## 過去の記録

#### 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

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.

(日本語)
[ 講演概要 ]

### 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

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

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 ]

### 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

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

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.

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

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

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

Concentrations for the travel cost of the simple random walk in random potentials

[ 講演概要 ]

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

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，

### 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

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

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

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．

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

#### 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

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

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

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

[ 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.

### 2015年10月22日(木)

#### FMSPレクチャーズ

16:00-16:50   数理科学研究科棟(駒場) 002号室

Hans-Otto Walther 氏 (University of Giessen)
The semiflow of a delay differential equation on its solution manifold (ENGLISH)
[ 講演概要 ]
The lecture surveys work after the turn of the millenium on well-posedness of initial value problems for di_erential equations with variable delay. The focus is on results which provide continuously di_erentiable solution operators, so that in case studies ingredients of dynamical systems theory, such as local invariant manifolds or Poincar_e return maps, become available. We explain why the familar theory of retarded functional di_erential equations [1,2,4] fails for equations with variable delay, discuss what has been achieved for the latter, for autonomous and for nonautonomous equations, with delays bounded or unbounded, and address open problems.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf

#### FMSPレクチャーズ

17:00-17:50   数理科学研究科棟(駒場) 002号室

Hans-Otto Walther 氏 (University of Giessen)
Shilnikov chaos due to state-dependent delay, by means of the fixed point index
(ENGLISH)
[ 講演概要 ]
What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional d(¥phi), with d(¥phi)=1 on a neighborhood of ¥phi=0, such that the equation x'(t)=-a x(t-d(x_t)) has a solution which is homoclinic to 0, with shift dynamics in its vicinity, whereas the linear equation x'(t)=-a x(t-1) with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.
The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf

#### 応用解析セミナー

16:00-17:50   数理科学研究科棟(駒場) 002号室
2つ講演があります．
Hans-Otto Walther 氏 (ギーセン大学)
(Part I) The semiflow of a delay differential equation on its solution manifold
(Part II) Shilnikov chaos due to state-dependent delay, by means of the fixed point index
(ENGLISH)
[ 講演概要 ]
(Part I) 16:00 - 16:50
The semiflow of a delay differential equation on its solution manifold
(Part II) 17:00 - 17:50
Shilnikov chaos due to state-dependent delay, by means of the fixed point index

(Part I)
The lecture surveys recent work on initial value problems for differential equations with variable delay. The focus is on differentiable solution operators.

The lecture explains why the theory for retarded functional differential equations which is familiar from monographs before the turn of the millenium fails in case of variable delay, discusses what has been achieved in this case, for autonomous and non-autonomous equations, with delays bounded and unbounded, and addresses open problems.

[detailed abstract]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf

(Part II)
What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional $d(\phi)$, with $d(\phi)=1$ on a neighborhood of $\phi=0$, such that the equation $x'(t)=-a x(t-d(x_t))$ has a solution which is homoclinic to $0$, with shift dynamics in its vicinity, whereas the linear equation $x'(t)=-a x(t-1)$ with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.

The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)

[detailed abstract]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf

[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf

### 2015年10月21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

The distribution of the duration of immunity determines the periodicity of Mycoplasma pneumoniae incidence. (JAPANESE)
[ 講演概要 ]
Estimating the periodicity of outbreaks is sometimes equivalent to the
prediction of future outbreaks. However, the periodicity may change
over time so understanding the mechanism of outbreak periodicity is
important. So far, mathematical modeling studies suggest several
drivers for outbreak periodicity including, 1) environmental factors
(e.g. temperature) and 2) host behavior (contact patterns between host
individuals). Among many diseases, multiple determinants can be
considered to cause the outbreak periodicity and it is difficult to
understand the periodicity quantitatively. Here we introduce our case
study of Mycoplasma pneumoniae (MP) which shows three to five year
periodic outbreaks, with multiple candidates for determinants for the
outbreak periodicity being narrowed down to the last one, the variance
of the length of the immunity duration. To our knowledge this is the
first study showing that the variance in the length of the immunity
duration is essential for the periodicity of the outbreaks.
[ 講演参考URL ]
http://researchers.general.hokudai.ac.jp/profile/ja.e3OkdvtshzEabOVZ2w5OYw==.html