## 過去の記録

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 126号室

Strong Tools in Free Probability Theory

### 2018年10月30日(火)

#### 解析学火曜セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室

Spectral structure of the Neumann-Poincaré operator in three dimensions: Willmore energy and surface geometry (日本語)
[ 講演概要 ]
The Neumann-Poincaré operator (abbreviated by NP) is a boundary integral operator naturally arising when solving classical boundary value problems using layer potentials. If the boundary of the domain, on which the NP operator is defined, is $C^{1, \alpha}$ smooth, then the NP operator is compact. Thus, the Fredholm integral equation, which appears when solving Dirichlet or Neumann problems, can be solved using the Fredholm index theory.
Regarding spectral properties of the NP operator, the spectrum consists of eigenvalues converging to $0$ for $C^{1, \alpha}$ smooth boundaries. Our main purpose here is to deduce eigenvalue asymptotics of the NP operators in three dimensions. This formula is the so-called Weyl's law for eigenvalue problems of NP operators. Then we discuss relationships among the Weyl's law, the Euler characteristic and the Willmore energy on the boundary surface.

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Piotr Rybka 氏 (University of Warsaw)
The least gradient problem in the plain (English)
[ 講演概要 ]
The least gradient problem arises in many application, e.g. in the free material design. We show existence of solutions in bounded, strictly convex planar regions, when the data are functions on bounded variation.

Our main goal is to show existence of solution in convex, but not necessarily strictly convex planar regions. In order to avoid technicalities we consider only continuous data, but BV data will do to. We formulate a set of admissibility conditions. We show that they are sufficient for existence.

This is a joint project with Wojciech Górny and Ahmad Sabra.

#### 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

The quasiconformal equivalence of Riemann surfaces and a universality of Schottky spaces (JAPANESE)
[ 講演概要 ]
In the theory of Teichmüller space of Riemann surfaces, we consider the set of Riemann surfaces which are quasiconformally equivalent. For topologically finite Riemann surfaces, it is quite easy to examine if they are quasiconformally equivalent or not. On the other hand, for Riemann surfaces of topologically infinite type, the situation is rather complicated.

In this talk, after constructing an example which shows the complexity of the problem, we give some geometric conditions for Riemann surfaces to be quasiconformally equivalent. Our argument enables us to see a universality of Schottky spaces.

#### 統計数学セミナー

15:30-16:40   数理科学研究科棟(駒場) 126号室
Ciprian A. Tudor 氏 (Université de Lille 1, Université de Panthéon-Sorbonne Paris 1)
Asymptotic expansion for random vectors
[ 講演概要 ]
We develop the asymptotic expansion theory for vector-valued sequences $F_{N}$ of random variables. We find the second-order term in the expansion of the density of $F_{N}$, based on assumptions in terms of the convergence of the Stein-Malliavin matrix associated to the sequence $F_{N}$ . Our approach combines the classical Fourier approach and the recent theory on Stein method and Malliavin calculus. We find the second order term of the asymptotic expansion of the density of $F_{N}$ and we discuss the main ideas on higher order asymptotic expansion. We illustrate our results by several examples.

### 2018年10月29日(月)

#### 東京確率論セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室
Sunder Sethuraman 氏 (University of Arizona)
On Hydrodynamic Limits of Young Diagrams (ENGLISH)
[ 講演概要 ]
We consider a family of stochastic models of evolving two-dimensional Young diagrams, given in terms of certain energies, with Gibbs invariant measures. Static' scaling limits of the shape functions, under these Gibbs measures, have been shown by several over the years. The purpose of this article is to study corresponding dynamical' limits of which less is understood. We show that the hydrodynamic scaling limits of the diagram shape functions may be described by different types of parabolic PDEs, depending on the energy structure.
The talk will be based on the article: https://arxiv.org/abs/1809.03592
[ 講演参考URL ]
http://math.arizona.edu/~sethuram/

#### 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

On morphisms of compact Kaehler manifolds with semi-positive holomorphic sectional curvature (JAPANESE)
[ 講演概要 ]
In this talk, we consider a smooth projective variety $X$ with semi-positive holomorphic "sectional" curvature, motivated by generalizing Howard-Smyth-Wu's structure theorem and Mok's result for compact Kaehler manifold with semi-positive "bisectional" curvature.
We prove that, if $X$ admits a holomorphic maximally rationally connected fibration $X ¥to Y$, then the morphism is always smooth (that is, a submersion), that the image $Y$ admits a finite ¥'etale cover $T ¥to Y$ by a complex
torus $T$, and further that all the fibers $F$ are isomorphic.
This gives a structure theorem for $X$ when $X$ is a surface.
Moreover we show that $X$ is rationally connected, if the holomorphic sectional curvature is quasi-positive.
This result gives a generalization of Yau's conjecture.

#### FMSPレクチャーズ

15:00-16:30   数理科学研究科棟(駒場) 117号室
Paul Baum 氏 (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (3/4)
Lecture 3. THE RIEMANN-ROCH THEOREM (ENGLISH)
[ 講演概要 ]
Topics in this talk :
1. Classical Riemann-Roch
2. Hirzebruch-Riemann-Roch (HRR)
3. Grothendieck-Riemann-Roch (GRR)
4. RR for possibly singular varieties (Baum-Fulton-MacPherson)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf

### 2018年10月26日(金)

#### 談話会・数理科学講演会

15:30-16:30   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

を記述するための理論であり，物理における散乱実験などに数学的裏付けを与え
る理論である．本講演では量子散乱理論の数学的定式化について概説したのち，

る．時間が許せば漸近的Euclid型や漸近的双曲型エンドを持つ多様体上への一般

### 2018年10月24日(水)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 126号室

The Mazur-Ulam property for unital C*-algebras (English)

#### FMSPレクチャーズ

15:00-16:30   数理科学研究科棟(駒場) 123号室
Paul Baum 氏 (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (2/4)
Lecture 2. THE DIRAC OPERATOR (ENGLISH)
[ 講演概要 ]
The Dirac operator of R^n will be defined. This is a first order elliptic differential operator with constant coefficients.
Next, the class of differentiable manifolds which come equipped with an order one differential operator which (at the symbol level)is locally isomorphic to the Dirac operator of R^n will be considered. These are the Spin-c manifolds.
Spin-c is slightly stronger than oriented, so Spin-c can be viewed as "oriented plus epsilon". Most of the oriented manifolds that occur in practice are Spin-c. The Dirac operator of a closed Spin-c manifold is the basic example for the Hirzebruch-Riemann-Roch theorem and the Atiyah-Singer index theorem.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf

### 2018年10月23日(火)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Jian-Guo Liu 氏 (Duke University)
Least action principle for incompressible flow with free boundary (English)
[ 講演概要 ]
In this talk I will describe a connection between Arnold's least-action principle for incompressible flows with free boundary and geodesic paths for Wasserstein distance. The least-action problem for geodesic distance on the "manifold" of fluid-blob shapes exhibits instability due to microdroplet formation. Using a conformal map formulation we investigate singularity formation in water-wave dynamics neglecting gravity. A connection with fluid mixture models via a variant of Brenier's relaxed least-action principle for generalized Euler flows will also be discussed.

#### 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
François Fillastre 氏 (Université de Cergy-Pontoise)
Co-Minkowski space and hyperbolic surfaces (ENGLISH)
[ 講演概要 ]
There are many ways to parametrize two copies of Teichmueller space by constant curvature -1 Riemannian or Lorentzian 3d manifolds (for example the Bers double uniformization theorem). We present the co-Minkowski space (or half-pipe space), which is a constant curvature -1 degenerated 3d space, and which is related to the tangent space of Teichmueller space. As an illustration, we give a new proof of a theorem of Thurston saying that, once the space of measured geodesic laminations on a compact hyperbolic surface is identified with the tangent space of Teichmueller space via infinitesimal earthquake, then the length of laminations is an asymmetric norm. Joint work with Thierry Barbot (Avignon).

### 2018年10月22日(月)

#### 東京確率論セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室
Trinh Khanh Duy 氏 (東北大学数理科学連携研究センター)
Limit theorems for random geometric complexes in the critical regime (ENGLISH)
[ 講演概要 ]
Geometric complexes (eg. Cech complexes or Rips complexes) are simplicial complexes defined on a finite set of points in a Euclidean space together with a radius parameter, which can be viewed as a higher dimensional generalization of geometric graphs. This talk concerns with random geometric complexes built over binomial point processes (collections of iid points). Like random geometric graphs, there are three regimes (subcritical(or dust, sparse) regime, critical (or thermodynamic) regime and supercritical regime) which are divided according the growth of the radius parameters in which the limiting behavior of random geometric complexes is totally different. This talk introduces some results on the strong law of large numbers and a central limit theorem in the critical regime.

#### 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

On certain hyperconvex manifolds without non-constant bounded holomorphic functions (JAPANESE)
[ 講演概要 ]
For each compact Riemann surface of genus > 1, we can construct a Riemann sphere bundle over the given Riemann surface using the projective structure induced by its uniformization.
The total space of this bundle is divided into two 1-convex domains by a closed Levi-flat real hypersurface. Although these two domains are not biholomorphic, we see that they have several function theoretic properties in common. In this talk, I would like to explain these common properties: hyperconvexity and expressions for certain Green function, and Liouville property and growth estimates of holomorphic functions.

#### 数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]
クリロフ部分空間法は，大規模疎行列を係数に持つ連立一次方程式に有効な反復法群である．そのうち，Bi-CG法などの短い漸化式を用いる解法は，反復毎の計算量やメモリ使用量が少なく済むため，計算効率がよいが，生成される残差ノルムは振動する．残差ノルムが大きく振動すると，丸め誤差が拡大され，収束速度の低下や近似解精度の劣化に繋がる．そこで，収束性を改善するための残差スムージングについて取り上げる．古典的な残差スムージングは，残差ノルムの収束振る舞いを滑らかにするものの，丸め誤差の拡大を防ぐ効果はほとんどないことが知られている．一方，最近提案された相互作用型の残差スムージングは，丸め誤差の蓄積を抑制することができ，近似解精度が向上するなどの付加価値がある．本講演では，行列ベクトル積から発生する丸め誤差が収束性に与える影響を考察した上で，新旧の残差スムージングの効果の違いについて議論する．

#### FMSPレクチャーズ

15:00-16:30   数理科学研究科棟(駒場) 123号室
Paul Baum 氏 (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (1/4)
Lecture 1.　WHAT IS K-THEORY AND WHAT IS IT GOOD FOR? (ENGLISH)
[ 講演概要 ]
This talk will consist of four points.
1. The basic definition of K-theory
2. A brief history of K-theory
3. Algebraic versus topological K-theory
4. The unity of K-theory
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf

### 2018年10月16日(火)

#### 解析学火曜セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]

#### 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
Daniel Matei 氏 (IMAR Bucharest)
Resonance varieties and matrix tree theorems (ENGLISH)
[ 講演概要 ]
We discuss the resonance varieties, encoding vanishing of cohomology cup products, of various classes of finitely presented groups of geometric and combinatorial origin. We describe the ideals defining those varieties in terms spanning trees in a similar vein with the classical matrix tree theorem in graph theory. We present applications of this description to 3-manifold groups and Artin groups.

#### 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
Tuyen Truong 氏 (Oslo)
A countable characterisation of smooth algebraic plane curves, and generalisations (English)
[ 講演概要 ]
Given a smooth algebraic curve X in C^3, I will present a way to construct a sequence of algebraic varieties (whose ideals are explicitly determined from the ideal defining X), whose solution set is non-empty iff the curve X can be algebraically embedded into C^2.
Various other questions, such as whether two given algebraic varieties are birational, can be similarly treated. Some related conjectures are stated.

### 2018年10月15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

Recent problems on Loewner theory (JAPANESE)
[ 講演概要 ]
Loewner Theory, which goes back to the parametric representation of univalent functions introduced by Loewner in 1923, has recently undergone significant development in various directions, including Schramm’s stochastic version of the Loewner differential equation and the new intrinsic approach suggested by Bracci, Contreras, Diaz-Madrigal and Gumenyuk.

In this talk, we firstly review the theory of Loewner equations in classical and modern treatments. Then we discuss some recent problems on the theory:
(i) Quasiconformal extensions of Loewner chains;
(ii) Hydrodynamics of multiple SLE.

#### 数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 002号室

MöbiusエネルギーのMöbius不変な離散化と分解 (Japanese)
[ 講演概要 ]
O'Haraによって提唱された結び目のエネルギーの一つであるMöbiusエネルギーは、Möbius不変性を持つ事がその名前の由来となっている。エネルギーは(少なくとも見かけ上は)特異性を有するエネルギー密度の積分で与えられる事もあり、エネルギー値を手計算で求める事は多くの場合困難である。そのため、結び目を多角形で近似しエネルギー値を近似的に求めるという考えが自然に浮かぶ。そのためには多角形に対するエネルギー(離散エネルギー)が必要である。実際、幾つかの離散エネルギーが提唱されているが、それらは元のエネルギーが有するMöbius不変という性質を失っている。ここでは、Möbius不変性という構造をもった離散エネルギーを提唱し、その収束性を論 じる。また、MöbiusエネルギーはMöbius不変な分解が知られている。提唱する離散エネルギーのMöbius不変分解も与える。本講演は、Simon Blatt (ザルツブルク大学) と石関 彩(千葉大学)との共同研究に基づく。

### 2018年10月11日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 118号室

Navier-Stokes方程式に対する摩擦型境界条件とその周辺 (Japanese)
[ 講演概要 ]

### 2018年10月10日(水)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 126号室
Kaijing Ling 氏 (Harbin Institute of Technology/Univ. Tokyo)
Extension modules over some conformal algebras related Virasoro algebra (English)

#### 代数学コロキウム

18:00-19:00   数理科学研究科棟(駒場) 056号室
Yichao Tian 氏 (Université de Strasbourg)
Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives (ENGLISH)
[ 講演概要 ]
In my talk, I will report on my ongoing collaborating project together with Yifeng Liu, Liang Xiao, Wei Zhang, and Xinwen Zhu, which concerns the rank 0 case of the Beilinson-Bloch-Kato conjecture on the relation between L-functions and Selmer groups for certain Rankin--Selberg motives for GL(n) x GL(n+1). I will state the main results with some examples coming from elliptic curves, sketch the strategy of the proof, and then focus on the key geometric ingredients, namely the semi-stable reduction of unitary Shimura varieties of type U(1,n) at non-quasi-split places.

（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．今回はパリからの中継です．）