過去の記録

2014年11月11日(火)

トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 Common Room
Kenneth Baker 氏 (University of Miami)
Unifying unexpected exceptional Dehn surgeries (ENGLISH)
[ 講演概要 ]
This past summer Dunfield-Hoffman-Licata produced examples of asymmetric, hyperbolic, 1-cusped 3-manifolds with pairs of lens space Dehn fillings through a search of the extended SnapPea census.
Examinations of these examples with Hoffman and Licata lead us to coincidences with other work in progress that gives a simple holistic topological approach towards producing and extending many of these families. In this talk we'll explicitly describe our construction and discuss related applications of the technique.

統計数学セミナー

16:30-17:40   数理科学研究科棟(駒場) 052号室

Local Ordinal Embedding
[ 講演概要 ]
Ordinal embeddingとは，対象間の非類似度の順序情報（ d(i,j) < d(k,l) ）の みが与えられた際に，順序情報を可能な限り再現するように対象をp次元のEuclid空間に埋め込む問題 である．Facebookのfriend networkのような非重み付きgraphが潜在的に幾何的な構造を もっていると考えれば，ordinal embeddingによりグラフの頂点を幾何的な構造を保持してp次元空間に埋 め込むことができる．本発表では，この問題に対して，先行研究であるgeneralized non-metric MDSやstructure preserving embeddingとは異なり，tuning parameterを必要とせず，計算量も少ない新たな方法 (Soft Ordinal Embedding; SOE) を提案する．次に，もし非重み付きgraphが潜在的なEuclid座標の近接情報によって構成され ているとした際に，(0,1)-近接行列のみから背後の座標を再現できるかという問題を考える．もしこの問題に対して肯定的な解を与える事ができれば，非重み付きgraphが従来の多変量データ解析に必要な情報を保持していると考えられる．本発表では，random geometric graphの観点からこの問題に対して解を与える事で，非重み付きgraphに対する機械学習の限界と可能性を示す．

2014年11月10日(月)

FMSPレクチャーズ

17:00-18:00   数理科学研究科棟(駒場) 128号室
Alfred Ramani 氏 (Ecole Polytechnique)
Discrete Painlevé equations with periodic coefficients (ENGLISH)
[ 講演概要 ]
We present a series of results on discrete Painlevé equations with coefficients which are periodic functions of the independent variable. We show by explicit construction that for each affine Weyl group there exists an equation the coefficients of which have maximal periodicity. New results on equations associated to the affine Weyl group E_8 are also presented.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ramani.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) 126号室

[ 講演概要 ]
In this talk, we study a geometric property of a continuous plurisubharmonic function which is a solution of the Monge-Ampere equation and has a convex level set. By using our results and Lempert's results, we show a relation between the supports of the Monge-Ampere currents and complex $k$-extreme points of closed balls for the Kobayashi　distance in a bounded convex domain in $C^n$.

古典解析セミナー

16:00-17:00   数理科学研究科棟(駒場) 122号室
Jean-Pierre RAMIS 氏 (Toulouse)
DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY OF DYNAMICAL SYSTEMS
[ 講演概要 ]
We will explain how to get obstructions to the integrability of analytic Hamiltonian Systems (in the classical Liouville sense) using Differential Galois Theory (introduced by Emile Picard at the end of XIX-th century). It is the so-called Morales-Ramis theory. Even if this sounds abstract, there exist efficient algorithms allowing to apply the theory and a lot of applications in various domains.

Firstly I will present basics on Hamiltonian Systems and integrability on one side and on Differential Galois Theory on the other side. Then I will state the main theorems. Afterwards I will describe some applications.

2014年11月07日(金)

幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]
２次元のリーマン多様体から双曲平面への調和写像は，古くから調べられており，さまざまな結果が知られている．また，ミンコフスキー空間の平均曲率一定曲面のガウス写像が双曲平面への調和写像になることから曲面への応用もさまざま知られている．一方，1998年にDorfmeister, PeditとWuは，ループ群の手法によって曲面から対称空間への調和写像を構成する方法を発表した．最近，双曲平面への調和写像がさまざまな曲面の研究に出現するようになった（ハイゼンベルグ群内の極小曲面，反ド・ジッター空間の極大曲面，双曲空間のガウス曲率一定曲面など）．本講演では，曲面から対称空間への調和写像のループ群を用いた一般的な構成法の話と，対称空間を双曲平面に具体的に絞った話をする．

2014年11月05日(水)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

On the noncommutativity of the central sequence $C^*$-algebra $F(A)$ (ENGLISH)

数理人口学・数理生物学セミナー

14:50-16:20   数理科学研究科棟(駒場) 122号室

[ 講演概要 ]

そこで、環境攪乱下での非拡散戦略が進化をする条件を探るために、分裂繁殖の際の分割比に着目した。今回の研究では、コロニーサイズを４種類にわけ、コロニーサイズが成長率に従って成長すると仮定し、サイズ構造のある差分方程式を構築した。最大のサイズ（サイズ４）になると分割するとした。分割比としては、２：２分割戦略（コロニー分割後の親と子コロニーのサイズがほぼ変わらない）と１：３分割戦略（親子のサイズ差が大きい）の２つの戦略を仮定した。
基本モデルでは、コロニー間の闘争は無く場所を巡る競争のみとし、コロニーサイズ依存の死亡率を仮定した。死亡を免れると、すぐに次のコロニーサイズへ推移するとした。小さなコロニーの死亡率が他のコロニーサイズの死亡率と比べて非常に高い時は、2：2分割戦略が有利になり、撹乱頻度の高い環境においても有利になるという結果となった。
次に、基本モデルにコロニーが死亡を免れてもすぐには成長せずに同じサイズの状態のままである確率を導入した。すると小コロニーの成長が他のサイズに比べて非常に遅い時に、２：２分割戦略が有利になる事を示した。
３つ目に、分巣先の候補地にコロニーが既にある場合にコロニー間の闘争が生じる場合と基本モデルのように闘争の無い場合を比較したところ、基本モデル（闘争無し）のほうが２：２分割戦略が有利になる事を示した。
以上により、サイズ依存性を考慮する事によって、環境攪乱下でも非拡散戦略が有利になる条件を示す事が出来た。

【参考文献】
Nakamaru, M., Takada, T., Ohtsuki, A., Suzuki, S.U., Miura, K. and Tsuji, K. (2014) Ecological conditions favoring budding in colonial organisms under environmental disturbance. PLoS ONE 9 (3), e91210.

[ 参考URL ]

2014年11月04日(火)

トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea : 16:00-16:30 Common Room
Brian Bowditch 氏 (University of Warwick)
The coarse geometry of Teichmuller space. (ENGLISH)
[ 講演概要 ]
We describe some results regarding the coarse geometry of the
Teichmuller space
of a compact surface. In particular, we describe when the Teichmuller
space admits quasi-isometric embeddings of euclidean spaces and
half-spaces.
We also give some partial results regarding the quasi-isometric rigidity
of Teichmuller space. These results are based on the fact that Teichmuller
space admits a ternary operation, natural up to bounded distance
which endows it with the structure of a coarse median space.

統計数学セミナー

16:30-17:40   数理科学研究科棟(駒場) 052号室

Conditions for consistency of a log-likelihood-based information criterion in normal multivariate linear regression models under the violation of normality assumption
[ 講演概要 ]

2014年10月29日(水)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
Sven Raum 氏 (RIMS, Kyoto Univ.)
The classification of easy quantum groups (ENGLISH)

Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室
Patrick Delorme 氏 (UER Scientifique de Luminy Universite d'Aix-Marseille II)
Harmonic analysis on reductive p-adic symmetric spaces. (ENGLISH)
[ 講演概要 ]
In this lecture we will review the Plancherel formula that
we got by looking to neighborhoods at infinity of the
symmetric spaces and then using the method of Sakellaridis-Venkatesh
for spherical varieties for a split group. For us the group
is not necessarily split. We will try to show what questions
are raised by this work for real spherical varieties.
We will present in the last part a joint work with Pascale
Harinck and Yiannis Sakellaridis in which we prove Paley-Wiener
theorems for symmetric spaces.

古典解析セミナー

16:00-17:00   数理科学研究科棟(駒場) 117号室
Whittaker functions and Barnes-Type Lemmas (ENGLISH)
[ 講演概要 ]
In the theory of automorphic forms on GL(n,R), which concerns harmonic analysis and representation theory of this group, certain special functions known as GL(n,R) Whittaker functions play an important role. These Whittaker functions are generalizations of classical Whittaker (or, more specifically, Bessel) functions.

Mellin transforms of products of GL(n,R) Whittaker functions may be expressed as certain Barnes type integrals, or equivalently, as hypergeometric series of unit argument. The general theory of automorphic forms predicts that these Mellin transforms reduce, in certain cases, to products of gamma functions. That this does in fact occur amounts to a whole family of generalizations of the so-called Barnes' Lemma and Barnes' Second Lemma, from the theory of hypergeometric series. We will explore these generalizations in this talk.

This talk will not require any specific knowledge of automorphic forms.

2014年10月28日(火)

代数学コロキウム

16:40-18:50   数理科学研究科棟(駒場) 002号室
いつもと曜日が異なりますのでご注意下さい
Judith Ludwig 氏 (Imperial college) 16:40-17:40
[ 講演概要 ]
Let B be a definite quaternion algebra over the rationals, G the algebraic group defined by the units in B and H the subgroup of G of norm one elements. Then the classical transfer of automorphic representations from G to H is well understood thanks to Labesse and Langlands, who proved formulas for the multiplicity of irreducible admissible representations of H(adeles) in the discrete automorphic spectrum.
The goal of this talk is to prove a p-adic version of this transfer. By this we mean an extension of the classical transfer to p-adic families of automorphic forms as parametrized by certain rigid analytic spaces called eigenvarieties. We will prove the p-adic transfer by constructing a morphism between eigenvarieties, which agrees with the classical transfer on points corresponding to classical automorphic representations.
Jan Nekovar 氏 (Université Paris 6) 17:50-18:50
Plectic cohomology (English)

2014年10月27日(月)

代数幾何学セミナー

14:50-16:20   数理科学研究科棟(駒場) 122号室
いつもと開始時間が異なります。
Meng Chen 氏 (Fudan University)
On projective varieties with very large canonical volume (ENGLISH)
[ 講演概要 ]
For any positive integer n>0, a theorem of Hacon-McKernan, Takayama and Tsuji says that there is a constant c(n) so that the m-canonical map is birational onto its image for all smooth projective n-folds and all m>=c(n). We are interested in the following problem "P(n)": is there a constant M(n) so that, for all smooth projective n-fold X with Vol(X)>M(n), the m-canonical map of X is birational for all m>=c(n-1). The answer to “P_n" is positive due to Bombieri when $n=2$ and to Todorov when $n=3$. The aim of this talk is to introduce my joint work with Zhi Jiang from Universite Paris-Sud. We give a positive answer in dimensions 4 and 5.

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室

On the minimality of canonically attached singular Hermitian metrics on certain nef line bundles (JAPANESE)
[ 講演概要 ]
We apply Ueda theory to a study of singular Hermitian metrics of a (strictly) nef line bundle $L$. Especially we study minimal singular metrics of $L$, metrics of $L$ with the mildest singularities among singular Hermitian metrics of $L$ whose local weights are plurisubharmonic. In some situations, we determine a minimal singular metric of $L$. As an application, we give new examples of (strictly) nef line bundles which admit no smooth Hermitian metric with semi-positive curvature.

2014年10月25日(土)

調和解析駒場セミナー

13:30-16:30   数理科学研究科棟(駒場) 128号室

Approximation in Banach space by linear positive operators (JAPANESE)
[ 講演概要 ]
We obtain a sufficient condition for the
convergence of positive linear operators in Banach
function spaces on Rn and derive a Korovkin type
theorem for these spaces. Also, we generalized
this result via statistical sense. This is a joint

Local ill-posedness of the Euler equations in a critical Besov space (JAPANESE)
[ 講演概要 ]

がなされてきているが、$H^{d/2+1}$や$W^{d/p+1,p}$ ($d$は

ついては未解決であった。昨年、BourgainとLiは$H^{d/2+1}$や
$W^{d/p+1,p}$でオイラー方程式が局所非適切であることを証明した。

するより精密な評価を進めており、実解析的にも大変興味深い。

この先駆的な結果を追うようにして、$C^1$クラスでの非適切性に関
しても3つの研究グループによって（それぞれ独自の手法によって）

Bourgain-Li May12)本講演では、解の存在と一意性が成り立って
いる$B^1_{¥infty,1}$というBesov空間(Pak-Park,2004）で

2014年10月22日(水)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Free independence in ultraproduct von Neumann algebras and applications (ENGLISH)

数理人口学・数理生物学セミナー

14:50-16:20   数理科学研究科棟(駒場) 122号室

[ 講演概要 ]

$({\rm P})^k \left\{ \begin{array}{ll} u_t=\Delta u- ku^{m_1}v^{m_3} \quad\quad & \mbox{in} \ Q_T:=\Omega \times (0, T), \\ v_t= -ku^{m_2}v^{m_4} \quad\quad&\mbox{in} \ Q_T, \\ \dfrac{\partial u}{\partial \nu}=0 \quad\quad&\mbox{on} \ S_T:=\partial \Omega \times (0, T), \\ u(x,0)=u_{0}(x),\quad v(x,0)=v_{0}(x) \quad\quad&\mbox{in} \ \Omega, \\ \end{array} \right.$

ただし、$\Omega$は$\mathbf{R}^n$の有界領域, $T$は正定数, $\nu$は$\partial \Omega$上の外向き単位法線ベクトル、$m_i(i=1,2,3,4)$は$1$より大きい正定数、$u_0, v_0$は非負の初期値を表す。このとき、適当な初期条件のもとで$k\to \infty$としたとき、次のような結果を得た(詳細は講演内で述べる):
$\begin{array}{cll} &\mbox{ (Case I)}\quad & {\bf m}=(m_1, 1, 1, 1)かつm_1> 3 \ &\Rightarrow \ uは\mbox{\Omega}上の熱方程式の解に近づく \\ &\mbox{ (Case II)}& {\bf m}=(1, m_2, 1, 1) かつm_2 >2 \ &\Rightarrow \ uは{\rm supp}\, u_0上の熱方程式の解に近づく \\ &\mbox{ (Case III)}& {\bf m}=(1, 1, m_3, 1)かつm_3> 0 &\Rightarrow \ uは一相{\rm Stefan}問題の解に近づく \\ &\mbox{ (Case IV)}& {\bf m}=(1, 1, 1, m_4)かつ2>m_4> 1 &\Rightarrow \ uは一相{\rm Stefan}問題の解に近づく \\ \end{array}$

2014年10月21日(火)

トポロジー火曜セミナー

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

Vanishing theorems for p-local homology of Coxeter groups and their alternating subgroups (JAPANESE)
[ 講演概要 ]
Given a prime number $p$, we estimate vanishing ranges of $p$-local homology groups of Coxeter groups (of possibly infinite order) and alternating subgroups of finite reflection groups. Our results generalize those by Nakaoka for symmetric groups and Kleshchev-Nakano and Burichenko for alternating groups. The key ingredient is the equivariant homology of Coxeter complexes.

2014年10月20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) 126号室

IV型モジュラー多様体の小平次元 (JAPANESE)
[ 講演概要 ]

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

Finite element method with various types of penalty on domain/boundary (ENGLISH)
[ 講演概要 ]
We are concerned with several penalty methods (on domain/boundary)
combining with finite element method to solve some partial differential equations. The penalty methods are very useful and widely applied to various problems. For example, to solve the Navier-Stokes equations in moving boundary domain, the finite element method requires to construct the boundary fitted mesh at every times step, which is very time-consuming. The fictitious domain method is proposed to tackle this problem. It is to reformulate the equation to a larger fixed domain, called the fictitious domain, to which we can take a uniform mesh independent on the original moving boundary. The reformulation is based on a penalty method on do- main. Some penalty methods are proposed to approximate the boundary conditions which are not easy to handle with general FEM, such as the slip boundary condition to Stokes/Navier-Stokes equations, the unilateral boundary condition of Signorini’s type to Stokes equations, and so on. It is known that the variational crimes occurs if the finite element spaces or the implementation methods are not chosen properly for slip boundary condition. By introducing a penalty term to the normal component of velocity on slip boundary, we can solve the equations in FEM easily. For the boundary of Signorini’s type, the variational form is an inequality, to which the FEM is not easy to applied. However, we can approximate the variational inequality by a variation equation with penalty term, which can be solve by FEM directly. In above, we introduced several penalty methods with finite element approximation. In this work, we investigate the well-posedness of those penalty method, and obtain the error estimates of penalty; moreover, we consider the penalty methods combining with finite element approximation and show the error estimates.

2014年10月17日(金)

幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 126号室

A finite diameter theorem on RCD spaces (JAPANESE)
[ 講演概要 ]

2014年10月15日(水)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Classification of actions of compact abelian groups on subfactors with index less than 4 (ENGLISH)

2014年10月14日(火)

諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Fluid flow and electromagnetic fields, from viewpoint of theoretical physics -- Is the Navier-Stokes Equation sufficient to describe turbulence at very high Reynolds numbers? -- (JAPANESE)
[ 講演概要 ]
There exists analogy between the fluid flow and electromagnetic fields with respect to their mathematical representations. This is reasonable because both are continuous physical fields having energy and momentum in space-time. In particular, fluid’s vorticity is analogous to magnetic field.

On the other hand, for simulation of atmospheric global motion on the giant computer Earth Simulator, many empirical physical parameters must be introduced in order to obtain realistic results for weather prediction, etc. This implies that the present system of equations of fluid flows may not be sufficient to describe fluid motions of large scales at very high Reynolds numbers. We consider whether the above-mentioned analogy is useful for improvement of the theory of turbulence at very high Reynolds numbers.