## 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) 118号室

Fraïssé Theory and Jiang-Su algebra

#### 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

Towards fast and reliable numerical computations of the stationary radiative transport equation (日本語)
[ 講演概要 ]
The radiative transport equation (RTE) is a mathematical model of near-infrared light propagation in human tissue, and its analysis is required to develop a new noninvasive monitoring method of our body or brain activities. Since stationary RTE describes light intensity depending on a position and a direction, a discretization model of 3D-RTE is essentially a five dimensional problem. Therefore to establish a reliable and practical numerical method, both theoretical numerical analysis and computing techniques are required.

We firstly introduce huge-scale computation examples of RTE with bio-optical data. A high-accurate numerical cubature on the unit sphere and a hybrid parallel computing technique using GPGPU realize fast computation. Secondly we propose a semi-discrete upwind finite volume method to RTE. We also show its error estimate in two dimensions.

This talk is based on joint works with Prof. Y.Iso, Prof. N.Higashimori, and Prof. N.Oishi (Kyoto University).

### 2016年07月05日(火)

#### 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
Dulip Piyaratne 氏 (IPMU)
Generalized Bogomolov-Gieseker type inequality for Fano 3-folds (English)
[ 講演概要 ]
Construction of Bridgeland stability conditions on a given smooth projective 3-fold is an important problem. A conjectural construction for any 3-fold was introduced by Bayer, Macri and Toda, and the problem is reduced to proving so-called Bogomolov-Gieseker type inequality holds for certain stable objects in the derived category. It has been shown to hold for Fano 3-folds of Picard rank one due to the works of Macri, Schmidt and Li. However, Schmidt gave a counter-example for a Fano 3-fold of higher Picard rank. In this talk, I will explain how to modify the original conjectural inequality for general Fano 3-folds and why it holds.

#### Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]
SL(n,C)のあるタイプの冪等元を含む部分群が離散部分群になるための必要条件を与える不等式が、n=2の場合(もともとの清水の補題の場合に相当)を拡張する形で得られることと、対応する対称空間へのその群の作用が不等式によって影響を受けることについて去年７月のこのセミナーでお話しいたしました。これはその後の進展の報告です。

### 2016年07月04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

Central limit theorems for non-symmetric random walks on nilpotent covering graphs
[ 講演概要 ]
ベキ零群を被覆変換群とするような有限グラフの被覆グラフのことをベキ零被覆グラフと呼ぶ。結晶格子(特に被覆変換群がアーベル群の場合)上のランダムウォークに関してはすでに様々なアプローチが図られ多くの結果が得られている。ベキ零被覆グラフ上のランダムウォークについては、対称な場合に幾つかの極限定理が知られているものの、非対称な場合にはあまり研究が進展していないように思われる。本講演では、ベキ零被覆グラフ上の非対称ランダムウォークを考察し、ある条件下で汎関数中心極限定理が成り立つことを報告する。本講演の内容は、石渡聡氏(山形大)および河備浩司氏(岡山大)との共同研究に基づく。

### 2016年06月28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

Strong algebraization of fixed point properties (JAPANESE)
[ 講演概要 ]
バナッハ空間（ないしは族）を固定したとき，有限生成群のそれ上の等長作用が常に大域的固定点を持つ，という性質を固定点性質と呼ぶ．ヒルベルト空間全体のなす族を考えたときの固定点性質は，「Kazhdan の性質(T)」と呼ばれる群の剛性と同値であることが知られている．

「有界生成」の成立がわからないような状況でもパッチワーク戦略を適用できうるようになった．系として，いろいろな離散群が強い固定点性質をもつことを示せ，しかも証明も非常にコンセプチュアルである．こうした応用面についても概観したい．

#### 解析学火曜セミナー

16:50-18:20   数理科学研究科棟(駒場) 126号室
Georgi Raikov 氏 (The Pontificia Universidad Católica de Chile)
Discrete spectrum of Schr\"odinger operators with oscillating decaying potentials (English)
[ 講演概要 ]
I will consider the Schr\"odinger operator $H_{\eta W} =-\Delta + \eta W$, self-adjoint in $L^2(\re^d)$, $d \geq 1$. Here $\eta$ is a non constant almost periodic function, while $W$ decays slowly and regularly at infinity. I will discuss the asymptotic behaviour of the discrete spectrum of $H_{\eta W}$ near the origin. Due to the irregular decay of $\eta W$, there exist some non semiclassical phenomena; in particular, $H_{\eta W}$ has less eigenvalues than suggested by the semiclassical intuition.

### 2016年06月27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
いつもと曜日が異なります。This week's seminar will be held on Monday, not on Tuesday.
Christopher Hacon 氏 (University of Utah)
Generic vanishing and birational geometry in char p>0 (ENGLISH)
[ 講演概要 ]
Many precise results on the birational geometry of irregular varieties have been obtained by combining the generic vanishing theorems of Green and Lazarsfeld with the Fourier-Mukai transform. In this talk we will discuss the failure of the generic vanishing theorems of Green and Lazarsfeld in positive characteristic. We will then explain a different approach to generic vanishing based on the theory of F-singularities that leads to concrete applications in birational geometry in positive characteristics
[ 参考URL ]
http://www.math.utah.edu/~hacon/

#### 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 a higher codimensional analogue of Ueda theory and its applications (JAPANESE)
[ 講演概要 ]
Let $Y$ be a compact complex manifold embedded in a complex manifold with unitary flat normal bundle. As a higher-codimensional generalization of Ueda's theory, we investigate the analytic structure of a neighborhood of $Y$. As an application, we give a criterion for the existence of a smooth Hermitian metric with semi-positive curvature on a nef line bundle.

### 2016年06月24日(金)

#### 幾何コロキウム

10:00-14:30   数理科学研究科棟(駒場) 118号室

[ 講演概要 ]

[ 講演概要 ]

#### 談話会・数理科学講演会

15:30-16:30   数理科学研究科棟(駒場) 123号室

[ 講演概要 ]
1980年代に確立した代数多様体に対する三次元極小モデル理論の高次元化および正標数体上の最近の進展の解説をし、自分の研究成果を交えて、その応用およびこれからの展望の話をする。あまり込み入った証明の話はしない予定である。

[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/teacher/gongyo.html

### 2016年06月23日(木)

#### 古典解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 118号室

Resurgence of formal series solutions of nonlinear differential and difference equations (JAPANESE)
[ 講演概要 ]
Resurgent analysis は1980年代に J. Ecalle により創始された. そこでは, alien derivatives 等の漸近解析における重要な概念が導入され, 近年数理物理学においても大きな注目を集めている. 本講演では Resurgent analysis の基本事項の概説から始め, 最近得られた非線形微(差)分方程式の形式解の resurgence に関する結果の紹介を行う.

#### FMSPレクチャーズ

15:00-16:30   数理科学研究科棟(駒場) 056号室
Klaus Mainzer 氏 (Technische Universität München)
Complexity and Computability: Complex Dynamical Systems beyond Turing-Computability (ENGLISH)
[ 講演概要 ]
The computational theory of complexity is founded by digital computing (e.g. Turing machine) which cannot fully grasp continuous concepts of mathematics. The mathematical theory of complex dynamical systems (with interdisciplinary applications in natural and economic sciences) is based on continuous concepts. Further on, there is an outstanding tradition in mathematics since Newton, Leibniz, Euler et al. with real algorithms in, e.g., numerical analysis. How can the gap between the digital and continuous world be mathematically overcome? The talk aims at mathematical and philosophical foundations and interdisciplinary applications of complex dynamical systems beyond Turing-computability.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Mainzer.pdf

### 2016年06月21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) 126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

Spaces of chord diagrams of spherical curves (JAPANESE)
[ 講演概要 ]
In this talk, the speaker introduces a framework to obtain (possibly infinitely many) new topological invariants of spherical curves under local homotopy moves (several types of Reidemeister moves). They are defined by chord diagrams, each of which is a configurations of even paired points on a circle. We see that these invariants have useful properties.

#### 統計数学セミナー

13:00-15:00   数理科学研究科棟(駒場) 052号室
Lorenzo Mercuri 氏 (University of Milan)
New Classes and Methods in YUIMA package

[ 講演概要 ]
In this talk, we present three new classes recently introduced in YUIMA package.
These classes allow the user to manage three different problems:
・Construction of a multidimensional stochastic differential equation driven by a general multivariate Levy process. In particular we show how to define and then simulate a SDE driven by a multivariate Variance Gamma process.
・Definition and simulation of a functional of a general SDE.
・Definition and simulation of the integral of an object from the class yuima.model. In particular, we are able to evaluate Riemann Stieltjes integrals,deterministic integrals with random integrand and stochastic integrals.
Numerical examples are given in order to explain the new methods and classes.

### 2016年06月20日(月)

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 123号室

De-Qi Zhang 氏 (National University of Singapore)
BUILDING BLOCKS OF POLARIZED ENDOMORPHISMS OF NORMAL PROJECTIVE VARIETIES (English)
[ 講演概要 ]
An endomorphism f of a normal projective variety X is polarized if f∗H ∼ qH for some ample Cartier divisor H and integer q > 1.

We first assert that a suitable maximal rationally connected fibration (MRC) can be made f-equivariant using a construction of N. Nakayama, that f descends to a polarized endomorphism of the base Y of this MRC and that this Y is a Q-abelian variety (quasi- ́etale quotient of an abelian variety). Next we show that we can run the minimal model program (MMP) f-equivariantly for mildly singular X and reach either a Q-abelian variety or a Fano variety of Picard number one.

As a consequence, the building blocks of polarized endomorphisms are those of Q- abelian varieties and those of Fano varieties of Picard number one.

Along the way, we show that f always descends to a polarized endomorphism of the Albanese variety Alb(X) of X, and that a power of f acts as a scalar on the Neron-Severi group of X (modulo torsion) when X is smooth and rationally connected.

Partial answers about X being of Calabi-Yau type or Fano type are also given with an extra primitivity assumption on f which seems necessary by an example.
This is a joint work with S. Meng.
[ 参考URL ]
http://www.math.nus.edu.sg/~matzdq/

#### 代数幾何学セミナー

14:45-16:15   数理科学研究科棟(駒場) 123号室

Zhixian Zhu 氏 (KIAS)
Fujita's freeness conjecture for 5-fold (English)
[ 講演概要 ]
Let X be a smooth projective variety of dimension n and L any ample line bundle. Fujita conjectured that the adjoint line bundle O(K_X+mL) is globally generated for any m greater or equal to dimX+1. By studying the singularity of pairs, we prove Fujita's freeness conjecture for smooth 5-folds.

#### 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 transcendental approach to injectivity theorems for log canonical pairs (JAPANESE)
[ 講演概要 ]

#### 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

Bi-exact groups, strongly ergodic actions and group measure space type III factors with no central sequence

### 2016年06月14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) 126号室

Schr¥"odinger operators on a periodically broken zigzag carbon nanotube (Japanese)

#### 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

Non-Kähler complex structures on R^4 (JAPANESE)
[ 講演概要 ]
We consider the following problem. "Is there any non-Kähler complex structure on R^{2n}?" If n=1, the answer is clearly negative. On the other hand, Calabi and Eckmann constructed non-Kähler complex structures on R^{2n} for n ≥ 3. In this talk, I will construct uncountably many non-Kähler complex structures on R^4, and give the affirmative answer to the case where n=2. For the construction, it is important to understand the genus-one achiral Lefschetz fibration S^4 → S^2 found by Yukio Matsumoto and Kenji Fukaya. This is a joint work with Antonio Jose Di Scala and Daniele Zuddas.

### 2016年06月13日(月)

#### 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

Dissection : A direct solver with kernel detection for finite element matrices
(日本語)
[ 講演概要 ]
Large-scale sparse matrices are solved in finite element analyses of elasticity and/or flow problems. In some cases, the matrix may be singular, e.g. due to pressure ambiguity of the Navier-Stokes equations, or due to rigid body movements of sub-domain elasticity problems by a domain decomposition method. Therefore, it is better the linear solver understands rank-deficiency of the matrix.
By assuming the matrix is factorized into LDU form with a symmetric partial permutation, and by introducing a threshold to postpone factorization for pseudo null pivots, solvability of the last Schur complement matrix will be examined. Usual procedure for rank-deficiency problem is based on computation of eigenvalues or singular values and an introduced threshold determines the null space. However, developed new algorithm in DOI:10.1002/nme.4729 is based on computation of residuals combined with orthogonal projections onto supposed image spaces and there is no necessary to introduce a threshold for understanding zero value in floating point. The algorithm uses higher precision arithmetic, e.g. quadruple precision, to distinguish numerical round-off errors that occurred during factorization of the whole sparse matrix from ones during the kernel detection procedure itself.
This is joint work with François-Xavier Roux (LJLL, UPMC/ONERA).

#### 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

Jump processes on boudaries of random trees

#### 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

(JAPANESE)
[ 講演概要 ]

（Judith Brinkschulte 氏（Leipzig 大）との共同研究に基づく）