## 過去の記録

### 2016年05月17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

On dual defects of toric varieties (TBA)
[ 講演概要 ]
For a projective variety embedded in a projective space,
we can define the dual variety in the dual projective space.
By dimension count, the codimension of the dual variety is expected to be one,
but it can be greater than one for some varieties.

For a smooth toric variety, it is known that the codimension of the dual variety is greater than one
if and only if the toric variety is a suitable projective bundle over some toric variety.
In this talk, I will explain a generalization of this result to toric varieties without the assumption of singularities.
This is a joint work with Katsuhisa Furukawa.
[ 講演参考URL ]

#### 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

Some dynamics of random walks on the mapping class groups (JAPANESE)
[ 講演概要 ]
The dynamics of random walks on the mapping class groups on closed surfaces of genus >1 will be discussed. We define the topological entropy of random walks. Then we prove that the drift with respect to Thurston or Teichmüller metrics and the Lyapunov exponent all coincide with the topological entropy. This is a "random version" of pseudo-Anosov dynamics observed by Thurston and I will begin this talk by recalling the work of Thurston.

### 2016年05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

２次元正規小平特異点の正規化接錐の被約性による特徴づけと、特異点解消および極大イデアル因子の性質 (JAPANESE)
[ 講演概要 ]

#### 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

Generation and propagation of fine transition layers for the Allen-Cahn equation with mild noise
[ 講演概要 ]

(1) 初期時刻の直後で起こる遷移層の形成 (generation of interface)

(2) 界面付近の遷移層の形状がノイズで破壊されないことの証明

### 2016年05月11日(水)

#### 代数学コロキウム

17:30-18:30   数理科学研究科棟(駒場) 056号室
Wiesława Nizioł 氏 (CNRS & ENS de Lyon)
Syntomic complexes and p-adic nearby cycles (English)
[ 講演概要 ]
I will present a proof of a comparison isomorphism, up to some universal constants, between truncated sheaves of p-adic nearby cycles and syntomic cohomology sheaves on semistable schemes over a mixed characteristic local rings. This generalizes the comparison results of Kato, Kurihara, and Tsuji for small Tate twists (where no constants are necessary) as well as the comparison result of Tsuji that holds over the algebraic closure of the field. This is a joint work with Pierre Colmez.

(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．)

### 2016年05月10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

[ 講演概要 ]
A handlebody-link is a disjoint union of handlebodies embedded in $S^3$ and HL-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes. A. Mizusawa and R. Nikkuni classified the set of HL-homotopy classes of 2-component handlebody-links completely using the linking numbers for handlebody-links. In this talk, by using Milnor's link-homotopy invariants, we construct an invariant for handlebody-links and give a bijection between the set of HL-homotopy classes of n-component handlebody-links with some assumption and a quotient of the action of the general linear group on a tensor product of modules. This is joint work with Atsuhiko Mizusawa at Waseda University.

### 2016年05月09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

Nevanlinna type theorems for meromorphic functions on negatively curved Kähler manifolds (JAPANESE)
[ 講演概要 ]
We discuss a generalization of classical Nevanlinna theory to meromorphic functions on complete Kähler manifolds. Several generalization of domains of functions are known in Nevanlinna theory, especially the results due to W.Stoll are well-known. In general Kähler case the remainder term of the second main theorem of Nevanlinna theory usually takes a complicated form. It seems that we have to modify classical
methods in order to simplify the second main theorem. We will use heat diffusion to do that and show some defect relations. We would also like to give some Liouville type theorems for holomorphic maps by using similar heat diffusion methods.

#### 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

[ 講演概要 ]

また、この密度保存性と長田-種村の結果を使うことによって、ある種類の無限次元SDEが一意的な強解を持つことを導出できる。時間があれば、どういう種類の無限次元SDEに応用できるかを説明したい。

#### 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

[ 講演概要 ]

このように，重み付きハーディ空間での関数や積分の近似は基本的な問題と言えるが，この空間において「最適」な公式はそれぞれどのようなものかは，これまで一部の場合についてしか分かっていなかった．本研究では，まず関数近似に対して，一般的な重み関数の場合について，最適な公式を求める問題をポテンシャル論の方法を用いて定式化した．そして，それを近似的に解くことで公式を設計し，また，それらの公式の理論的誤差評価も与えた．これらの公式の厳密な最適性はまだ示せてはいないものの，従来のSinc公式よりも高精度になることが数値実験で観察できている．さらに，数値積分に対しても，類似の方法によって構成した関数近似公式を積分することで公式を設計した．これらについては理論的な誤差評価は得られていないが，やはり数値実験によって，従来の公式よりも高精度な公式が得られていることが観察できた．特に，重み関数が二重指数関数的な減衰を持つ場合について，設計した公式がDE公式よりも高精度となることが観察できた．本研究は，岡山友昭氏（広島市立大学），杉原正顯氏（青山学院大学）との共同研究である．

#### 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
Mikael Pichot 氏 (McGIll大学/東大数理)
Surgery theory and discrete groups (English)

#### FMSPレクチャーズ

15:00-17:00   数理科学研究科棟(駒場) 002号室
Michael Tuite 氏 (National University of Ireland, Galway)
Vertex Operator Algebras according to Newton (ENGLISH)
[ 講演概要 ]
In this lecture I will give an introduction to Vertex Operator Algebras (VOAs) using elementary methods originally due to Isaac Newton. I will also discuss a class of exceptional VOAs including the Moonshine module which share a number of fundamental properties in common.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tuite.pdf

### 2016年04月27日(水)

#### PDE実解析研究会

15:00-16:00   数理科学研究科棟(駒場) 056号室

Elijah Liflyand 氏 (Bar-Ilan University, Israel)
Fourier transform versus Hilbert transform (English)
[ 講演概要 ]
We present several results in which the interplay between the Fourier transform and the Hilbert transform is of special form and importance.
1. In 50-s (Kahane, Izumi-Tsuchikura, Boas, etc.), the following problem in Fourier Analysis attracted much attention: Let $\{a_k\},$ $k=0,1,2...,$ be the sequence of the Fourier coefficients of the absolutely convergent sine (cosine) Fourier series of a function $f:\mathbb T=[-\pi,\pi)\to \mathbb C,$ that is $\sum |a_k|<\infty.$ Under which conditions on $\{a_k\}$ the re-expansion of $f(t)$ ($f(t)-f(0)$, respectively) in the cosine (sine) Fourier series will also be absolutely convergent?
We solve a similar problem for functions on the whole axis and their Fourier transforms. Generally, the re-expansion of a function with integrable cosine (sine) Fourier transform in the sine (cosine) Fourier transform is integrable if and only if not only the initial Fourier transform is integrable but also the Hilbert transform of the initial Fourier transform is integrable.
2. The following result is due to Hardy and Littlewood: If a (periodic) function $f$ and its conjugate $\widetilde f$ are both of bounded variation, their Fourier series converge absolutely.
We generalize the Hardy-Littlewood theorem (joint work with U. Stadtmüller) to the Fourier transform of a function on the real axis and its modified Hilbert transform. The initial Hardy-Littlewood theorem is a partial case of this extension, when the function is taken to be with compact support.
3. These and other problems are integrated parts of harmonic analysis of functions of bounded variation. We have found the maximal space for the integrability of the Fourier transform of a function of bounded variation. Along with those known earlier, various interesting new spaces appear in this study. Their inter-relations lead, in particular, to improvements of Hardy's inequality.
There are multidimensional generalizations of these results.
[ 講演参考URL ]
http://u.math.biu.ac.il/~liflyand/

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 056号室

On the endoscopic lifting of simple supercuspidal representations (Japanese)

### 2016年04月26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

On microlocal analysis of Gauss-Manin connections for boundary singularities (Japanese)

#### 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
This talk is given in Japanese due to the speaker's intension.

A gentle introduction to K-stability and its recent development (Japanese)
[ 講演概要 ]
K安定性とは複素代数多様体上の「標準的な」ケーラー計量の存在問題に端を発する，代数幾何的な概念です．二木先生や満渕先生等の先駆的な仕事に感化されて導入され，特に近年ホットに研究され始めている一方，未だその大半はより微分幾何的な研究者の方々や背景の中でなされているように講演者には感じられます．

[ 講演参考URL ]

#### 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

Arithmetic topology on branched covers of 3-manifolds (JAPANESE)
[ 講演概要 ]
The analogy between 3-dimensional topology and number theory was first pointed out by Mazur in the 1960s, and it has been studied systematically by Kapranov, Reznikov, Morishita, and others. In their analogies, for example, knots and 3-manifolds correspond to primes and number rings respectively. The study of these analogies is called arithmetic topology now.
In my talk, based on their dictionary of analogies, we study analogues of idelic class field theory, Iwasawa theory, and Galois deformation theory in the context of 3-dimensional topology, and establish various foundational analogies in arithmetic topology.

#### 統計数学セミナー

16:10-17:10   数理科学研究科棟(駒場) 123号室
Teppei Ogihara 氏 (Institute of Statistical Mathematics, JST PRESTO, JST CREST)
LAMN property and optimal estimation for diffusion with non synchronous observations
[ 講演概要 ]
We study so-called local asymptotic mixed normality (LAMN) property for a statistical model generated by nonsynchronously observed diffusion processes using a Malliavin calculus technique. The LAMN property of the statistical model induces an asymptotic minimal variance of estimation errors for any estimators of the parameter. We also construct an optimal estimator which attains the best asymptotic variance.

#### 統計数学セミナー

13:00-14:20   数理科学研究科棟(駒場) 123号室
Ciprian Tudor 氏 (Université de Lille 1)
Stochastic heat equation with fractional noise 1
[ 講演概要 ]
In the first part, we introduce the bifractional Brownian motion, which is a Gaussian process that generalizes the well- known fractional Brownian motion. We present the basic properties of this process and we also present its connection with the mild solution to the heat equation driven by a Gaussian noise that behaves as the Brownian motion in time.

#### 統計数学セミナー

14:30-15:50   数理科学研究科棟(駒場) 123号室
Ciprian Tudor 氏 (Université de Lille 1)
Stochastic heat equation with fractional noise 2
[ 講演概要 ]
We will present recent result concerning the heat equation driven by q Gaussian noise which behaves as a fractional Brownian motion in time and has a correlated spatial structure. We give the basic results concerning the existence and the properties of the solution. We will also focus on the distribution of this Gaussian process and its connection with other fractional-type processes.

#### 数理人口学・数理生物学セミナー

15:00-16:00   数理科学研究科棟(駒場) 128演習室号室
Lev Idels 氏 (Vanvouver Island University)
Delayed Models of Cancer Dynamics: Lessons Learned in Mathematical Modelling (ENGLISH)
[ 講演概要 ]
In general, delay differential equations provide a richer mathematical
framework (compared with ordinary differential equations) for the
analysis of biosystems dynamics. The inclusion of explicit time lags in
tumor growth models allows direct reference to experimentally measurable
and/or controllable cell growth characteristics. For three different
types of angiogenesis models with variable delays, we consider either
continuous or impulse therapy that eradicates tumor cells and suppresses
angiogenesis. It was shown that with the growth of delays, even
constant, the equilibrium can lose its stability, and sustainable
oscillation, as well as chaotic behavior, can be observed. The analysis
outlines the difficulties which occur in the case of unbounded growth
rates, such as classical Gompertz model, for small volumes of cancer
cells compared to available blood vessels. The Wheldon model (1975) of a
Chronic Myelogenous Leukemia (CML) dynamics is revisited in the light of
recent discovery that this model has a major drawback.
[ 講演参考URL ]
https://web.viu.ca/idelsl/

### 2016年04月25日(月)

#### 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

Graded twisting of quantum groups, actions, and categories

#### 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 representative domain and its applications (JAPANESE)
[ 講演概要 ]
Bergman introduced the notion of a representative domain to choose a nice holomorphic equivalence class of domains. In this talk, I will explain that the representative domain is also useful to obtain an analogue of Cartan's linearity theorem for some special class of domains.

#### 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

Concentration results for directed polymer with unbouded jumps

### 2016年04月22日(金)

#### 統計数学セミナー

10:30-11:50   数理科学研究科棟(駒場) 002号室
Ciprian Tudor 氏 (Université de Lille 1)
Stein method and Malliavin calculus : theory and some applications to limit theorems 1
[ 講演概要 ]
In this first part, we will present the basic ideas of the Stein method for the normal approximation. We will also describe its connection with the Malliavin calculus and the Fourth Moment Theorem.

#### 統計数学セミナー

12:50-14:10   数理科学研究科棟(駒場) 002号室
Ciprian Tudor 氏 (Université de Lille 1)
Stein method and Malliavin calculus : theory and some applications to limit theorems 2
[ 講演概要 ]
In the second presentation, we intend to do the following: to illustrate the application of the Stein method to the limit behavior of the quadratic variation of Gaussian processes and its connection to statistics. We also intend to present the extension of the method to other target distributions.