過去の記録

過去の記録 ~08/17本日 08/18 | 今後の予定 08/19~

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
Francis Sergeraert 氏 (L'Institut Fourier, Univ. de Grenoble)
Discrete vector fields and fundamental algebraic topology.
(ENGLISH)
[ 講演概要 ]
Robin Forman invented the notion of Discrete Vector Field in 1997.
A recent common work with Ana Romero allowed us to discover the notion
of Eilenberg-Zilber discrete vector field. Giving the topologist a
totally new understanding of the fundamental tools of combinatorial
algebraic topology: Eilenberg-Zilber theorem, twisted Eilenberg-Zilber
theorem, Serre and Eilenberg-Moore spectral sequences,
Eilenberg-MacLane correspondence between topological and algebraic
classifying spaces. Gives also new efficient algorithms for Algebraic
Topology, considerably improving our computer program Kenzo, devoted
to Constructive Algebraic Topology. The talk is devoted to an
introduction to discrete vector fields, the very simple definition of
the Eilenberg-Zilber vector field, and how it can be used in various
contexts.

2013年04月24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
今井直毅 氏 (東京大学数理科学研究科)
Good reduction of ramified affinoids in the Lubin-Tate perfectoid space (ENGLISH)
[ 講演概要 ]
Recently, Weinstein finds some affinoids in the Lubin-Tate perfectoid space and computes their reduction in equal characteristic case. The cohomology of the reduction realizes the local Langlands correspondence for some representations of GL_h, which are unramified in some sense. In this talk, we introduce other affinoids in the Lubin-Tate perfectoid space in equal characteristic case, whose reduction realizes "ramified" representations of conductor exponent h+1. We call them ramified affinoids. We study the cohomology of the reduction and its relation with the local Langlands correspondence. This is a joint work with Takahiro Tsushima.

(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.)

Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
金沢 篤 氏 (University of British Columbia)
Calabi-Yau threefolds of Type K (ENGLISH)
[ 講演概要 ]
We will provide a full classification of Calabi-Yau threefolds of Type
K studied by Oguiso and Sakurai. Our study completes the
classification of Calabi-Yau threefolds with infinite fundamental
group. I will then discuss special Lagrangian T3-fibrations of
Calabi-Yau threefolds of type K. This talk is based on a joint work
with Kenji Hashimoto.

2013年04月23日(火)

数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室
野津裕史 氏 (早稲田大学高等研究所)
流れ問題のための圧力安定化特性曲線有限要素スキーム (JAPANESE)
[ 講演概要 ]
特性曲線法は流体粒子の軌跡に沿った離散化手法であり,上流化のアイデアが自然に入るため流れ問題に強靭である.さらに,大規模連立一次方程式の係数行列が対称という固有の長所をもつ.特性曲線法と有限要素法を組み合わせた特性曲線有限要素法は,それぞれの特徴を併せ持っており流れ問題の有力な数値解法である.我々は3次元問題をより簡便に行うことを念頭に圧力安定化特性曲線有限要素スキームを開発した.その理論解析および 2,3 次元数値計算の結果を示す.本講演では理論面に重点をおく予定である.特に,安定性評価における定数の拡散係数(Reynolds 数)依存性に注目して話したい.
[ 講演参考URL ]
http://www.infsup.jp

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
Andrei Pajitnov 氏 (Univ. de Nantes)
Twisted Novikov homology and jump loci in formal and hyperformal spaces (ENGLISH)
[ 講演概要 ]
Let X be a CW-complex, G its fundamental group, and R a repesentation of G.
Any element of the first cohomology group of X gives rise to an exponential
deformation of R, which can be considered as a curve in the space of
representations. We show that the cohomology of X with local coefficients
corresponding to the generic point of this curve is computable from a spectral
sequence starting from the cohomology of X with R-twisted coefficients. We
compute the differentials of the spectral sequence in terms of Massey products,
and discuss some particular cases arising in Kaehler geometry when the spectral
sequence degenerates. We explain the relation of these invariants and the
twisted Novikov homology. This is a joint work with Toshitake Kohno.

2013年04月22日(月)

講演会

16:45-18:15   数理科学研究科棟(駒場) 126号室
Stefano Olla 氏 (Univ. Paris-Dauphine)
Thermal conductivity and weak coupling (ENGLISH)
[ 講演概要 ]
We investigate the macroscopic thermal conductivity of a chain of anharmonic oscillators and more general systems, under weak coupling limits and energy conserving stochastic perturbations of the dynamics. In particular we establish a series expansion in the coupling parameter.

代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室
Professor Igor Reider 氏 (Universite d'Angers / RIMS)
Kodaira-Spencer classes, geometry of surfaces of general type and Torelli
theorem (ENGLISH)
[ 講演概要 ]
In this talk I will explain a geometric interpretation of Kodaira-Spencer classes and apply
it to the study of the differential of the period map of weight 2 Hodge structures for surfaces
of general type.
My approach is based on interpreting Kodaira-Spencer classes as higher rank bundles and
then studing their stability. This naturally leads to two parts:
1) unstable case
2) stable case.
I will give a geometric characterization of the first case and show how to relate the second
case to a special family of vector bundles giving rise to a family of rational curves. This family
of rational curves is used to recover the surface in question.

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
千葉 優作 氏 (東京工業大学)
Kobayashi hyperbolic imbeddings into low degree surfaces in three dimensional projective spaces (JAPANESE)
[ 講演概要 ]
We construct smooth irreducible curves of the lowest possible degree in quadric and cubic surfaces whose complements are Kobayashi hyperbolically imbedded into those surfaces. This is a joint work with Atsushi Ito.

2013年04月20日(土)

調和解析駒場セミナー

13:00-18:00   数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.
斉藤 洋樹 氏 (首都大学東京) 13:30-15:00
Directional maximal operators and radial weights on the plane
(JAPANESE)
[ 講演概要 ]
Let $\\Omega$ be a set of unit vectors and $w$ be a radial weight on the plane. We consider the weighted directional maximal operator defined by
$M_{\\Omega,w}f(x):=\\sup_{x\\in R\\in \\cB_{\\Omega}}\\frac{1}{w(R)}\\int_{R}|f(y)|w(y)dy$,
where $\\cB_{\\Omega}$ denotes the all rectangles on the plane whose longest side is parallel to some unit vector in $\\Omega$ and $w(R)$ denotes $\\int_{R}w$.
In this talk we give a sufficient condition of the weight
for an almost-orthogonality principle related to these maximal operators to hold. The condition allows us to get weighted norm inequality
$\\|M_{\\Omega,w}f\\|_{L^2(w)}\\le C \\log N \\|f\\|_{L^2(w)}$,
when $w(x)=|x|^a$, $a>0$, and $\\Omega$ is a set of unit vectors on the plane with cardinality $N\\gg 1$.
野井 貴弘 氏 (中央大学) 15:30-17:00
変動指数ベゾフ空間におけるトレース作用素の有界性について (JAPANESE)
[ 講演概要 ]
変動指数ベゾフ空間はAlmeidaとHasto(2010, J.Funct.Anal)により導入された関数空間であり, ベゾフ空間の可積分指数, 数列指数, 滑らかさを表す指数をlog-Holder連続な関数に置き換えた関数空間である. (可積分指数, 数列指数に対しては, さらに値域が[1, $\\infty$)に含まれる条件を課す. )変動指数トリーベル-リゾルキン空間についてはDiening, HastoとRoudenko(2009, J.Funct.Anal)により導入され, 原子分解によりトレース作用素の有界性を示した. 変動指数ベゾフ空間に関するトレース作用素の結果については, 数列指数が定数である場合のみAlmeidaとHastoにより2011年に開催された国際研究集会(2nd International workshop on Interpolation Theory, Function spaces and Related Topics)で実補間を応用することにより得られている.
本発表では, クォーク分解を用いることにより, 数列指数も変動指数である変動指数ベゾフ空間におけるトレース作用素の有界性を示していきたい.

2013年04月19日(金)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
北海道大学のHPには、第1回(2004年9月29日)~第38回(2008年10月15日)までの情報が掲載されております。
石井 克幸 氏 (神戸大学)
An approximation scheme for the anisotropic and the planar crystalline curvature flow (JAPANESE)
[ 講演概要 ]
In 2004 Chambolle proposed an algorithm for the mean curvature flow based on a variational problem. Since then, some extensions of his algorithm have been studied.
In this talk we would like to discuss the convergence of the anisotropic variant of his algorithm by use of the anisotropic signed distance function. An application to the approximation for the planar motion by crystalline curvature is also discussed.

2013年04月18日(木)

幾何コロキウム

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.
長友康行 氏 (明治大学)
Harmonic maps into Grassmannian manifolds (JAPANESE)
[ 講演概要 ]
A harmonic map from a Riemannian manifold into a Grassmannian manifold is characterized by a vector bundle, a space of sections of the bundle and the Laplace operator. This characterization can be considered as a generalization of Theorem of Takahashi on minimal immersions into a sphere (J.Math.Soc.Japan 18 (1966)) and implies the well-known fact that the Kodaira embedding is a harmonic map.

We apply the main result to generalize a Theorem of do Carmo and Wallach (Ann.of Math. 93 (1971)) and describe a moduli space of harmonic maps with constant energy densities and some properties about pull-back bundles and connections from a Riemannian homogeneous space into a Grassmannian. We give some applications including a rigidity of minimal immersions from the complex projective line to complex projective spaces (S.Bando and Y.Ohnita, J. Math. Soc. Japan 39 (1987)).

The ADHM-construction of instantons gives a family of maps into Grassmannians via monad theory on the twistor space. These maps are, in general, not harmonic maps, but are similar to maps obtained in our generalized do Carmo-Wallach theorem. We compare these two constructions of moduli spaces.

2013年04月17日(水)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室
Tamar Friedmann 氏 (Univ. Rochester)
Singularities, algebras, and the string landscape (ENGLISH)

2013年04月16日(火)

Lie群論・表現論セミナー

16:30-18:30   数理科学研究科棟(駒場) 126号室
Michael Pevzner 氏 (Reims University) 16:30-17:30
Non-standard models for small representations of GL(n,R) (ENGLISH)
[ 講演概要 ]
We shall present new models for some parabolically induced
unitary representations of the real general linear group which involve Weyl symbolic calculus and furnish very efficient tools in studying branching laws for such representations.
Pierre Clare 氏 (Penn. State University, USA) 17:30-18:30
Degenerate principal series of symplectic groups (ENGLISH)
[ 講演概要 ]
We will discuss properties of representations of symplectic groups induced from maximal parabolic subgroups of Heisenberg type, including K-types formulas, expressions of intertwining operators and the study of their spectrum.

2013年04月15日(月)

講演会

15:00-16:30   数理科学研究科棟(駒場) 126号室
Janna Lierl 氏 (University of Bonn)
Two-sided bounds for the Dirichlet heat kernel on inner uniform domains (ENGLISH)
[ 講演概要 ]
I will present sharp two-sided bounds for the heat kernel in domains with Dirichlet boundary conditions. The domain is assumed to satisfy an inner uniformity condition. This includes any convex domain, the complement of any convex domain in Euclidean space, and the interior of the Koch snowflake.
The heat kernel estimates hold in the abstract setting of metric measure spaces equipped with a (possibly non-symmetric) Dirichlet form. The underlying space is assumed to satisfy a Poincare inequality and volume doubling.
The results apply, for example, to the Dirichlet heat kernel associated with a divergence form operator with bounded measurable coefficients and symmetric, uniformly elliptic second order part.
This is joint work with Laurent Saloff-Coste.

講演会

16:45-18:15   数理科学研究科棟(駒場) 126号室
Amir Dembo 氏 (Stanford University)
Persistence Probabilities (ENGLISH)
[ 講演概要 ]
Persistence probabilities concern how likely it is that a stochastic process has a long excursion above fixed level and of what are the relevant scenarios for this behavior. Power law decay is expected in many cases of physical significance and the issue is to determine its power exponent parameter. I will survey recent progress in this direction (jointly with Jian Ding, Fuchang Gao, and Sumit Mukherjee), dealing with random algebraic polynomials of independent coefficients, iterated partial sums and other auto-regressive sequences, and with the solution to heat equation initiated by white noise.

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
Nikolay Shcherbina 氏 (University of Wuppertal)
On defining functions for unbounded pseudoconvex domains (ENGLISH)
[ 講演概要 ]
We show that every strictly pseudoconvex domain $\Omega$ with smooth boundary in a complex manifold $M$ admits a global defining function, i.e. a smooth plurisubharmonic function $\varphi \colon U \to \mathbf{R}$ defined on an open neighbourhood $U \subset M$ of $\Omega$ such that $\Omega =\{ \varphi < 0 \}$, $d\varphi \not= 0$ on $b\Omega$ and $\varphi$ is strictly plurisubharmonic near $b\Omega$. We then introduce the notion of the kernel $K(\Omega)$ of an arbitrary domain $\Omega \subset M$ as the set of all points where every smooth and bounded from above plurisubharmonic function on $\Omega$ fails to be strictly plurisubharmonic. If $\Omega$ is not relatively compact in $M$, then in general $K(\Omega)$ is nonempty, even in the case when $M$ is Stein. It is shown that every strictly pseudoconvex domain $\Omega \subset M$ with smooth boundary admits a global defining function that is strictly plurisubharmonic precisely in the complement of $K(\Omega)$. We then investigate properties of the kernel. Among other results we prove 1-pseudoconcavity of the kernel, we show that in general the kernel does not possess any analytic structure, and we investigate Liouville type properties of the kernel.

2013年04月11日(木)

幾何コロキウム

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.
Jeff Viaclovsky 氏 (University of Wisconsin)
Critical metrics on connected sums of Einstein four-manifolds (ENGLISH)
[ 講演概要 ]
I will discuss a gluing procedure designed to obtain critical metrics of quadratic Riemannian functionals on connected sums of certain Einstein four-manifolds. Start with two Einstein four-manifolds of positive scalar curvature which are "rigid". Using the Green's function for the conformal Laplacian, convert one of these into an asymptotically flat (AF) scalar-flat metric. A "naive" approximate critical metric is obtained by identifying the boundary of a large ball in the AF metric with the boundary of a small ball in the other compact Einstein metric, using cutoff functions to glue together the AF metric with a suitably scaled compact metric in order to obtain a smooth metric on the connected sum. It turns out that this naive approximate metric is too rough, and must be refined in order to compute the leading term of the Kuranishi map. The main application is an existence result using two well-known Einstein manifolds as building blocks: the Fubini-Study metric on $¥mathbb{CP}^2$ and the product metric on $S^2 ¥times S^2$. Using these factors in various gluing configurations, a zero of the Kuranishi map is then found for a specific quadratic Riemannian functional on certain connected sums. The exact functional depends on the geometry of the factors, and also on the mass of the AF metric. Using certain quotients of $S^2 ¥times S^2$ as one of the gluing factors, several non-simply connected examples are also obtained. This is joint work with Matt Gursky.

2013年04月10日(水)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室
武石拓也 氏 (東大数理)
On nuclearity of $C^*$-algebras associated with Fell bundles over \\'etale groupoids (ENGLISH)

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
Deepam Patel 氏 (University of Amsterdam)
Motivic structure on higher homotopy of non-nilpotent spaces (ENGLISH)
[ 講演概要 ]
In his fundamental paper on the projective line minus three points, Deligne constructed certain extensions of mixed Tate motives arising from the fundamental group of the projective line minus three points. Since then, motivic structures on homotopy groups have been studied by many authors. In this talk, we will construct a motivic structure on the (nilpotent completion of) n-th homotopy group of P^{n} minus n+2 hyperplanes in general position.

(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.)

2013年04月09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
藤 博之 氏 (東京大学大学院数理科学研究科)
色付きHOMFLYホモロジーと超A-多項式 (JAPANESE)
[ 講演概要 ]
本講演では,結び目に対する色付きHOMFLYホモロジーとその漸近的振る舞いに関する研究を紹介する.近年,色付きHOMFLY多項式の圏化がスペクトル系列に基づく公理系による定義と位相的弦理論に基づく物理的定義の双方が提唱され,それらの興味深い一致が様々な形で確かめられている.我々の研究では,完全対称表現に対する色付きHOMFLYホモロジーの漸近的振る舞いに関して,体積予想と類似の解析を行い,その結果,A-多項式の一般化となる“超 A-多項式”を通じて,色付きHOMFLYホモロジーのある量子構造が見出された.本講演では,こうした圏化の側面について,物理的解釈を交えながら紹介したい.尚,本講演はS. Gukov, M. Stosic, P. Sulkowski の3氏との共同研究に基づく.

Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
笹木集夢 氏 (東海大学)
A characterization of non-tube type Hermitian symmetric spaces by visible actions
(JAPANESE)
[ 講演概要 ]
We consider a non-symmetric complex Stein manifold D
which is realized as a line bundle over the complexification of a non-compact irreducible Hermitian symmetric space G/K.

In this talk, we will explain that the compact group action on D is strongly visible in the sense of Toshiyuki Kobayashi if and only if G/K is of non-tube type.
In particular, we focus on our construction of slice which meets every orbit in D from the viewpoint of group theory, namely,
we find an A-part of a generalized Cartan decomposition for homogeneous space D.

We note that our choice of A-part is an abelian.

2013年04月08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
二木 昭人 氏 (東大数理)
ケーラー・アインシュタイン計量と K 安定性 (JAPANESE)
[ 講演概要 ]
ケーラー・アインシュタイン計量の存在と K 安定性の同値性に関する Chen-Donaldson-Sun, Tian の証明の概略を解説する.

2013年04月02日(火)

Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
大島芳樹 氏 (Kavli IPMU, the University of Tokyo)
Zuckerman導来関手加群の離散的分岐則 (JAPANESE)
[ 講演概要 ]
We consider the restriction of Zuckerman's derived functor modules with respect to symmetric pairs of real reductive groups. When they are discretely decomposable, explicit formulas for the branching laws are obtained by using a realization as D-module on the flag variety and the generalized BGG resolution. In this talk we would like to illustrate how to derive the formulas with a few examples.

2013年03月30日(土)

東京無限可積分系セミナー

13:30-15:30   数理科学研究科棟(駒場) 002号室
Simon Wood 氏 (Kavli IPMU)
On the extended algebra of type sl_2 at positive rational level (ENGLISH)
[ 講演概要 ]
I will be presenting my recent work with Akihiro Tsuchiya
(arXiv:1302.6435).
I will explain how to construct a certain VOA called the "extended
algebra of type sl_2 at positive rational level"
as a subVOA of a lattice VOA, by means of screening operators. I will
then show that this VOA carries a kind of exterior sl_2 action and then
show how one can compute the structure Zhu's algebra and the Poisson
algebra as well as classify all simple modules by using the screening
operators and the sl_2 action. Important concepts such as screening
operators or Zhu's algebra and the Poisson algebra of a VOA will be
reviewed in the talk.

2013年03月19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) 002号室
Tea: 16:00 - 16:30 コモンルーム
川室 圭子 氏 (University of Iowa)
Open book foliation and application to contact topology (ENGLISH)
[ 講演概要 ]
Open book foliation is a generalization of Birman and Menasco's braid foliation. Any 3-manifold admits open book decompositions. Open book foliation is a singular foliation on an embedded surface, and is define by the intersection of a surface and the pages of the open book decomposition. By Giroux's identification of open books and contact structures one can use open book foliation method to study contact structures. In this talk I define the open book foliation and show some applications to contact topology. This is joint work with Tetsuya Ito (University of British Columbia).

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