過去の記録 ~08/18本日 08/19 | 今後の予定 08/20~


15:30-17:00   数理科学研究科棟(駒場) 122号室
Alexandru Dimca 氏 (Institut Universitaire de France )
Syzygies of jacobian ideals and Torelli properties (ENGLISH)
[ 講演概要 ]
Let $C$ be a reduced complex projective plane curve defined by a homogeneous equation $f(x,y,z)=0$. We consider syzygies of the type $af_x+bf_y+cf_z=0$, where $a,b,c$ are homogeneous polynomials and $f_x,f_y,f_z$ stand for the partial derivatives of $f$. In our talk we relate such syzygies with stable or splittable rank two vector bundles on the projective plane, and to Torelli properties of plane curves in the sense of Dolgachev-Kapranov.



13:30-16:00   数理科学研究科棟(駒場) 123号室
岡崎龍太郎 氏 (元・同志社大学) 13:30-14:30
実数上既約な、整数係数斉次4次形式$F(X,Y)$ に対する、$F(X,Y)=1$の解の個数の評価
岡崎龍太郎 氏 (元・同志社大学) 15:00-16:00
種数2の代数曲線と、その不分岐7次拡大の組のモジュライ (JAPANESE)



10:00-11:30   数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
野澤 啓 氏 (立命館大学)
Lie葉層構造の剛性について (JAPANESE)
[ 講演概要 ]
Lie葉層の葉たちが高実階非コンパクト型対称空間と計量同型であるとき、そのLie葉層のホロノミー群は超剛性や数論性などの高実階半単純群Lie群の一様格子と似た剛性を持つことが、Zimmerの定理により知られている。本講演では、Mostow剛性の変種の応用による、実階数1の場合を含むZimmerの定理の拡張について述べる。(Ga¥"el Meigniezとの共同研究。)



16:30-18:00   数理科学研究科棟(駒場) 122号室
武石拓也 氏 (東大数理)
Bost-Connes system for local fields of characteristic zero (ENGLISH)


16:40-17:40   数理科学研究科棟(駒場) 002号室
三枝洋一 氏 (東京大学数理科学研究科)
Non-tempered A-packets and the Rapoport-Zink spaces (JAPANESE)


14:50-16:20   数理科学研究科棟(駒場) 128号室
中田行彦 氏 (東京大学大学院数理科学研究科)
Age-structured epidemic model with infection during transportation (JAPANESE)
[ 講演概要 ]
現代、航空路を手段とした大陸間移動が身近であるがゆえに、多くの感染症が世界中に蔓延することが容易となっている。本発表では、Volterra型積分方程式と遅延微分方程式を用いて、感染者個体の感染齢(age since infection)を連続的なパラメータとして組み込みながら、複数領域に広がる感染病の伝染ダイナミクスを記述する数理モデルを紹介する。領域間の個体群移動を記述するために、非自励な遅延微分方程式の解が陰的に用いられる。最後に、領域間の移動においては、それぞれの感染個体の発生状態がその交通機関内での滞在時間に連続的に依存することから、無限次元のVolterra型積分方程式が得られることを示したい。本研究はD.H.KniplおよびG. Röstとの共同研究となっている。



16:30-18:00   数理科学研究科棟(駒場) 128号室
筒井 容平 氏 (東大 数理)
拡散性を有しない誘因因子に対する走化性方程式の小さな有界な解 (JAPANESE)
[ 講演概要 ]
We consider a chemotaxis system with a logarithmic
sensitivity and a non-diffusive chemical substance. For some chemotactic
sensitivity constants, Ahn and Kang proved the existence of bounded
global solutions to the system. An entropy functional was used in their
argument to control the cell density by the density of the chemical
substance. Our purpose is to show the existence of bounded global
solutions for all the chemotactic sensitivity constants. Assuming the
smallness on the initial data in some sense, we can get uniform
estimates for time. These estimates are used to extend local solutions.
This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu
Univ.) and Juan J. L. Vel\\'azquez (Univ. of Bonn).



16:30-18:00   数理科学研究科棟(駒場) 056号室
中澤嵩 氏 (東北大学大学院理学研究科)
人工血管の最適設計を目的としたNavier-Stokes方程式の周期解に対する形状最化問題 (JAPANESE)
[ 講演概要 ]
Stokes方程式やNavier-Stokes方程式の定常解に対する形状最適化問題は,これまで多く行われてきた.しかし, Navier-Stokes方程式の周期解に対しては十分に行われていない.本講演では,安定性理論を活用することで,Navier-Stokes方程式の周期解に対する形状最適化問題を人工血管の最適設計という現実の問題を通して考察する.
[ 講演参考URL ]


10:30-12:00   数理科学研究科棟(駒場) 126号室
山本 光 氏 (東大数理)
ラグランジュ平均曲率流とその具体例について (JAPANESE)



13:30-17:00   数理科学研究科棟(駒場) 128号室
高田 了 氏 (東北大学) 13:30-15:00
Strichartz estimates for incompressible rotating fluids (JAPANESE)
[ 講演概要 ]
3次元全空間において,回転による Coriolis 力の影響を考慮した
非圧縮性 Euler 方程式または Navier-Stokes 方程式を考察する.
Coriolis 力から生成される時間発展作用素に対して,
またその応用として,Euler 方程式の長時間可解性を考察する.
上記の Strichartz 評価と Beale-Kato-Majda 型爆発判定法を
尚,本講演の前半部分は,Seoul National University の
Youngwoo Koh 氏と Sanghyuk Lee 氏との共同研究に基づくものである.
岡田 正巳 氏 (首都大学東京) 15:30-16:30
不規則配置点で観測された関数値の補間近似サンプリング定理について (JAPANESE)
[ 講演概要 ]
(参考:H. Wendland, Scattered Data Approximation,
Cambridge U.P., 2005)



17:30-18:30   数理科学研究科棟(駒場) 056号室
Olivier Wittenberg 氏 (ENS and CNRS)
On the cycle class map for zero-cycles over local fields (ENGLISH)
[ 講演概要 ]
The Chow group of zero-cycles of a smooth and projective variety defined over a field k is an invariant of an arithmetic and geometric nature which is well understood only when k is a finite field (by higher-dimensional class field theory). In this talk, we will discuss the case of local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus over p-adic fields. The same statement holds for semistable K3 surfaces over C((t)), but does not hold in general for surfaces over C((t)) or over the maximal unramified extension of a p-adic field. This is a joint work with Hélène Esnault.

(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.)



16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
内藤 貴仁 氏 (東京大学大学院数理科学研究科)
On the rational string operations of classifying spaces and the
Hochschild cohomology (JAPANESE)
[ 講演概要 ]
Chataur and Menichi initiated the theory of string topology of
classifying spaces.
In particular, the cohomology of the free loop space of a classifying
space is endowed with a product
called the dual loop coproduct. In this talk, I will discuss the
algebraic structure and relate the rational dual loop coproduct to the
cup product on the Hochschild cohomology via the Van den Bergh isomorphism.


10:30-11:30   数理科学研究科棟(駒場) 056号室
筒井 容平 氏 (東京大学)
An application of weighted Hardy spaces to the Navier-Stokes equations (JAPANESE)
[ 講演概要 ]
The purpose of this talk is to investigate decay orders of the L^2 energy of solutions to the incompressible homogeneous Navier-Stokes equations on the whole spaces by the aid of the theory of weighted Hardy spaces. The main estimates are two weighted inequalities for heat semigroup on weighted Hardy spaces and a weighted version of the div-curl lemma due to Coifman-Lions-Meyer-Semmes. It turns out that because of the use of weighted Hardy spaces, our decay orders of the energy can be close to the critical one of Wiegner.


16:30-18:00   数理科学研究科棟(駒場) 126号室
土岡俊介 氏 (東京大学大学院数理科学研究科)
Toward the graded Cartan invariants of the symmetric groups (JAPANESE)
[ 講演概要 ]
We propose a graded analog of Hill's conjecture which is equivalent to K\\"ulshammer-Olsson-Robinson's conjecture on the generalized Cartan invariants of the symmetric groups.
We give justifications for it and discuss implications between the variants.
Some materials are based on the joint work with Anton Evseev.



10:30-12:00   数理科学研究科棟(駒場) 126号室
山ノ井 克俊 氏 (東京工業大学)
幾何学的対数微分の補題の別証明 (JAPANESE)



10:00-11:30   数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
河井 公大朗 氏 (東大数理)
等質ケーリー錐部分多様体の変形について (JAPANESE)
[ 講演概要 ]
Cayley 部分多様体は、Spin(7) 多様体内の極小部分多様体で Harvey, Lawson により導入された calibrated submanifold の一種である。calibrated submanifold の変形は、最初 Mclean により研究された。彼はコンパクトな場合を調べ、現在では錐、漸近的に錐な場合など非コンパクトな場合への拡張が試みられている。Cayley 錐の変形のモジュライ空間は、一般には滑らかでないことが知られているが、本講演では、R^8の等質 Cayley 錐の場合に着目し、具体的に変形の様子を調べることを考える。



16:30-18:00   数理科学研究科棟(駒場) 122号室
Ryszard Nest 氏 (Univ. Copenhagen)
Index and determnant of n-tuples of commuting operators (ENGLISH)



16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
正井 秀俊 氏 (東京大学大学院数理科学研究科)
On the number of commensurable fibrations on a hyperbolic 3-manifold. (JAPANESE)
[ 講演概要 ]
By work of Thurston, it is known that if a hyperbolic fibred
$3$-manifold $M$ has Betti number greater than 1, then
$M$ admits infinitely many distinct fibrations.
For any fibration $\\omega$ on a hyperbolic $3$-manifold $M$,
the number of fibrations on $M$ that are commensurable in the sense of
Calegari-Sun-Wang to $\\omega$ is known to be finite.
In this talk, we prove that the number can be arbitrarily large.


13:00-14:10   数理科学研究科棟(駒場) 052号室
Alexandre Brouste 氏 (Universite du Maine, France)
Parametric estimation in fractional Ornstein-Uhlenbeck process (ENGLISH)
[ 講演概要 ]
Several statistical models that imply the fractional Ornstein-Uhlenbeck (fOU) process will be presented: direct observations of the process or partial observations in an additive independent noise, continuous observations or discrete observations. In this different settings, we exhibit large sample (or high-frequency) asymptotic properties of the estimators (maximum likelihood estimator, quadratic variation based estimator, moment estimator, …) for all parameters of interest of the fOU. We also illustrate our results with the R package yuima.
[ 講演参考URL ]



16:00-17:00   数理科学研究科棟(駒場) 128号室
Anton Dzhamay 氏 (University of Northern Colorado)
Discrete Schlesinger Equations and Difference Painlevé Equations (ENGLISH)
[ 講演概要 ]
The theory of Schlesinger equations describing isomonodromic
dynamic on the space of matrix coefficients of a Fuchsian system
w.r.t.~continuous deformations is well-know. In this talk we consider
a discrete version of this theory. Discrete analogues of Schlesinger
deformations are Schlesinger transformations that shift the eigenvalues
of the coefficient matrices by integers. By discrete Schlesinger equations
we mean the evolution equations on the matrix coefficients describing
such transformations. We derive these equations, show how they can be
split into the evolution equations on the space of eigenvectors of the
coefficient matrices, and explain how to write the latter equations in
the discrete Hamiltonian form. We also consider some reductions of those
equations to the difference Painlevé equations, again in complete parallel
to the differential case.

This is a joint work with H. Sakai (the University of Tokyo) and
T.Takenawa (Tokyo Institute of Marine Science and Technology).



16:00-16:50   数理科学研究科棟(駒場) 118号室
Kazufumi Ito 氏 (North Carolina State Univ.)
A new finite difference scheme based on staggered grids for Navier Stokes equations (ENGLISH)
[ 講演概要 ]
We develop a new method that uses the staggered grid only for the pressure node, i.e., the pressure gird is the center of the square cell and the velocities are at the node. The advantage of the proposed method compared to the standard staggered grid methods is that it is very straight forward to treat the boundary conditions for the velocity field, the fluid structure interaction, and to deal with the multiphase flow using the immersed interface methods. We present our analysis and numerical tests.


17:00-17:50   数理科学研究科棟(駒場) 118号室
Jun Zou 氏 (The Chinese University of Hong Kong)
Efficient Domain Decomposition Methods for a Class of Linear and Nonlinear Inverse Problems (ENGLISH)
[ 講演概要 ]
In this talk we shall present several new domain decomposition methods for solving some linear and nonlinear inverse problems. The motivations and derivations of the methods will be discussed, and numerical experiments will be demonstrated.



10:15-11:45   数理科学研究科棟(駒場) 470号室
Michele Triestino 氏 (Ecole Normale Superieure de Lyon)
Almost sure triviality of the $C^1$-centralizer of random circle diffeomorphisms with periodic points (ENGLISH)
[ 講演概要 ]
By the end of the 80s, Malliavin and Shavgulidze introduced a measure on the space of C^1 circle diffeomorphisms which carries many interesting features. Perhaps the most interesting aspect is that it can be considered as an analog of the Haar measure for the group Diff^1_+(S^1).
The nature of this measure has been mostly investigated in connection to representation theory.
For people working in dynamical systems, the MS measure offers a way to quantify dynamical phenomena: for example, which is the probability that a random diffeomorphism is irrational? Even if this question have occupied my mind for a long time, it remains still unanswered, as many other interesting ones. However, it is possible to understand precisely what are the typical features of a diffeomorphism with periodic points.


17:00-18:00   数理科学研究科棟(駒場) 122号室
Bernadette Miara 氏 (Univ. Paris-Est)
[ 講演参考URL ]



10:15-11:45   数理科学研究科棟(駒場) 470号室
Michele Triestino 氏 (Ecole Normale Superieure de Lyon)
Invariant distributions for circle diffeomorphisms of
irrational rotation number and low regularity (ENGLISH)
[ 講演概要 ]
The main inspiration of this joint work with Andrés Navas is the beautiful result of Ávila and Kocsard: if f is a C^\\infty circle diffeomorphism of irrational rotation number, then the unique invariant probability measure is also the unique (up to rescaling) invariant distribution.
Using conceptual geometric arguments (Hahn-Banach...), we investigate the uniqueness of invariant distributions for C^1 circle diffeomorphisms of irrational rotation number, with particular attention to sharp regularity.
We prove that If the diffeomorphism is C^{1+bv}, then there is a unique invariant distribution of order 1. On the other side, examples by Douady and Yoccoz, and by Kodama and Matsumoto exhibit differentiable dynamical systems for which the uniqueness does not hold.

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