過去の記録

過去の記録 ~08/17本日 08/18 | 今後の予定 08/19~

2015年11月17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 : Common Room 16:30 -- 17:00
片長 敦子 氏 (信州大学)
Topology of some three-dimensional singularities related to algebraic geometry (ENGLISH)
[ 講演概要 ]
In this talk, we deal with hypersurface isolated singularities. First, we will recall
some topological results of singularities. Next, we will sketch the classification of
singularities in algebraic geometry. Finally, we will focus on the three-dimensional
case and discuss some results obtained so far.

代数学コロキウム

18:00-19:00   数理科学研究科棟(駒場) 117号室
いつもと曜日が異なりますのでご注意ください
Dennis Gaitsgory 氏 (Harvard University & IHES)
The Tamagawa number formula over function fields. (English)
[ 講演概要 ]
Let G be a semi-simple and simply connected group and X an algebraic curve. We consider $Bun_G(X)$, the moduli space of G-bundles on X. In their celebrated paper, Atiyah and Bott gave a formula for the cohomology of $Bun_G$, namely $H^*(Bun_G)=Sym(H_*(X)\otimes V)$, where V is the space of generators for $H^*_G(pt)$. When we take our ground field to be a finite field, the Atiyah-Bott formula implies the Tamagawa number conjecture for the function field of X.

The caveat here is that the A-B proof uses the interpretation of $Bun_G$ as the space of connection forms modulo gauge transformations, and thus only works over complex numbers (but can be extend to any field of characteristic zero). In the talk we will outline an algebro-geometric proof that works over any ground field. As its main geometric ingredient, it uses the fact that the space of rational maps from X to G is homologically contractible. Because of the nature of the latter statement, the proof necessarily uses tools from higher category theory. So, it can be regarded as an example how the latter can be used to prove something concrete: a construction at the level of 2-categories leads to an equality of numbers.

(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.)

2015年11月16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) 128号室
宮地 秀樹 氏 (大阪大学)
Towards the complex geometry of Teichmuller space with extremal length (English)
[ 講演概要 ]
In this talk, in aiming for studying a relation between the topological aspect and the complex analytical aspect of Teichmuller space, I will discuss a complex analytic property of extremal length functions. More precisely, I will give a concrete formula of the Levi form of the extremal length functions for ``generic” measured foliations and show that the reciprocal of the extremal length function is plurisuperharmonic. As a corollary, I will give alternate proofs of S. Krushkal results that the distance function for the Teichmuller distance is plurisubharmonic, and Teichmuller space is hyperconvex. If time permits, I will give a topological description of the Levi form with using the Thurston's symplectic form.

FMSPレクチャーズ

15:00-16:00,16:30-17:00   数理科学研究科棟(駒場) 大講義室号室
中央大学ENCOUNTER with MATHEMATICS共催
Yakov Eliashberg 氏 (Stanford University)
Crossroads of symplectic rigidity and flexibility (ENGLISH)
[ 講演概要 ]
The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.
In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.
[ 講演参考URL ]
http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
Artan Sheshmani 氏 (IPMU/ Ohio State University)
Counting curves on surface in Calabi-Yau threefolds and the proof of S-duality modularity conjecture (English)
[ 講演概要 ]
I will talk about recent joint works with Amin Gholampour, Richard Thomas and Yukinobu Toda, on an algebraic-geometric proof of the S-duality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic Calabi-Yau threefold. Our strategy is to first use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over the relative Hilbert scheme of points on surfaces and then prove modularity; More precisely, together with Gholampour we have proven that the generating series, associated to the top intersection numbers of the Hilbert scheme of points, relative to an effective divisor, on a smooth quasi-projective surface is a modular form. This is a generalization of the result of Okounkov-Carlsson, where they used representation theory and the machinery of vertex operators to prove this statement for absolute Hilbert schemes. These intersection numbers eventually, together with the generating series of Noether-Lefschetz numbers as I will explain, will provide the ingredients to achieve a complete algebraic-geometric proof of S-duality modularity conjecture.

2015年11月14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
中村 昌平 氏 (首都大学東京) 13:30-15:00
The sufficient condition for the Fatou property of weighted block spaces
(日本語)
[ 講演概要 ]
In this talk, we discuss the weighted block space which corresponds to the predual space of the Samko type weighted Morrey space. Recently, Prof.s Sawano and Tanaka proved the Fatou property of unweighted block spaces.
Meanwhile, we proposed a new condition, so called the weighted integral condition, to show the boundedness of some classical operators on weighted Morrey spaces.
Our purpose is to prove that the weighted integral condition becomes a sufficient condition for the Fatou property of the weighted block space.
町原 秀二 氏 (埼玉大学) 15:30-17:00
空間1次元Chern-Simons-Dirac方程式系の初期値問題の非適切性
(日本語)
[ 講演概要 ]
空間1次元Chern-Simons-Dirac方程式系の初期値問題の適切性をソボレフ空間で考える。問題が適切である指数の範囲と非適切である指数の範囲を紹介し、
方程式の構造やソボレフ空間の積評価との関係を観察する。証明は特に非適切性に関して紹介したい。特殊な初期値を設定することにより、解表示を得て、その解関数に対するソボレフ空間での取り扱いについて議論する。本研究は信州大学岡本葵氏との共同研究である。

2015年11月13日(金)

FMSPレクチャーズ

15:00-16:00,16:30-17:30   数理科学研究科棟(駒場) 大講義室号室
中央大学ENCOUNTER with MATHEMATICS共催
Yakov Eliashberg 氏 (Stanford University)
Crossroads of symplectic rigidity and flexibility (ENGLISH)
[ 講演概要 ]
The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.
In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.
[ 講演参考URL ]
http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html

幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 126号室
正井 秀俊 氏 (東京大学)
ランダム閉3次元写像トーラスの対称性について (Japanese)
[ 講演概要 ]
閉曲面の写像類群上のランダムウォークを考え,それらから得られる写像トーラスをランダム写像トーラスと呼ぶ.ランダム写像トーラスは漸近的に確率1で閉双曲多様体になることが知られている.また,閉双曲多様体の写像類群は有限群となることが知られている.この講演ではランダム写像トーラスの写像類群は漸近的に確率1で自明となることを証明する.

2015年11月10日(火)

トポロジー火曜セミナー

17:30-18:30   数理科学研究科棟(駒場) 056号室
Tea : Common Room 17:00 -- 17:30
五味 清紀 氏 (信州大学理学部)
Topological T-duality for "Real" circle bundle (JAPANESE)
[ 講演概要 ]
Topological T-duality originates from T-duality in superstring theory,
and is first studied by Bouwkneght, Evslin and Mathai. The duality
basically consists of two parts: The first part is that, for any pair
of a principal circle bundle with `H-flux', there is another `T-dual'
pair on the same base space. The second part states that the twisted
K-groups of the total spaces of principal circle bundles in duality
are isomorphic under degree shift. This is the most simple topological
T-duality following Bunke and Schick, and there are a number of
generalizations. The generalization I will talk about is a topological
T-duality for "Real" circle bundles, motivated by T-duality in type II
orbifold string theory. In this duality, a variant of Z_2-equivariant
K-theory appears.

2015年11月09日(月)

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
伊藤由佳理 氏 (名古屋大学)
3-dimensional McKay correspondence (English)
[ 講演概要 ]
The original McKay correspondence is a relation between group theory of a finite subgroup G of SL(2,C) and geometry of the minimal resolution of the quotient singularity by G, and was generalized several ways. In particular, 3-dimensional generalization was extended to derived categorical eqivalence and the G-Hilbert scheme was useful to explain the correspondence. However, most results hold only for abelian subgroups. In this talk, I would like to introduce an iterated G-Hilbert scheme and show more geometrical McKay correspondence for non-abelian subgroups.

2015年11月05日(木)

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 126号室
いつもと部屋と曜日が違います。The day of the week and room are different from usual.
大川新之介 氏 (阪大)
Compact moduli of marked noncommutative del Pezzo surfaces via quivers (English)
[ 講演概要 ]
I will introduce certain GIT construction via quivers of compactified moduli spaces of marked noncommutative del Pezzo surfaces. For projective plane, quadric surface, and those of degree 3, 2, 1, we obtain projective toric varieties of dimension 2, 3, 8, 9, 10, respectively. Then I will discuss relations with deformation theory of abelian categories, blow-up of noncommutative projective planes, and three-block exceptional collections due to Karpov and Nogin. This talk is based on joint works in progress with Tarig Abdelgadir and Kazushi Ueda.

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 123号室
部屋が普段と異なるのでご注意ください
Henri Berestycki 氏 (フランス高等社会科学院(EHESS))
The effect of a line with fast diffusion on Fisher-KPP propagation (ENGLISH)
[ 講演概要 ]
I will present a system of equations describing the effect of inclusion of a line (the "road") with fast diffusion on biological invasions in the plane. Outside of the road, the propagation is of the classical Fisher-KPP type. We find that past a certain precise threshold for the ratio of diffusivity coefficients, the presence of the road enhances the speed of global propagation. I will discuss several further effects such as transport or reaction on the road. I will also discuss the influence of various parameters on the asymptotic behaviour of the invasion speed and shape. I report here on results from a series of joint works with Jean-Michel Roquejoffre and Luca Rossi.

2015年11月02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) 128号室
下部 博一 氏 (大阪大学)
A class of non-Kahler manifolds (Japanese)
[ 講演概要 ]
We consider a special case of compact complex manifolds which are said to be super strongly Gauduchon manifolds. A super strongly Gauduchon manifold is a complex manifold with a super strongly Gauduchon metric. We mainly consider non-Kähler super strongly Gauduchon manifolds. We give a cohomological condition for a compact complex manifold to have a super strongly Gauduchon metric, and give examples of non-trivial super strongly Gauduchon manifolds from nil-manifolds. We also consider its stability under small deformations and proper modifications of super strongly Gauduchon manifolds.

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
久保田 直樹 氏 (日本大学理工学部)
Concentrations for the travel cost of the simple random walk in random potentials

[ 講演概要 ]
多次元正方格子の各点に,(独立同分布に)ランダムなポテンシャルを配置する.
このとき,ポテンシャルによって重み付けられた測度の下で,ランダムウォークが
原点からある点へ移動するために必要とするコスト(到達コスト)を考える.
到達コストの大まかな漸近挙動は,ZernerやMourratにより既に調べられている.
そこで本講演では到達コストに対するconcentration inequalityを取り扱うことで,
到達コストとその期待値の誤差を評価し,漸近挙動についてより詳しく調べる.

2015年10月30日(金)

FMSPレクチャーズ

15:00-16:15   数理科学研究科棟(駒場) 128号室
Arnaud Ducrot 氏 (University of Bordeaux)
Asymptotic behaviour of a nonlocal logistic equation (ENGLISH)
[ 講演概要 ]
In this talk we consider a nonlocal logistic equation endowed with periodic boundary conditions modelling the motion of cells. This equation takes into account birth and death process using a simple logistic effect while the motion of particles follows a nonlocal Darcy law with a smooth kernel.
We first investigate the well-posedness of the problem before investigating the long time behaviour of the solutions. The lack of asymptotic compactness of the semiflow is overcome by using a Young measure framework. Using a suitable energy functional, we
establish the convergence of the solutions with respect to the Young measure topology.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ducrot.pdf

FMSPレクチャーズ

16:30-17:45   数理科学研究科棟(駒場) 128号室
Peter Bates 氏 (Michigan State University)
How should a drop of liquid on a smooth curved surface move in zero gravity? (ENGLISH)
[ 講演概要 ]
Questions such as this may be formulated as questions regarding solutions to nonlinear evolutionary partial differential equations having a small coefficient on the leading order derivative term. Evolutionary partial differential equations may be regarded as (semi-) dynamical systems in an infinite-dimensional space. An abstract theorem is proved giving the existence of an invariant manifold for a semi-dynamical system when an approximately invariant manifold exists with a certain topological nondegeneracy condition in a neighborhood. This is then used to prove the existence of eternal solutions to the nonlinear PDE and answer the question about the motion of a droplet on a curved manifold. The abstract theorem extends fundamental work of Hirsch-Pugh-Shub and Fenichel on the perturbation of invariant manifolds from the 1970's to infinite-dimensional semi-dynamical systems.
This represents joint work with Kening Lu and Chongchun Zeng.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bates.pdf

2015年10月28日(水)

数理人口学・数理生物学セミナー

14:55-16:40   数理科学研究科棟(駒場) 128演習室号室
大泉嶺 氏 (厚生労働省)
r/K選択説における確率制御理論の応用 (JAPANESE)
[ 講演概要 ]
r/K 選択説が提唱されてから半世紀になろうとしている.この仮説は生物の生活
史戦略の中で現れる、短命多産多死、長寿少産少死の戦略を持つ種の違いをロジ
スティック方程式を構成するパラメータ、内的増加率rと環境収容力Kをもちいて
種がその人口規模に応じてどちらか一方のパラメータを最大化させる戦略の違い
であると論じたものである.この説は発表当初から賛否両論を巻き起こしてきた.
特に論争の的となったのは人口密度が環境収容力付近にある場合に、生活史進化
が環境収容力を最大化するために少産少死長寿という特質を獲得するという主張
である.実証研究はこの主張をウミガメや樹木、サルの群れ構造などの例を用い
て反駁してきた.2000年代に入るまでに様々な理論モデルや実証研究結果が示さ
れたが、議論の盛り上がりは“飽和した人口の中で起こる生活史進化とは何か?”
という疑問を残したまま停滞している.そこで、本研究では非線形齢―状態構造
モデルと生活史戦略理論を確率制御理論によって統合したモデルを構築し、この
問題に適用した.その結果、密度効果と確率制御理論の持つ生活史ノイズを組み
合わせることによって、飽和人口における最適戦略は従来のr/K選択説よりも多
様である事が示せた.本講演では、その結果を紹介したい.

作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 118号室
酒匂宏樹 氏 (新潟大)
Uniformly locally finite metric spaces and Folner type conditions

2015年10月27日(火)

代数学コロキウム

18:00-19:00   数理科学研究科棟(駒場) 002号室
曜日・部屋がいつもと異なりますのでご注意ください
朝倉政典 氏 (北海道大学)
On the period conjecture of Gross-Deligne for fibrations (English)
[ 講演概要 ]
The period conjecture of Gross-Deligne asserts that the periods of algebraic varieties with complex multiplication are products of values of the gamma function at rational numbers. This is proved for CM elliptic curves by Lerch-Chowla-Selberg, and for abelian varieties by Shimura-Deligne-Anderson. However the question in the general case is still open. In this talk, we verify an alternating variant of the period conjecture for the cohomology of fibrations with relative multiplication. The proof relies on the Saito-Terasoma product formula for epsilon factors of integrable regular singular connections and the Riemann-Roch-Hirzebruch theorem. This is a joint work with Javier Fresan.

(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.)

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 : Common Room 16:30 -- 17:00
Yuanyuan Bao 氏 (東京大学大学院数理科学研究科)
Heegaard Floer homology for graphs (JAPANESE)
[ 講演概要 ]
Ozsváth and Szabó defined the Heegaard Floer homology (HF) for a closed oriented 3-manifold. The definition was then generalized to links embedded in a 3-manifold and the manifolds with boundary (sutured and bordered manifolds). In the case of links, there is a beautiful combinatorial way to rewrite the original definition of HF, which was defined on a Heegaard diagram of the given link, by using grid diagram. For a balanced bipartite graph, we defined its Heegaard diagram and the HF for it. Around the same time, Harvey and O’Donnol defined the combinatorial HF for transverse graphs (see the definition in [arXiv:1506.04785v1]). In this talk, we compare these two methods.

トポロジー火曜セミナー

15:00-16:30   数理科学研究科棟(駒場) 056号室
Jianfeng Lin 氏 (UCLA)
The unfolded Seiberg-Witten-Floer spectrum and its applications
(ENGLISH)
[ 講演概要 ]
Following Furuta's idea of finite dimensional approximation in
the Seiberg-Witten theory, Manolescu defined the Seiberg-Witten-Floer
stable homotopy type for rational homology three-spheres in 2003. In
this talk, I will explain how to construct similar invariants for a
general three-manifold and discuss some applications of these new
invariants. This is a joint work with Tirasan Khandhawit and Hirofumi
Sasahira.

2015年10月26日(月)

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室
Lawrence Ein 氏 (University of Illinois at Chicago)
Asymptotic syzygies and the gonality conjecture (English)
[ 講演概要 ]
We'll discuss my joint work with Lazarsfeld on the gonality conjecture about the syzygies of a smooth projective curve when it is embedded into the projective space by the complete linear system of a sufficiently very ample line bundles. We'll also discuss some results about the asymptotic syzygies f higher dimensional varieties.

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
松本 和子 氏 (東京理科大学)
The Fubini-distance functions to pseudoconvex domains in $\mathbb{C}\mathbb{P}^2$ (Japanese)
[ 講演概要 ]
In this talk, we would like to present two explicit formulas for the Levi forms of the Fubini-Study distance functions to complex or real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. This is the first step for us to approach the non-existence conjecture of Levi-flat real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. We would like to also discuss a certain important quantity found in the formulas.

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
Fredrik Lindgren 氏 (大阪大学)
Numerical approximation of spinodal decomposition in the presence of noise (English)
[ 講演概要 ]
Numerical approximations of stochastic partial differential equations (SPDE) has evolved to a vivid subfield of computational mathematics in the last decades. It poses new challenges both for numerical analysis and the theory of SPDE.

In this talk we will discuss the strength and weaknesses of the \emph{semigroup approach} to SPDE when it is combined with the idea of viewing a single-step method in time as a \emph{rational approximation of a semigroup}. We shall apply this framework to the stochastic Allen-Cahn equation, a parabolic semi-linear SPDE where the non-linearity is non-globally Lipschitz continuous, but has a \emph{one-sided Lipschitz condition}, and the deterministic equation has a Lyapunov functional.

We focus on semi-discretisation in time, the first step in Rothe's method, and show how the semigroup approach allows for convergence proofs under the assumption that the numerical solution admits moment bounds. However, this assumption turns out to be difficult to verify in the semi-group framework, and the rates achieved are not sharp. This is due to the fact that the one-sided Lipschitz condition, being a variational inequality, can't be utilised. We thus turn to variational methods to solve this issue.

If time admits we shall also comment on the stochastic Cahn-Hilliard equation where the non-linearity has a one-sided Lipschitz condition in a lower norm, only. However, the fact of convergence can still be proved.

This is joint work with Daisuke Furihata (Osaka University), Mih\'aly Kov\'acs (University of Otago, New Zealand), Stig Larsson (Chalmers University of Technology, Sweden) and Shuji Yoshikawa (Ehime University).

2015年10月23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
大鳥羽 暢彦 氏 (慶應義塾大学)
球面束上のスカラー曲率一定計量 (Japanese)
[ 講演概要 ]
この講演は Jimmy Petean 氏との共同研究に基づく.
2つの Riemann 多様体の捻れ積 (より正確には, 全測地的ファイバーを持つ Riemann 沈め込みの全空間) の上で山辺 PDE を解析する我々の試みについて話す. 例として, それぞれ内積つきのベクトル束 $E$ と直線束 $L$ の Whitney 和の単位球面束 $U(E \oplus L)$ の上にスカラー曲率一定計量を構成し, この場合にはどのようにして山辺 PDE の解の個数を評価できるか説明する.

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