

統計数学セミナー

16:50-17:40   数理科学研究科棟(駒場) 123号室
Giovanni Peccati 氏 (Universite du Luxembourg)
New Functionals inequalities via Stein's discrepancies
[ 講演概要 ]
I will present a new set of functional inequalities involving the following four parameters associated with a given multidimensional distribution: the relative entropy, the relative Fisher information, the 2-Wasserstein distance, and the Stein discrepancy (which is a natural object arising in the framework of the Malliavin-Stein method on a Gaussian space). Our results improve the classical log-Sobolev inequality, as well Talagrand's transport inequality, and allow one to deduce new quantitative entropic limit theorems on Gaussian spaces. Joint works (JFA 2014 and GAFA 2015) with M. Ledoux (Toulouse), I. Nourdin (Luxembourg) and Y. Swan (Liège).

統計数学セミナー

17:40-18:30   数理科学研究科棟(駒場) 123号室
Giovanni Peccati 氏 (Université du Luxembourg)
Stochastic geometry and Malliavin calculus on configuration spaces
[ 講演概要 ]
I will present some recent advances in the domain of quantitative limit theorems for geometric Poisson functionals, associated e.g. with random geometric graphs and random tessellations, obtained by means of Malliavin calculus techniques. One of our main results consists in a general (optimal) Berry-Esseen bound for stabilizing functionals, based on Stein’s method, iterated Poincaré inequalities and a variant of Mehler’s formula. Based on several joint works with S. Bourguin, R. Lachièze-Rey, G. Last and M. Schulte, as well as on the recent monograph that I co-edited with M. Reitzner.

2016年10月28日(金)

数理人口学・数理生物学セミナー

13:30-14:30   数理科学研究科棟(駒場) 126号室
原 朱音 氏 (九州大学システム生命科学府)
When is the allergen immunotherapy effective? (JAPANESE)
[ 講演概要 ]
Allergen immunotherapy is a method to treat allergic symptoms, for example rhinitis and sneezing in Japanese cedar pollen allergy (JCPA). In the immunotherapy of JCPA, patients take in a small amount of pollen over several years, which suppress severe allergic symptoms when exposed to a large amount of environmental pollen after the therapy. We develop a simple mathematical model to identify the condition for successful therapy. We consider the dynamics of type 2 T helper cells (Th2) and regulatory T cells (Treg) and both of them are differentiated from naive T cells. We assume that Treg cells have a much longer lifespan than Th2 cells, which makes Treg cells accumulate over many years during the therapy.
We regard that the therapy is successful if (1) without therapy the patient develops allergic symptoms upon exposure to the environmental pollen, (2) the patient does not develop allergic symptoms caused by the therapy itself, and (3) with therapy the patient does not develop symptoms upon exposure. We find the conditions of each parameter for successful therapy. We also find that the therapy of linearly increasing dose is able to reduce the risk of allergic symptoms caused by the therapy itself, rather than constant dose. We would like to consider application of this model to other kind of allergy, such as food allergy.

2016年10月27日(木)

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室
Fred Weissler 氏 (パリ第13大学)
Sign-changing solutions of the nonlinear heat equation with positive initial value
(ENGLISH)
[ 講演概要 ]
We consider the nonlinear heat equation with a power nonlinear source term on all of N-dimensional space. It is well known that the associated Cauchy problem is locally well-posed in a variety of function spaces, including certain Lebesgue spaces, depending on the power. In other Lebesgue spaces, it can happen that the Cauchy problem is not well-posed. In particular, there exist non-negative initial values for which no local (in time) non-negative solution exists. This can happen also for some homogeneous functions, where the homogeneity is linked to the scaling properties of the equation.

I will discuss recent work, in collaboration with T. Cazenave, F. Dickstein and I. Naumkin. We show that for a certain class of non-negative initial values which, as mentioned above, do not admit local non-negative solutions, there exist in fact local (or global) solutions which change sign. In particular, in the case of non-negative homogeneous initial data which do not admit non-negative solutions, we construct sign-changing self-similar solutions with the given initial data.


http://www.ms.u-tokyo.ac.jp/~miyamoto/Weissler-abstract.pdf
数式を含むアブストラクト(英語)は,上記のURLからダウンロードできます.

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
佐藤 僚 氏 (東大数理)
Non-unitary highest-weight modules over the $N=2$ superconformal algebra (JAPANESE)
[ 講演概要 ]
$N=2$超共形代数とは,超対称性をもつVirasoro代数の一般化
である.そのユニタリ最高ウェイト表現の形式指標は古典的なテータ関数を用い
て記述することができ,モジュラー不変性という著しい性質を持つ.一方,Kac-
WakimotoはW代数の手法を用いて,ある特別な非ユニタリ最高ウェイト表現の形
式指標がaffine ${sl}_{2|1}$に付随する擬テータ関数を用いて記述されること
を示した.彼らはZwegersによる擬テータ関数の修正項を用いて,それらの指標
を実解析的モジュラー形式と関連付けた.

このセミナーでは,W代数の手法とは異なるKazama-Suzukiコセット構成を用いて,
affine ${sl}_{2}$の表現から上記の非ユニタリ表現を構成する手法を解説する.
また,その構成を用いて得られる擬テータ関数と古典的なテータ関数との関係に
ついて述べる.

2016年10月25日(火)

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
Yongnam Lee 氏 (KAIST/RIMS)
Q-Gorenstein deformation theory and it applications to algebraic surfaces (English)
[ 講演概要 ]
The notion of Q-Gorenstein variety is important for the minimal model theory and the compact moduli theory of algebraic varieties in characteristic 0. Also Q-Gorenstein deformation theory can be applied to construct (simply connected) surfaces of general type with geometric genus 0 over the field of any characteristic. In this talk, some applications of Q-Gorenstein deformation theory to algebraic surfaces and some interesting examples related to Q-Gorenstein morphisms will be presented.

解析学火曜セミナー

16:50-18:20   数理科学研究科棟(駒場) 126号室
山根 英司 氏 (関西学院大学理工学部数理科学科)
可積分離散非線型シュレーディンガー方程式の漸近解析 (JAPANESE)

2016年10月24日(月)

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
清水 悟 氏 (東北大学)
Structure and equivalence of a class of tube domains with solvable groups of automorphisms (JAPANESE)
[ 講演概要 ]
In the study of the holomorphic equivalence problem for tube domains, it is fundamental to investigate tube domains with polynomial infinitesimal automorphisms. To apply Lie group theory to the holomorphic equivalence problem for such tube domains $T_\Omega$, investigating certain solvable subalgebras of $\frak g(T_{\Omega})$ plays an important role, where $\frak g(T_{\Omega})$ is the Lie algebra of all complete polynomial vector fields on $T_\Omega$. Related to this theme, we discuss the structure and equivalence of a class of tube domains with solvable groups of automorphisms. Besides, we give a concrete example of a tube domain whose automorphism group is solvable and contains nonaffine automorphisms.

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 117号室
磯野優介 氏 (京大数理研)
Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors

2016年10月18日(火)

トポロジー火曜セミナー

17:30-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30
橋本 義武 氏 (東京都市大学)
拡大W代数に対する共形場理論 (JAPANESE)
[ 講演概要 ]
This talk is based on a joint work with A. Tsuchiya (Kavli IPMU) and T. Matsumoto (Nagoya Univ). In 2006 Feigin-Gainutdinov-Semikhatov-Tipunin introduced vertex operator algebras M called extended W-algebras. Tsuchiya-Wood developed representation theory of M by the method of
"infinitesimal deformation of parameter" and Jack symmetric polynomials.

In this talk I will discuss the following subjects:
1. "factorization" in conformal field theory,
2. tensor structure of the category of M-modules and "module-bimodule correspondence".

2016年10月17日(月)

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
野村 隆昭 氏 (九州大学)
等質開凸錐の実現 (JAPANESE)
[ 講演概要 ]
等質開凸錐は等質ジーゲル領域の構成要素の一つである.その観点で,等質開凸錐の研究を,伊師英之,中島秀斗,山崎貴史等,若い研究者達と一緒にここ10年ほど続けてきて得られた成果のいくつかを紹介したい.中心となる話題は等質開凸錐の実現であり,これは山崎との共著論文として昨年の Kyushu J. Math.に出版されたもので,向き付けグラフを援用しながら,5次元の非対称等質開凸錐の記述にVinbergが用いたアイデア(露語オリジナルは1960年)が,そのままの形で一般の等質開凸錐の実現に通用することを示すものである.基本相対不変式における伊師等による成果を用いる証明を完全にブラックボックス化し,結果としては単に手続きを述べる形になっているので,非専門家にもアクセスが容易で,統計学等への応用も可能であると考えている.また,一般の非対称等質開凸錐に付随する管状領域の正則同型群やその構造の研究への応用も十分に見込める.さらに,Graczyk-Ishi による等質開凸錐の presentation (2014)の内で最小サイズのものも,上述の実現からやはり単なる手続き論で得られる.呈示される行列のサイズ等や零行列となるブロック・小ブロック等も,付随する向き付けグラフから読み取れる.

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
安藤浩志 氏 (千葉大)
Unitarizability, Maurey-Nikishin factorization and Polish groups of finite type (English)

2016年10月12日(水)

代数学コロキウム

17:30-18:30   数理科学研究科棟(駒場) 056号室
Uwe Jannsen 氏 (Universität Regensburg, 東京大学数理科学研究科)
Filtered de Rham Witt complexes and wildly ramified higher class field theory over finite fields (joint work with Shuji Saito and Yigeng Zhao) (English)
[ 講演概要 ]
We will consider abelian coverings of smooth projective varieties over finite fields which are wildly ramified along a divisor D with normal crossings, and will describe the corresponding abelianized fundamental group via modified logarithmic de Rham-Witt sheaves.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

2016年10月11日(火)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Nam Quang Le 氏 (Indiana University)
Global solutions to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations (English)
[ 講演概要 ]
The second boundary value problem of the prescribed affine mean curvature equation is a nonlinear, fourth order, geometric partial differential equation. It was introduced by Trudinger and Wang in 2005 in their investigation of the affine Plateau problem in affine geometry. The previous works of Trudinger-Wang, Chau-Weinkove and the author solved this global problem under some restrictions on the sign or integrability of the affine mean curvature. In this talk, we explain how to remove these restrictions and obtain global solutions under optimal integrability conditions on the affine mean curvature. Our analysis also covers the case of Abreu's equation arising in complex geometry.

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
江尻 祥 氏 (東大数理)
On varieties with splittings of relative Frobenius morphisms of Albanese maps
[ 講演概要 ]
Varieties with splittings of Frobenius morphisms are called F-split varieties, which satisfy strong properties such as Kodaira vanishing. However, some important varieties are not F-split. For example, an abelian variety is F-split if and only if its p-rank is maximum. In this talk, we discuss the class of varieties with splittings of relative Frobenius morphisms of Albanese maps, which includes abelian varieties. As a consequence of Sannai and Tanaka's characterization of ordinary abelian varieties, we see that this class also includes F-split varieties. Furthermore, for varieties in this class, we show that the Kodaira vanishing theorem holds, and that Albanese maps are algebraic fiber spaces.

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) 056号室
Tea: Common Room 16:30-17:00
河澄 響矢 氏 (東京大学大学院数理科学研究科)
The Kashiwara-Vergne problem and the Goldman-Turaev Lie bialgebra in genus zero (JAPANESE)
[ 講演概要 ]
In view of results of Goldman and Turaev, the free vector space over the free loops on an oriented surface has a natural Lie bialgebra structure. The Goldman bracket has a formal description by using a special (or symplectic) expansion of the fundamental group of the surface. It is natural to ask for a formal description of the Turaev cobracket. We will show how to obtain a formal description of the Goldman-Turaev Lie bialgebra for genus 0 using a solution of the Kashiwara-Vergne problem. A similar description was recently obtained by Massuyeau using the Kontsevich integral. Moreover we propose a generalization of the Kashiwara-Vergne problem in the context of the Goldman-Turaev Lie bialgebra. This talk is based on a joint work with A. Alekseev, Y. Kuno and F. Naef.

統計数学セミナー

16:50-18:00   数理科学研究科棟(駒場) 052号室
磯貝 孝 氏 (首都大学東京)
ネットワーク理論を応用した相関クラスタリングによる株価の自動分類
[ 講演概要 ]
本研究では、東証1部上場の株価の日次収益率データを用いて、株価の銘柄間の
相関行列を推定し、銘柄をノードとする相関ネットワークを構築した。この相関
ネットワークに対して複雑ネットワーク理論で用いられているクラスタリング手
法を適用し、業種分類とは別の銘柄グループを構成し、それらの銘柄グループが
どのような特徴を持つのか、業種分類とどのような関係があるのか、などについ
て明らかとなった点について紹介する。

2016年10月04日(火)

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
鈴木拓 氏 (早稲田大学)
Higher order minimal families of rational curves and Fano manifolds with nef Chern characters (Japanese. Writing in English. )
[ 講演概要 ]
In this talk, we introduce higher order minimal families $H_i$ of rational curves
associated to Fano manifolds $X$. We prove that $H_i$ is also a Fano manifold
if the Chern characters of $X$ satisfy some positivity conditions. We also provide
a sufficient condition for Fano manifolds to be covered by higher rational manifolds.

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
Odo Diekmann 氏 (Utrecht University)
Waning and boosting : on the dynamics of immune status (ENGLISH)
[ 講演概要 ]
A first aim is to briefly review various mathematical models of infectious disease dynamics that incorporate waning and boosting of immunity. The focus will be on models that are described by delay equations, in particular renewal equations [1]. Concerning within-host dynamics, we limit ourselves to the rather caricatural models of Aron [2] and de Graaf e.a. [3].From a biomedical point of view the main conclusion is that a higher force of infection may lead to less disease,see [4] and the references given there.

[1] O.Diekmann, M.Gyllenberg, J.A.J.Metz, H.R.Thieme, On the formulation and analysis
of general deterministic structured population models. I. Linear theory, J. Math. Biol. (1998) 36 : 349 - 388
[2] J.L. Aron, Dynamics of acquired immunity boosted by exposure to infection, Math. Biosc. (1983) 64 : 249-259
[3] W.F. de Graaf, M.E.E. Kretzschmar, P.M.F. Teunis, O. Diekmann, A two-phase within host model for immune response and its application to seriological profiles of pertussis, Epidemics (2014) 9 : 1-7
[4] A.N. Swart, M. Tomasi, M. Kretzschmar, A.H. Havelaar, O. Diekmann, The protective effect of temporary immunity under imposed infection pressure, Epidemics (2012) 4 : 43-47
[ 講演参考URL ]
http://www.uu.nl/staff/ODiekmann

2016年10月03日(月)

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
島内 宏和 氏 (山梨英和大学)
Visualizing the radial Loewner flow and the evolution family (JAPANESE)
[ 講演概要 ]
Herglotz 関数が1つ与えられたとき,対応する radial Loewner 方程式は単位円板から拡張する単連結領域族への等角写像族を定め,それは evolution family と呼ばれる単位円板の自己正則写像族と密接に関係する.本講演では, 与えられた Herglotz 関数に対する radial Loewner flow と evolution family を可視化するアルゴリズムを提示し,近似解の収束性と数値実験結果について紹介する.本研究は,堀田一敬氏(山口大学)との共同研究である.

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
荒野悠輝 氏 (東大数理)
$C^*$-tensor categories and subfactors for totally disconnected groups
(English)

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