## 今後の予定

### 2015年07月06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

On the structure of holomorphic automorphism groups of generalized complex ellipsoids and generalized Hartogs triangles (JAPANESE)
[ 講演概要 ]
In this talk, we first review the structure of holomorphic automorphism groups of generalized complex ellipsoids and, as an application of this, we clarify completely the structure of generalized Hartogs triangles. Finally, if possible, I will mention some known results on proper holomorphic self-mappings of generalized complex ellipsoids, generalized Hartogs triangles, and discuss a related question to these results.

### 2015年07月07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

Representation varieties detect essential surfaces (JAPANESE)
[ 講演概要 ]
Extending Culler-Shalen theory, Hara and I presented a way to construct
certain kinds of branched surfaces (possibly without any branch) in a 3-
manifold from an ideal point of a curve in the SL_n-character variety.
There exists an essential surface in some 3-manifold known to be not
detected in the classical SL_2-theory. We show that every essential
surface in a 3-manifold is given by the ideal point of a line in the SL_
n-character variety for some n. The talk is partially based on joint
works with Stefan Friedl and Matthias Nagel, and also with Takashi Hara.

### 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

### 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

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．

べたい．

[ 講演概要 ]
n 次元トンプソン群 nV (n は 1 以上の自然数)は、トンプソン群 V の一般化として Brin により 2004 年に定義された。V がカントール集合 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 では nV のエンド数が 1 であること、また相対エンド数を無限大とする部分群が存在する ことについて述べる。相対エンド数を無限大とする部分群を構成する際の議論から、nV が Haagerup property を持つことが示される。また、nV がコンパクトケーラー多様体の 基本群でないことも示される。これらの結果は、V を扱った Farley の結果の拡張である。

### 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

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

An intrinsic square function on weighted Herz spaces with variable exponent
(日本語)
[ 講演概要 ]

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。

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 1Let 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

$L^2$ 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

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 Fu of (closed) Morse 1-forms in this class. In Morse theory, it is important to equip each α in Fu 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 Fu.
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 Fu 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 Fu which is naturally co-oriented. The stratum Sg is made of elements (α, X) such that X has exactly one homoclinic orbit ? 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.

### 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

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 ]

### 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

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.

### 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

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

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.

### 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23日(木)

#### 代数学コロキウム

14:00-15:00   数理科学研究科棟(駒場) 056号室
Haoyu Hu 氏 (東京大学数理科学研究科)
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.

#### 代数学コロキウム

15:15-16:15   数理科学研究科棟(駒場) 056号室

Explicit computation of the number of dormant opers and duality (Japanese)

### 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

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).

### 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

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28日(火)

#### 講演会

17:00-18:00   数理科学研究科棟(駒場) 056号室
Vincent Alberge 氏 (Université de Strasbourg)
Convergence of some horocyclic deformations to the Gardiner-Masur
boundary of Teichmueller space. (ENGLISH)
[ 講演概要 ]
It is well known that a point of the Teichmueller space and a measured foliation determine an isometric embedding of the hyperbolic disc to the Teichmueller space equipped with the so-called Teichmueller metric. In this talk, we will consider the image by this embedding of a particular horocycle whose points will be called an horocyclic deformation. To be more precise, we will be interested in the closure of this subset in the Gardiner-Masur compactification. As the embedding of the disc does not admit a continuous extension to boundaries, we cannot say that the boundary of the set of horocyclic deformations consists of one point.
However, according to Miyachi's results, we will see that it is the case if the given foliation is either a simple closed curve or a uniquely ergodic foliation.

### 2015年07月29日(水)

#### 博士論文発表会

16:00-17:15   数理科学研究科棟(駒場) 128号室

Accelerating convergence and tractability of multivariate numerical integration when the L1-norms of the higher order derivatives of the integrand grow at most exponentially（被積分関数の高階偏微分のL1ノルムの増大度が高々指数的である場合の多次元数値積分の加速的な収束と計算容易性） (JAPANESE)