過去の記録

過去の記録 ~11/14本日 11/15 | 今後の予定 11/16~

2015年07月27日(月)

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
鈴木 康平 氏 (京都大学大学院理学研究科)
Convergence of Brownian motions on RCD*(K,N) spaces
[ 講演概要 ]
RCD*(K,N)空間とは, Erbar-Kuwada-Sturmによって導入された測度距離空間のクラスで, 「次元N以下, Ricci曲率K以上」という概念を測度距離空間上に一般化した概念である. RCD*(K,N)空間上では, Cheeger energyから定まるDirichle形式が正則になることが知られており, 対応するMarkov過程は, Brown運動と呼ばれる. 本講演では, RCD*(K,N)空間で直径D以下という条件の下, 「 空間がmeasured Gromov-Hausdorff収束する」ことと,「 Brown運動が収束する」ことが同値であることを示す.

2015年07月24日(金)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 122号室
Mikael Pichot 氏 (McGill Univ.)
Applications of Boltzmann's S=k log W in algebra and analysis

幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 126号室
高津飛鳥 氏 (首都大学東京)
High-dimensional metric-measure limit of Stiefel manifolds (Japanese)
[ 講演概要 ]
A metric measure space is the triple of a complete separable metric space with a Borel measure on this space. Gromov defined a concept of convergence of metric measure spaces by the convergence of the sets of 1-Lipschitz functions on the spaces. We study and specify the high-dimensional limit of Stiefel manifolds in the sense of this convergence; the limit is the infinite-dimensional Gaussian space, which is drastically different from the manifolds. This is a joint work with Takashi SHIOYA (Tohoku univ).

FMSPレクチャーズ

16:00-19:00   数理科学研究科棟(駒場) 268号室
Fikret Golgeleyen 氏 (Bulent Ecevit University)
Solvability and approximate solution of a coefficient inverse problem for the kinetic equation (ENGLISH)
[ 講演概要 ]
The existence, uniqueness and stability of the solution of a coefficient inverse problem for the kinetic equation are proven.
The approximate solution of the problem in one-dimensional case is investigated by using two different techniques: finite difference approximation (FDA) and symbolic computation approach (SCA).
A comparison among the exact solution of the problem, the numerical solution obtained from FDA and the approximate analytical solution obtained from SCA is presented.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Fikret.pdf

2015年07月23日(木)

代数学コロキウム

13:00-16:30   数理科学研究科棟(駒場) 056号室
Lasse Grimmelt 氏 (ゲッティンゲン大学/早稲田大学) 13:00-14:00
Representation of squares by cubic forms - Estimates for the appearing exponential sums (English)
Haoyu Hu 氏 (東京大学数理科学研究科) 14:15-15:15
Ramification and nearby cycles for $\ell$-adic sheaves on relative curves (English)
[ 講演概要 ]
I will present a new approach for a formula of Deligne and Kato that computes the dimension of the nearby cycle complex of an $\ell$-adic sheaf on a smooth relative curve over a strictly henselian trait such that $p$ is not one of its uniformizer. Deligne considered the case where the sheaf has no vertical ramification and Kato extended the formula to the general case. My approach is based on ramification theory of Abbes and Saito. It computes the nearby cycle complex in terms of the refined Swan conductor. In fact, I compare Abbes-Saito's refined Swan conductor with Kato's Swan conductor with differential values, which is the key ingredient in Kato's formula; the case of rank one sheaves is due to Abbes and Saito. My approach provides also a new independent proof of Deligne-Kato's formula.
若林 泰央 氏 (東京大学数理科学研究科) 15:30-16:30
Explicit computation of the number of dormant opers and duality (Japanese)

2015年07月22日(水)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 122号室
George Elliott 氏 (Univ. Toronto)
Recent progress in the classification of amenable $C^*$-algebras

FMSPレクチャーズ

16:45-18:15   数理科学研究科棟(駒場) 122号室
George Elliott 氏 (Univ. Toronto)
Recent progress in the classification of amenable C*-algebras (ENGLISH)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

2015年07月21日(火)

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 : 16:30-17:00 Common Room
田神 慶士 氏 (東京工業大学)
Ribbon concordance and 0-surgeries along knots (JAPANESE)
[ 講演概要 ]
Akbulut and Kirby conjectured that two knots with
the same 0-surgery are concordant. Recently, Yasui
gave a counterexample of this conjecture.
In this talk, we introduce a technique to construct
non-ribbon concordant knots with the same 0-surgery.
Moreover, we give a potential counterexample of the
slice-ribbon conjecture. This is a joint work with
Tetsuya Abe (Osaka City University, OCAMI).

解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
蘆田 聡平 氏 (京都大学理学研究科)
Born-Oppenheimer approximation for an atom in constant magnetic fields (Japanese)
[ 講演概要 ]
We obtain a reduction scheme for the study of the quantum evolution of an atom in constant magnetic fields using the method developed by Martinez, Nenciu and Sordoni based on the construction of almost invariant subspace. Martinez and Sordoni also dealt with such a case but their reduced Hamiltonian includes the vector potential terms. Using the center of mass coordinates and constructing the almost invariant subspace different from theirs, we obtain the reduced Hamiltonian which does not include the vector potential terms. Using the reduced evolution we also obtain the asymptotic expantion of the evolution for a specific localized initial data, which verifies the straight motion of an atom in constatnt magnetic fields.

Lie群論・表現論セミナー

17:00-18:30   数理科学研究科棟(駒場) 122号室
Paul Baum 氏 (Penn State University)
GEOMETRIC STRUCTURE IN SMOOTH DUAL
[ 講演概要 ]
Let G be a connected split reductive p-adic group. Examples are GL(n, F) , SL(n, F) , SO(n, F) , Sp(2n, F) , PGL(n, F) where n can be any positive integer and F can be any finite extension of the field Q_p of p-adic numbers. The smooth (or admissible) dual of G is the set of equivalence classes of smooth irreducible representations of G. This talk will first review the theory of the Bernstein center. According to this theory, the smooth dual of G is the disjoint union of subsets known as the Bernstein components. The talk will then explain the ABPS (Aubert-Baum-Plymen-Solleveld) conjecture which states that each Bernstein component is a complex affine variety. Each of these complex affine varieties is explicitly identified as the extended quotient associated to the given Bernstein component.

The ABPS conjecture has been proved for GL(n, F), SO(n, F), and Sp(2n, F).

Lie群論・表現論セミナー

15:30-16:30   数理科学研究科棟(駒場) 122号室
服部俊昭 氏 (東京工業大学)
清水の補題のSL(3,R)/SO(3)の場合への拡張について (Japanese)
[ 講演概要 ]
PSL(2,C)の部分群の離散性に関する必要条件である清水の補題,Jorgensenの不等式を双曲空間から他の階数1の対称空間の場合に拡張しようという研究が現在進行中であるが, 高階の対称空間についてそのような結果はまだないようである。階数が2の対称空間で最も簡単なSL(3,R)/SO(3)の場合に清水の補題を拡張する試みについてお話しする。

2015年07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
西納武男 氏 (立教大学)
Realization of tropical curves in complex tori (Japanese)
[ 講演概要 ]
Tropical curves are combinatorial object satisfying certain harmonicity condition. They reflect properties of holomorphic curves, and rather precise correspondence is known between tropical curves in real affine spaces and holomorphic curves in toric varieties. In this talk we extend this correspondence to the periodic case. Namely, we give a correspondence between periodic plane tropical curves and holomorphic curves in complex tori. This is a joint work with Tony Yue Yu.

東京無限可積分系セミナー

14:00-16:00   数理科学研究科棟(駒場) 002号室
Simon Wood 氏 (The Australian National University)
Classifying simple modules at admissible levels through symmetric polynomials (ENGLISH)
[ 講演概要 ]
From infinite dimensional Lie algebras such as the Virasoro
algebra or affine Lie (super)algebras one can construct universal
vertex operator algebras. These vertex operator algebras are simple at
generic central charges or levels and only contain proper ideals at so
called admissible levels. The simple quotient vertex operator algebras
at these admissible levels are called minimal model algebras. In this
talk I will present free field realisations of the universal vertex
operator algebras and show how they allow one to elegantly classify
the simple modules over the simple quotient vertex operator algebras
by using a deep connection to symmetric polynomials.

2015年07月16日(木)

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室
利根川吉廣 氏 (東京工業大学大学院理工学研究科)
ネットワーク曲率流の3重点周りの正則性について (Japanese)
[ 講演概要 ]
幾何学的測度論の枠組みで考える、一般化された極小曲面に対しては様々な正則性定理が知られている。その中で最も基本的なAllardの正則性定理は、局所的に「弱い測度の意味で一般化された極小曲面が平面に近ければ、その曲面は滑らかである」ことを主張する。さらに面積最小等の仮定があれば様々な特異点集合に対する結果がある。一方で面積最小等の仮定が一切無ければ、本質的にはSimonによる3重点周りの正則性定理が知られているのみである。3重点周りの正則性は元々Taylorによって面積最小の仮定の下で示されていたが、Simonは最小性を使わない証明を与えたのである。
講演者は数年前に一般化された平均曲率流に対して、Allardの正則性定理に対応する結果を示した。それを踏み台にして、さらに最近Simonの正則性定理に対応する結果を1次元曲率流ではあるが証明することができたので、その結果と証明の概略を講演では解説する。

2015年07月14日(火)

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 : 16:30-17:00 Common Room
Carlos Moraga Ferrandiz 氏 (東京大学大学院数理科学研究科, 日本学術振興会)
How homoclinic orbits explain some algebraic relations holding in Novikov rings. (ENGLISH)
[ 講演概要 ]
Given u, a de-Rham cohomology class of degree 1 of a closed manifold M, we consider the space F_u of (closed) Morse 1-forms in this class. In Morse theory, it is important to equip each α in F_u with a descending pseudo-gradient X. The case u=0 yields usual Morse theory, while u ≠ 0 yields Morse-Novikov theory, which is devoted to the understanding of the space of equipped 1-forms (α,X) with α in F_u.
Here, X is a descending pseudo-gradient, which is said to be adapted to α.

The morphism π1(M) → R induced by u (given by the integral of any α in F_u over a loop of M) determines a set of u-negative loops.

We show that for every u-negative g in π1(M), there exists a co-dimension 1 C∞-stratum Sg of F_u which is naturally co-oriented. The stratum Sg is made of elements (α, X) such that X has exactly one homoclinic orbit L whose homotopy class is g.

The goal of this talk is to show that there exists a co-dimension 1 C∞-stratum Sg (0) of Sg which lies in the closure of Sg^2. This result explains geometrically an easy algebraic relation holding in the Novikov ring associated with u.
We will mention how this study generalizes to produce some non-evident symmetric formulas holding in the Novikov ring.

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Lin Wang 氏 (Tsinghua University)
Viscosity solutions of Hamilton-Jacobi equations from a dynamical viewpoint (English)
[ 講演概要 ]
By establishing an implicit variational principle for contact Hamiltonian systems, we detect some properties of viscosity solutions of Hamilton-Jacobi equations of certain Hamilton-Jacobi equations depending on unknown functions, including large time behavior and regularity on certain sets. Besides, I will talk about some connections with contact geometry, thermodynamics and nonholonomic mechanics.

解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
Li Yutian 氏 (Department of Mathematics, Hong Kong Baptist University)
Small-time Asymptotics for Subelliptic Heat Kernels (English)
[ 講演概要 ]
Subelliptic operators are the natural generalizations of the Laplace- Beltrami operators, and they play important roles in geometry, several complex variables, probability and physics. As in the classical spectral theory for the elliptic operators, some geometrical properties of the induced subRiemannian geometry can be extracted from the analysis of the heat kernels for subelliptic operators. In this talk we shall review the recent progress in the heat kernel asymptotics for subelliptic operators. We concentrate on the small-time asymptotics of the heat kernel on the diagonal, or equivalently, the asymptotics for the trace. Our interest is to find the exact form of the leading term, and this will lead to a Weyl’s asymptotic formula for the subelliptic operators. This is a joint work with Professor Der-Chen Chang.

Lie群論・表現論セミナー

17:00-18:30   数理科学研究科棟(駒場) 122号室
Paul Baum 氏 (Penn State University)
MORITA EQUIVALENCE REVISITED
[ 講演概要 ]
Let X be a complex affine variety and k its coordinate algebra. A k- algebra is an algebra A over the complex numbers which is a k-module (with an evident compatibility between the algebra structure of A and the k-module structure of A). A is not required to have a unit. A k-algebra A is of finite type if as a k-module A is finitely generated. This talk will review Morita equivalence for k-algebras and will then introduce --- for finite type k-algebras ---a weakening of Morita equivalence called geometric equivalence. The new equivalence relation preserves the primitive ideal space (i.e. the set of isomorphism classes of irreducible A-modules) and the periodic cyclic homology of A. However, the new equivalence relation permits a tearing apart of strata in the primitive ideal space which is not allowed by Morita equivalence.

Let G be a connected split reductive p-adic group, The ABPS (Aubert- Baum-Plymen-Solleveld) conjecture states that the finite type algebra which Bernstein assigns to any given Bernstein component in the smooth dual of G, is geometrically equivalent to the coordinate algebra of the associated extended quotient. The second talk will give an exposition of the ABPS conjecture.

2015年07月13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
松本 佳彦 氏 (東京工業大学)
$L^2$ cohomology and deformation of Einstein metrics on strictly pseudo convex domains
[ 講演概要 ]
Consider a bounded domain of a Stein manifold, with strictly pseudo convex smooth boundary, endowed with an ACH-Kähler metric (examples being domains of $\mathbb{C}^n$ with their Bergman metrics or Cheng-Yau’s Einstein metrics). We give a vanishing theorem on the $L^2$ $\overline{\partial}$-cohomology group with values in the holomorphic tangent bundle. As an application, Einstein perturbations of the Cheng-Yau metric are discussed.

東京確率論セミナー

16:30-18:20   数理科学研究科棟(駒場) 128号室
講演者2名のため,開催時間がいつもと異なります.ご注意ください.
Mykhaylo Shkolnikov 氏 (Mathematics Department, Princeton University) 16:30-17:20
On interacting particle systems in beta random matrix theory
[ 講演概要 ]
I will first introduce multilevel Dyson Brownian motions and review how those extend to the setting of beta random matrix theory. Then, I will describe a connection between multilevel Dyson Brownian motions and interacting particle systems on the real line with local interactions. This is the first connection of this kind for values of beta different from 1 and 2. Based on joint work with Vadim Gorin.
Stefan Adams 氏 (Mathematics Institute, Warwick University) 17:30-18:20
Random field of gradients and elasticity
[ 講演概要 ]
Random fields of gradients are a class of model systems arising in the studies of random interfaces, random geometry, field theory, and elasticity theory. These random objects pose challenging problems for probabilists as even an a priori distribution involves strong correlations, and are likely to be an universal class of models combining probability, analysis and physics in the study of critical phenomena. They emerge in the following three areas, effective models for random interfaces, Gaussian Free Fields (scaling limits), and mathematical models for the Cauchy-Born rule of materials, i.e., a microscopic approach to nonlinear elasticity. The latter class of models requires that interaction energies are non-convex functions of the gradients. Open problems over the last decades include unicity of Gibbs measures, the scaling to GFF and strict convexity of the free energy. We present in the talk first results for the free energy and the scaling limit at low temperatures using Gaussian measures and rigorous renormalisation group techniques yielding an analysis in terms of dynamical systems. The key ingredient is a finite range decomposition for parameter dependent families of Gaussian measures. (partly joint work with S. Mueller & R. Kotecky)

2015年07月11日(土)

調和解析駒場セミナー

13:30-17:00   数理科学研究科棟(駒場) 128号室
出耒 光夫 氏 (岡山大学) 13:30 -15:00
An intrinsic square function on weighted Herz spaces with variable exponent
(日本語)
[ 講演概要 ]
本講演では、まずはじめに変動指数を用いて一般化されたMuckenhouptのウェイトのクラスについて解説する。このウェイトのクラスそのものの性質や重み付き変動指数Lebesgue空間でのHardy-Littlewoodの極大作用素の有界性との関連について述べる予定である。さらに、このウェイトをもつ重み付き変動指数Herz空間における
あるintrinsic square functionの有界性を各指数に適当な条件を仮定したもとで証明する。本講演の内容は、首都大学東京野井貴弘氏との共同研究に基づく。
堀内 利郎 氏 (茨城大学) 15:30 -17:00
Remarks on the strong maximum principle involving p-Laplacian
(日本語)
[ 講演概要 ]
Let $\Omega$ be a bounded domain of ${\bf R}^N (N\ge 1)$.
In this article, we shall study the strong maximum principle
for the following operator:
 $-\Delta_p+a(x)Q(\cdot)$.
Here $1 < p < \infty$, $0\le a\in L^1(\Omega)$, $a\ge 0$ a.e. in $\Omega$, $\Delta_p$ is a p-Laplacian and $Q(\cdot)$ is a nonlinear term satisfying the conditions $[Q_0]$ and $[Q_1]$.
Let $p^* = \max(1, p-1)$ and let $u\in L^1(\Omega)$, $u\ge 0$ a.e. in $\Omega$ such that
 $Q(u)\in L^1(\Omega), |\nabla u|\in L^{p^*}_{loc}(\Omega)$
and
 $\Delta_pu$ is a Radon measure on $\Omega$.
In addition, we assume that
 $-\Delta_pu+a(x)Q(u)\ge 0$ in $\Omega$
in the measure sense:
$\int_E\Delta_pu\le \int_EaQ(u)$
for every Borel set E $\subset$ $\Omega$. Then we prove that if $\tilde{u}=0$ on a set of positive p-capacity in $\Omega$,then $u=0$ a.e. in $\Omega$. Here $\tilde{u}$ is a quasicontinuous representative of $u$.
We also see the sharpness of the condition $[Q_1]$ by
constructing counter-examples.

2015年07月10日(金)

博士論文発表会

13:30-14:45   数理科学研究科棟(駒場) 128号室
中安 淳 氏 (東京大学大学院数理科学研究科)
On stability of viscosity solutions under non-Euclidean metrics(非ユークリッド距離構造の下での粘性解の安定性) (JAPANESE)

2015年07月09日(木)

東京無限可積分系セミナー

15:00-18:30   数理科学研究科棟(駒場) 056号室
野崎雄太 氏 (東大数理) 15:00-16:30
LMO 関手の拡張と形式的 Gauss 積分 (JAPANESE)
[ 講演概要 ]
Cheptea-葉廣-Massuyeau は,閉 3 次元多様体の LMO 不変量の拡張とし
て LMO 関手を導入した.
LMO 関手は「高々 1 個の境界成分を持つ曲面の間の Lagrangian コボルディズ
ムを射とするモノイダル圏」から「ある Jacobi 図の形式的級数を射とするモノ
イダル圏」へのテンソル積を保つ関手である.
本講演では,曲面が任意個数の境界成分を持つ場合に対する LMO 関手の拡張を
紹介する.
特に LMO 関手の構成において本質的である形式的 Gauss 積分について詳しく述
べたい.
加藤本子 氏 (東大数理) 17:00-18:30
高次元トンプソン群の相対エンド数について (JAPANESE)
[ 講演概要 ]
n 次元トンプソン群 nV (n は 1 以上の自然数)は、トンプソン群 V の一般化として Brin により 2004 年に定義された。V がカントール集合 C の自己同相群の部分群として表 されるのに対し、各 nV は C の n 個の直積の、自己同相群の部分群となっている。本講演 では nV のエンド数が 1 であること、また相対エンド数を無限大とする部分群が存在する ことについて述べる。相対エンド数を無限大とする部分群を構成する際の議論から、nV が Haagerup property を持つことが示される。また、nV がコンパクトケーラー多様体の 基本群でないことも示される。これらの結果は、V を扱った Farley の結果の拡張である。

2015年07月08日(水)

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 122号室
Marcel Bischoff 氏 (Vanderbilt Univ.)
Conformal field theory, subfactors and planar algebras

FMSPレクチャーズ

16:45-18:15   数理科学研究科棟(駒場) 122号室
Marcel Bischoff 氏 (Vanderbilt Univ.)
Conformal field theory, subfactors and planar algebras (ENGLISH)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

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