過去の記録 ~08/17本日 08/18 | 今後の予定 08/19~



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
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.


16:30-17:40   数理科学研究科棟(駒場) 052号室
栁原 宏和 氏 (広島大学理学系研究科)
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 ]
本発表では,正規性を仮定した多変量線形回帰モデルにおいて,最大対数尤度の-2倍に罰則項を加えることで定義されるLog-Likelihood-Based Information Criterion (LLBIC) を用いた変数選択法が一致性を持つための条件について考察する.Yanagihara et al. (2012) では,LLBICを用いた変数選択法が一致性を持つために必要な条件を,真のモデルの分布が正規分布であるという仮定の下で,標本数と観測値の次元を共に大きくする高次元漸近理論により導出した.しかしながら,多変量分布において正規性を満たすことは稀であり,仮定した分布と真の分布のずれの影響を調べることは非常に重要である.本発表の目的は,候補のモデルに正規性は仮定したが真のモデルの分布が正規分布ではないという条件の下で,高次元漸近理論に基づき評価された一致性を満たすための条件がどう変化するかを調べることにある.実際には,Yanagihara et al. (2012) で得られた条件よりも若干条件が狭くなるが, ほぼ同じ条件となり,その条件は真のモデルの非正規性に依存しないことがわかった.



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)


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.


16:00-17:00   数理科学研究科棟(駒場) 117号室
Eric Stade 氏 (University of Colorado Boulder)
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.



16:40-18:50   数理科学研究科棟(駒場) 002号室
Judith Ludwig 氏 (Imperial college) 16:40-17:40
A p-adic Labesse-Langlands transfer (English)
[ 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)



14:50-16:20   数理科学研究科棟(駒場) 122号室
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.


10:30-12:00   数理科学研究科棟(駒場) 126号室
小池 貴之 氏 (東大数理)
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.



13:30-16:30   数理科学研究科棟(駒場) 128号室
数理科学研究科の建物は基本的に土・日・祭日は施錠されています。 セミナー当日は正面の入口のみを12:30 から解錠いたします。
澤野 嘉宏 氏 (首都大学東京) 13:30-14:30
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
work with Professor Arash Ghorbanalizadeh.
米田 剛 氏 (東京工業大学) 15:00-16:30
Local ill-posedness of the Euler equations in a critical Besov space (JAPANESE)
[ 講演概要 ]
本研究はノートルダム大学のGerard Misiolek氏との共同
がなされてきているが、$H^{d/2+1}$や$W^{d/p+1,p}$ ($d$は

示された。(Misiolek-Y2014 May 8, Elgindi-Masmoudi May 10,
Bourgain-Li May12)本講演では、解の存在と一意性が成り立って



16:30-18:00   数理科学研究科棟(駒場) 122号室
磯野優介 氏 (京大理)
Free independence in ultraproduct von Neumann algebras and applications (ENGLISH)


14:50-16:20   数理科学研究科棟(駒場) 122号室
物部治徳 氏 (明治大学先端数理科学インスティテュート)
異なる反応項を持つある系の急速反応極限問題 (JAPANESE)
[ 講演概要 ]


近年、D. Hilhorstらにより\cite{HHP1}, \cite{HHP2}反応拡散系における``急速反応極限"の解析が進められ,様々な方程式において極限問題が考察されている。この解析の発展により、線型拡散を持つ反応拡散系と自由境界問題がある意味で繋がりを持つことが確認されている。しかしながら、それらのほとんどの結果は、反応項に対称性があり、非対称の場合に関する急速反応極限の解析結果はほとんど確認されていない。そこで、我々は最初のステップとして次のような単純な非対称な多項式を持つ反応拡散系の急速極限を考察し、多項式の指数の組み合わせと極限問題の関係について考察を行った:
({\rm P})^k
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, \\

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):
&\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 \\



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
秋田 利之 氏 (北海道大学)
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.



10:30-12:00   数理科学研究科棟(駒場) 126号室
馬 昭平 氏 (東京工業大学)
IV型モジュラー多様体の小平次元 (JAPANESE)
[ 講演概要 ]


16:30-18:00   数理科学研究科棟(駒場) 056号室
周冠宇 氏 (東京大学大学院数理科学研究科)
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.



10:00-11:30   数理科学研究科棟(駒場) 126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.
北別府 悠 氏 (京都大学)
A finite diameter theorem on RCD spaces (JAPANESE)
[ 講演概要 ]
本講演では有限次元とは限らない RCD 空間の直径の有限性定理について述べる. RCD 空間とは Ricci 曲率が下に有界な多様体の一般化である. Savar¥’e は self-improving property と呼ばれるものを RCD 空間上 Gamma calculus によって得た. 彼の結果及び桑田の双対定理を用いることで heat kernels のL^{¥infty}-contraction と呼ばれるものを得ることが出来る. この contraction property とある単純な補題から結果が導けることを示す.



16:30-18:00   数理科学研究科棟(駒場) 122号室
嶌田洸一 氏 (Univ. Tokyo)
Classification of actions of compact abelian groups on subfactors with index less than 4 (ENGLISH)



10:30-11:30   数理科学研究科棟(駒場) 056号室
神部 勉 氏 (東京大学)
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.


17:30-18:30   数理科学研究科棟(駒場) 002号室
Fabrizio Andreatta 氏 (Università Statale di Milano)
A p-adic criterion for good reduction of curves (ENGLISH)
[ 講演概要 ]
Given a curve over a dvr of mixed characteristic 0-p with smooth generic fiber and with semistable reduction, I will present a criterion for good reduction in terms of the (unipotent) p-adic étale fundamental group of its generic fiber.

(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.)



13:30-16:00   数理科学研究科棟(駒場) 123号室
織田孝幸 氏 (東京大学数理科学研究科) 13:30-14:30
$SU(3,1)$ の離散系列表現の第2種の行列係数について(宮崎直君の計算に基づく) (JAPANESE)
[ 講演概要 ]
高柳秀史 氏 (作新学院大学) 15:00-16:00
$Sp(2, R)$ 上の保型形式のFourier展開に向けて (JAPANESE)
[ 講演概要 ]



16:30-17:30   数理科学研究科棟(駒場) 002号室
お茶&Coffee&お菓子: 16:00~16:30 (コモンルーム)
三枝 洋一 氏 (東京大学大学院数理科学研究科)
局所志村多様体のエタールコホモロジーと局所ラングランズ対応 (JAPANESE)
[ 講演概要 ]



16:30-18:00   数理科学研究科棟(駒場) 122号室
鈴木悠平 氏 (東大数理/京大数理研)
Realization of hyperbolic group $C^*$-algebras as decreasing intersection of Cuntz algebras $O_2$ (ENGLISH)


14:50-16:20   数理科学研究科棟(駒場) 128号室
江夏洋一 氏 (東京大学大学院数理科学研究科)
再生方程式による感染症流行ダイナミクスの定性解析およびその周辺 (JAPANESE)
[ 講演概要 ]
本講演では, Bolyai Institute, University of Szeged (セゲド大学ボリアイ研究所) とのオープンパートナーシップ共同研究に基づく, Epidelay Research Group との研究交流の報告を行う.
感受性個体の新規感染を規定する incidence rate に関する再生方程式や, 対応する偏微分方程式系の解の漸近挙動に関する近年の結果を述べながら, cyclic な個体の性質変化が与える感染平衡解の安定性に関する open problem も議論する. また, 感受性個体への感染力を保ったまま, 病原体が産生する毒素
が無毒化される効果を含めた系のダイナミクスも, 現地での研究討論によって得た課題として併せて紹介する.



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
入江 慶 氏 (京都大学数理解析研究所)
Transversality problems in string topology and de Rham chains (JAPANESE)
[ 講演概要 ]
講演では,de Rham 鎖というものを用いることでこの困難を回避し,鎖レベルの構造が部分的に実現できるということを説明したい.



13:30-17:00   数理科学研究科棟(駒場) 002号室
笹本 智弘 氏 (東工大理物) 13:30-15:00
KPZ方程式とMacdonald過程 (JAPANESE)
[ 講演概要 ]
古川 俊輔 氏 (東大理物) 15:30-17:00
Entanglement spectra in topological phases and coupled Tomonaga-Luttinger liquids (JAPANESE)
[ 講演概要 ]
The entanglement spectrum (ES) has been found to provide useful probes of topological phases of matter and other exotic strongly correlated states. For the system's ground state, the ES is defined as the full eigenvalue spectrum of the reduced density matrix obtained by tracing out the degrees of freedom in part of the system. A key result observed in various topological phases and other gapped systems has been the remarkable correspondence between the ES and the edge-state spectrum. While this correspondence has been analytically proven for some topological phases, it is interesting to ask what systems show this correspondence more generally and how the ES changes when the bulk energy gap closes.

We here study the ES in two coupled Tomonaga-Luttinger liquids (TLLs) on parallel periodic chains. In addition to having direct applications to ladder systems, this problem is closely related to the entanglement properties of two-dimensional topological phases. Based on the calculation for coupled chiral TLLs, we provide a simple physical proof for the correspondence between edge states and the ES in quantum Hall systems consistent with previous numerical and analytical studies. We also discuss violations of this correspondence in gapped and gapless phases of coupled non-chiral TLLs.

Reference: R. Lundgren, Y. Fuji, SF, and M. Oshikawa, Phys. Rev. B 88, 245137 (2013).



16:30-18:00   数理科学研究科棟(駒場) 126号室
Hanfeng Li 氏 (SUNY Buffalo)
Entropy and $L^2$-torsion (ENGLISH)

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