過去の記録

過去の記録 ~11/14本日 11/15 | 今後の予定 11/16~

東京確率論セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室
中島 秀太 氏 (数理解析研究所)
Concentration results for directed polymer with unbouded jumps

2016年04月22日(金)

統計数学セミナー

10:30-11:50   数理科学研究科棟(駒場) 002号室
Ciprian Tudor 氏 (Université de Lille 1)
Stein method and Malliavin calculus : theory and some applications to limit theorems 1
[ 講演概要 ]
In this first part, we will present the basic ideas of the Stein method for the normal approximation. We will also describe its connection with the Malliavin calculus and the Fourth Moment Theorem.

統計数学セミナー

12:50-14:10   数理科学研究科棟(駒場) 002号室
Ciprian Tudor 氏 (Université de Lille 1)
Stein method and Malliavin calculus : theory and some applications to limit theorems 2
[ 講演概要 ]
In the second presentation, we intend to do the following: to illustrate the application of the Stein method to the limit behavior of the quadratic variation of Gaussian processes and its connection to statistics. We also intend to present the extension of the method to other target distributions.

統計数学セミナー

14:20-15:50   数理科学研究科棟(駒場) 002号室
Seiichiro Kusuoka 氏 (Okayama University)
Equivalence between the convergence in total variation and that of the Stein factor to the invariant measures of diffusion processes

[ 講演概要 ]
We consider the characterization of the convergence of distributions to a given distribution in a certain class by using Stein's equation and Malliavin calculus with respect to the invariant measures of one-dimensional diffusion processes. Precisely speaking, we obtain an estimate between the so-called Stein factor and the total variation norm, and the equivalence between the convergence of the distributions in total variation and that of the Stein factor. This talk is based on the joint work with C.A.Tudor (arXiv:1310.3785).

統計数学セミナー

16:10-17:10   数理科学研究科棟(駒場) 002号室
Nakahiro Yoshida 氏 (University of Tokyo, Institute of Statistical Mathematics, JST CREST)
Asymptotic expansion and estimation of volatility
[ 講演概要 ]
Parametric estimation of volatility of an Ito process in a finite time horizon is discussed. Asymptotic expansion of the error distribution will be presented for the quasi likelihood estimators, i.e., quasi MLE, quasi Bayesian estimator and one-step quasi MLE. Statistics becomes non-ergodic, where the limit distribution is mixed normal. Asymptotic expansion is a basic tool in various areas in the traditional ergodic statistics such as higher order asymptotic decision theory, bootstrap and resampling plans, prediction theory, information criterion for model selection, information geometry, etc. Then a natural question is to obtain asymptotic expansion in the non-ergodic statistics. However, due to randomness of the characteristics of the limit, the classical martingale expansion or the mixing method cannot not apply. Recently a new martingale expansion was developed and applied to a quadratic form of the Ito process. The higher order terms are characterized by the adaptive random symbol and the anticipative random symbol. The Malliavin calculus is used for the description of the anticipative random symbols as well as for obtaining a decay of the characteristic functions. In this talk, the martingale expansion method and the quasi likelihood analysis with a polynomial type large deviation estimate of the quasi likelihood random field collaborate to derive expansions for the quasi likelihood estimators. Expansions of the realized volatility under microstructure noise, the power variation and the error of Euler-Maruyama scheme are recent applications. Further, some extension of martingale expansion to general martingales will be mentioned. References: SPA2013, arXiv:1212.5845, AISM2011, arXiv:1309.2071 (to appear in AAP), arXiv:1512.04716.

2016年04月21日(木)

幾何コロキウム

17:00-18:00   数理科学研究科棟(駒場) 123号室
集中講義に続いて行います.いつもと違う部屋ですのでご注意下さい.
本多正平 氏 (東北大学)
Spectral convergence under bounded Ricci curvature (Japanese)
[ 講演概要 ]
For a noncollapsed Gromov-Hausdorff convergent sequence of Riemannian manifolds with a uniform bound of Ricci curvature, we establish two spectral convergence. One of them is on the Hodge Laplacian acting on differential one-forms. The other is on the connection Laplacian acting on tensor fields of every type, which include all differential forms. These are sharp generalizations of Cheeger-Colding's spectral convergence of the Laplacian acting on functions to the cases of tensor fields and differential forms. These spectral convergence have two direct corollaries. One of them is to give new bounds on such eigenvalues, in terms of bounds on volume, diameter and the Ricci curvature. The other is that we show the upper semicontinuity of the first Betti numbers with respect to the Gromov-Hausdorff topology, and give the equivalence between the continuity of them and the existence of a uniform spectral gap. On the other hand we also define measurable curvature tensors of the noncollapsed Gromov-Hausdorff limit space of a sequence of Riemannian manifolds with a uniform bound of Ricci curvature, which include Riemannian curvature tensor, the Ricci curvature, and the scalar curvature. As fundamental properties of our Ricci curvature, we show that the Ricci curvature coincides with the difference between the Hodge Laplacian and the connection Laplacian, and is compatible with Gigli's one and Lott's Ricci measure. Moreover we prove a lower bound of the Ricci curvature is compatible with a reduced Riemannian curvature dimension condition. We also give a positive answer to Lott's question on the behavior of the scalar curvature with respect to the Gromov-Hausdorff topology by using our scalar curvature. This talk is based on arXiv:1510.05349.

FMSPレクチャーズ

15:00-16:00, 16:10-17:10   数理科学研究科棟(駒場) 002号室
Aniceto Murillo et al 氏 (Universidad de Malaga)
Rational homotopy theory : Quillen and Sullivan approach.(2) (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Murillo.pdf

2016年04月20日(水)

FMSPレクチャーズ

15:00-16:00, 16:10-17:10   数理科学研究科棟(駒場) 002号室
Aniceto Murillo et al 氏 (Universidad de Malaga)
Rational homotopy theory : Quillen and Sullivan approach.(1) (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Murillo.pdf

代数学コロキウム

17:00-18:00   数理科学研究科棟(駒場) 056号室
戸次鵬人 氏 (東京大学数理科学研究科)
On periodicity of geodesic continued fractions (Japanese)

2016年04月19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
小木曽 啓示 氏 (東京大学大学院数理科学研究科)
Isomorphic quartic K3 surfaces and Cremona transformations (JAPANESE)
[ 講演概要 ]
We show that

(i) there is a pair of smooth complex quartic K3 surfaces such that they are isomorphic as abstract varieties but not Cremona equivalent.

(ii) there is a pair of smooth complex quartic K3 surfaces such that they are Cemona equivalent but not projectively equivalent.

These two results are much inspired by e-mails from Professors Tuyen Truong and J\'anos Koll\'ar.

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
Błażej Szepietowski 氏 (Gdansk University)
Topological rigidity of finite cyclic group actions on compact surfaces (ENGLISH)
[ 講演概要 ]
Two actions of a group on a surface are called topologically equivalent if they are conjugate by a homeomorphism of the surface. I will describe a method of enumeration (and classification) of topological equivalence classes of actions of a finite group on a compact surface, based on the combinatorial theory of noneuclidean crystallographic groups (NEC groups in short) and a relationship between the outer automorphism group of an NEC group and certain mapping class group. By this method we study topological equivalence of actions of a finite cyclic group on a compact surface, in the situation where the order of the group is large relative to the genus of the surface.

2016年04月18日(月)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室
Juan Orendain 氏 (UNAM/東大数理)
On the functoriality of Haagerup's $L^2$-space construction: Verticalizing decorated 2-categories

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
小櫃 邦夫 氏 (鹿児島大学)
Weil-Petersson計量の漸近展開についての最近の進展 (JAPANESE)
[ 講演概要 ]
リーマン面のモジュライ空間上のWeil-Petersson計量の境界における漸近展開は、H. Masurが1976年に与えた結果を初めとし、その後Yamada, Wolpert, Obitsu-Wolpertによって改良された。最近、Melrose, X. Zhu, Mazzeo, Swobodaにより、その漸近展開の形が完全に決定された。彼らの仕事を紹介し、残された問題や関連する話題について解説する。

数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
柏原崇人 氏 (東京大学大学院数理科学研究科)
滑らかな領域における有限要素法の誤差評価について (日本語)
[ 講演概要 ]
滑らかな領域$\Omega$上の偏微分方程式を有限要素法で離散化する場合,$\Omega$をフラットな三角形で厳密に分割するのは不可能なので,$\Omega$を多角形領域$\Omega_h$で近似した上で,$\Omega_h$に対して三角形分割や有限要素空間を考えるのが一般的である.よって誤差評価を行う際には,$\Omega$と$\Omega_h$のギャップ,つまり「領域の摂動」を定量的に評価する必要が生じる.このような状況を考慮した誤差評価の結果は存在するものの,標準的な手法が体系化されているとは言えないと思われる(特に,$L^2$誤差評価に関しては驚くほど結果が少ない).本講演では,ポアソン方程式の(1)ノイマン問題,(2)ニーチェの方法によるディリクレ問題,をモデルケースとして,「領域の摂動」を考慮した$H^1$および$L^2$誤差評価を証明する.他の方程式や境界条件への応用を見込んで,できるだけ一般的かつ標準的な証明の枠組みを提案することを目標とする.

東京確率論セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室
李 嘉衣 氏 (東京大学大学院数理科学研究科)
Sharp interface limit for one-dimensional stochastic Allen-Cahn equation with Dirichlet boundary condition
[ 講演概要 ]
本講演では、確率反応拡散方程式に対する鋭敏な界面極限を扱う。具体的にはディリクレ境界条件を持つ1次元確率アレン・カーン方程式を考察する。この方程式は界面の挙動を記述し、十分小さいパラメータ$\varepsilon > 0$により界面の幅が特徴付けられる。特に$\varepsilon$を限りなく小さくした時の解の挙動に興味がある。この場合、ディリクレ境界条件のため極限における界面の運動は反射壁を持つブラウン運動になることが予想される。そこで解を$L^2$-値のマルコフ過程とみなし、それに対応するディリクレ形式のモスコ収束により、極限での界面の挙動を特定する。

2016年04月14日(木)

FMSPレクチャーズ

15:30-17:00   数理科学研究科棟(駒場) Lecture Hall, Kavli IPMU号室
全2回講演の(2)
Alan Weinstein 氏 (University of California, Berkeley)
Lecture 2: Geometric and algebraic Poisson modules (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Weinstein.pdf

2016年04月13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
玉川安騎男 氏 (京都大学数理解析研究所)
Semisimplicity of geometric monodromy on etale cohomology (joint work with Anna Cadoret and Chun Yin Hui)

(English)
[ 講演概要 ]
Let K be a function field over an algebraically closed field of characteritic p \geq 0, X a proper smooth K-scheme, and l a prime distinct from p. Deligne proved that the Q_l-coefficient etale cohomology groups of the geometric fiber of X --> K are always semisimple as G_K-modules. In this talk, we consider a similar problem for the F_l-coefficient etale cohomology groups. Among other things, we show that if p=0 (resp. in general), they are semisimple for all but finitely many l's (resp. for all l's in a set of density 1).

(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.)

FMSPレクチャーズ

13:30-14:30   数理科学研究科棟(駒場) 126号室
Yavar Kian 氏 (Aix-Marseille Univ.)
Determination of time-dependent coefficients for wave equations from partial data (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kian.pdf

2016年04月12日(火)

Lie群論・表現論セミナー

17:00-18:30   数理科学研究科棟(駒場) 128号室
Piotr Pragacz 氏 (Institute of Mathematics, Polish Academy of Sciences)
Universal Gysin formulas for flag bundles
[ 講演概要 ]
We give generalizations of the formula for the push-forward of a power of the hyperplane class in a projective bundle to flag bundles of type A, B, C, D. The formulas (and also the proofs) involve only the Segre classes of the original vector bundles and characteristic classes of universal bundles. This is a joint work with Lionel Darondeau.

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
Aniceto Murillo 氏 (Universidad de Malaga)
Homotopy theory of differential graded Lie algebras (ENGLISH)
[ 講演概要 ]
Having as motivation the Deligne's principle by which every deformation functor is governed by a differential graded Lie algebra, we build a homotopy theory for these algebras which extend the classical Quillen approach and let us model any (non necessarily 1-connected nor path connected) complex. This is joint work with Urtzi Buijs, Yves Félix and Daniel Tanré.

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
Jussi Behrndt 氏 (Graz University of Technology)
Scattering matrices and Dirichlet-to-Neumann maps (English)
[ 講演概要 ]
In this talk we discuss a recent result on the representation of the scattering matrix in terms of an abstract Titchmarsh-Weyl m-function. The general result can be applied to scattering problems for Schrödinger operators with $\delta$-type interactions on curves and  hypersurfaces, and scattering problems involving Neumann and Robin realizations of Schrödinger operators on unbounded domains. In both applications we obtain formulas for the corresponding scattering matrices in terms of Dirichlet-to-Neumann maps. This talk is based on joint work with Mark Malamud and Hagen Neidhardt.

2016年04月11日(月)

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
Piotr Pragacz 氏 (Institute of Mathematics, Polish Academy of Sciences )
Gysin maps, duality and Schubert classes
(English)
[ 講演概要 ]
We establish a Gysin formula for Schubert bundles
and a strong version of the duality theorem in Schubert calculus
on Grassmann bundles. We then combine them to compute the fundamental
classes of Schubert bundles in Grassmann bundles, which yields a new
proof of the Giambelli formula for vector bundles. This is a joint
work with Lionel Darondeau.
[ 講演参考URL ]
https://www.impan.pl/~pragacz/main.htm

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室
Ryszard Nest 氏 (Univ. Copenhagen)
On analytic construction of the group three-cocycles
(English)

FMSPレクチャーズ

15:30-17:00   数理科学研究科棟(駒場) Lecture Hall, Kavli IPMU号室
全2回講演の(1)
Alan Weinstein 氏 (University of California, Berkeley)
Lecture 1: Special subspaces in symplectic vector spaces (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Weinstein.pdf

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
足助 太郎 氏 (東京大学)
Defining the Julia sets on CP^2 (JAPANESE)
[ 講演概要 ]
The Julia sets play a central role in the study of complex dynamical systems as well as Kleinian groups where they appear as limit sets. They are also known to be meaningful for complex foliations without singularities, however still not defined for singular ones. In this talk, I will discuss some expected properties of the Julia sets for singular foliations and difficulties for defining them.

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