## 過去の記録

### 2012年05月23日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Xingfei Xiang 氏 (East China Normal University)
$L^p$ Estimates of the Vector Fields and their Applications (ENGLISH)
[ 講演概要 ]
For $1< p < \\infty$, the estimates of $W^{1,p}$ norm of the vector fields in bounded domains in $\\mathbb R^3$ in terms of their divergence and curl have been well studied. In this talk, we shall present the $L^{{3}/{2}}$ estimates of vector fields with the $L^1$ norm of the $\\curl$ in bounded domains. By a similar discussion, we establish the $L^p$ estimates of the vector fields for $1 < p < \\infty$. As an application of the $L^p$ estimates, the Global $\\dv-\\curl$ lemma in Sobolev spaces of negative indices is given.

#### 代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室

Simply connected elliptic surfaces (JAPANESE)
[ 講演概要 ]
We characterize simply connected elliptic surfaces by their singular fibers in any characteristic case. To this end, we study orbifolds of curves, local canonical bundle formula, and resolutions of multiple fibers. The result was known for the complex analytic case. Our method can be applied to the rigid analytic case.

### 2012年05月22日(火)

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室
この日だけ部屋を118に変更します.
Norbert Pozar 氏 (Graduate School of Mathematical Sciences, The University of Tokyo)
Viscosity solutions for nonlinear elliptic-parabolic problems (ENGLISH)
[ 講演概要 ]
We introduce a notion of viscosity solutions for a general class of
elliptic-parabolic phase transition problems. These include the
Richards equation, which is a classical model in filtration theory.
Existence and uniqueness results are proved via the comparison
principle. In particular, we show existence and stability properties
of maximal and minimal viscosity solutions for a general class of
initial data. These results are new even in the linear case, where we
also show that viscosity solutions coincide with the regular weak
solutions introduced in [Alt&Luckhaus 1983]. This talk is based on a
recent work with Inwon Kim.

#### 数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室

https://www.ms.u-tokyo.ac.jp/gcoe/index.html

[ 講演概要 ]

Grote [J. Comput. Phys. 201, 630--650 (2004)]は,各散乱体を囲む複数の人工境界を導入し, その上で多重DtN(Dirichlet-to-Neumann)写像を定式化し,その写像を用いた境界条件を人工境界上で課し, 元の問題を人工境界で囲まれた複数の互いに素な有界領域における問題に帰着させ,有限要素法で解くという方法を見出した.

[ 講演参考URL ]
http://www.infsup.jp/utnas/

#### トポロジー火曜セミナー

17:10-18:10   数理科学研究科棟(駒場) 056号室
Tea: 16:50 - 17:10 コモンルーム

Gamma Integral Structure in Gromov-Witten theory (JAPANESE)
[ 講演概要 ]
The quantum cohomology of a symplectic
manifold undelies a certain integral local system
defined by the Gamma characteristic class.
This local system originates from the natural integral
local sysmem on the B-side under mirror symmetry.
In this talk, I will explain its relationships to the problem
of analytic continuation of Gromov-Witten theoy (potentials),
including crepant resolution conjecture, LG/CY correspondence,
modularity in higher genus theory.

### 2012年05月21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

Characterizations of projective spaces and hyperquadrics
(JAPANESE)
[ 講演概要 ]
After Mori's works on Hartshorne's conjecture, many results to
characterize projective spaces and hyperquadrics in terms of
positivity properties of the tangent bundle have been provided.
Kov\\'acs' conjecture states that smooth complex projective
varieties are projective spaces or hyperquadrics if the $p$-th
exterior product of their tangent bundle contains the $p$-th
exterior product of an ample vector bundle. This conjecture is
the generalization of many preceding results. In this talk, I will
explain the idea of the proof of Kov\\'acs' conjecture for varieties
with Picard number one by using a method of slope-stabilities
of sheaves.

#### 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

Local cohomology and hypersurface isolated singularities I (JAPANESE)
[ 講演概要 ]

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Emanuel Scheidegger 氏 (The University of Freiburg)
Topological Strings on Elliptic Fibrations (ENGLISH)
[ 講演概要 ]
We will explain a conjecture that expresses the BPS invariants
(Gopakumar-Vafa invariants) for elliptically fibered Calabi-Yau
threefolds in terms of modular forms. In particular, there is a
recursion relation which governs these modular forms. Evidence comes
from the polynomial formulation of the higher genus topological string
amplitudes with insertions.

### 2012年05月19日(土)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

[ 講演概要 ]
3次体の判別式を数える関数は2つ主要項があるが,判別式を算術級数中で数えると,第2主要項に偏りが現れることがある.この必要十分条件を与え,また主要項の公式を与える.証明には,2元3次形式の概均質ベクトル空間のL関数を用いる.(Frank Thorne 氏との共同研究)

Asai L関数の中心値の平均とレベルアスペクト劣凸評価 (JAPANESE)

### 2012年05月18日(金)

#### 統計数学セミナー

14:50-16:00   数理科学研究科棟(駒場) 006号室

PAC-Bayesian Bound for Gaussian Process Regression and Multiple Kernel Additive Model (JAPANESE)
[ 講演概要 ]
スパース加法モデルの推定法として,マルチプルカーネル学習(MKL)が提案されているが, 本発表ではそのベイズ的な変種について考察し,PAC-Bayesの手法を用いてその性能解析 を行う.標準的なMKLの解析では,restricted eigenvalue conditionのような強い仮定をデザ インに課するが,我々はPAC-Bayesの技法を用いてベイズ的なMKLがそのような仮定を設け ないで最適レートを達成することを示す.我々の結果は,近年発展しているガウシアンプロ セス回帰に関する理論を包含しており,PAC-Bayesを使ったより単純な証明を与える.我々 の考える推定量はガウシアンプロセスのスケール混合であり,スケール混合を取ることに よって適応的に最適レートを達成することが示される.また,有限次元のグループラッソに 対応する状況も考え,その収束レートを与える.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/04.html

### 2012年05月16日(水)

#### 代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 002号室

On uniform bound of the maximal subgroup of the inertia group acting unipotently on $¥ell$-adic cohomology (JAPANESE)
[ 講演概要 ]
For a smooth projective variety over a local field,
the action of the inertia group on the $¥ell$-adic cohomology group is
unipotent if it is restricted to some open subgroup.
In this talk, we give a uniform bound of the index of the maximal open
subgroup satisfying this property.
This bound depends only on the Betti numbers of $X$ and certain Chern
numbers depending on a projective embedding of $X$.

### 2012年05月15日(火)

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Strichartz estimates for Schr\\"odinger equations with variable coefficients and unbounded electromagnetic potentials (JAPANESE)
[ 講演概要 ]
In this talk we consider the Cauchy problem for Schr\\"odinger equations with variable coefficients and unbounded potentials. Under the assumption that the Hamiltonian is a long-range perturbation of the free Schr\\"odinger operator, we construct an outgoing parametrix for the propagator near infinity, and give applications to sharp Strichartz estimates. The basic idea is to combine the standard approximation by using a time dependent modifier, which is not in the semiclassical regime, with the semiclassical approximation of Isozaki-Kitada type. We also show near sharp Strichartz estimates without asymptotic conditions by using local smoothing effects.

### 2012年05月14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

### 2012年05月11日(金)

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 002号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

Moduli spaces and symplectic derivation Lie algebras (JAPANESE)
[ 講演概要 ]
First we overview Kontsevich's theorem describing a deep connection between homology of certain infinite dimensional Lie algebras (symplectic derivation Lie algebras) and cohomology of various moduli spaces. Then we discuss some computational results on the Lie algebras together with their applications (joint work with Shigeyuki Morita and Masaaki Suzuki).

#### 統計数学セミナー

14:50-16:00   数理科学研究科棟(駒場) 006号室

Efficient Discretization of Stochastic Integrals (JAPANESE)
[ 講演概要 ]
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly. The result is directly applicable to practical hedging problem in mathematical finance; it gives an asymptotically optimal way to choose rebalancing dates and portofolios with respect to transaction costs. The asymptotically efficient strategies in fact reflect the structure of transaction costs. In particular a specific biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs follow a convex model. The problem is discussed also in terms of the exponential utility maximization.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/03.html

### 2012年05月08日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

Infinite examples of non-Garside monoids having fundamental elements (JAPANESE)
[ 講演概要 ]
The Garside group, as a generalization of Artin groups,
is defined as the group of fractions of a Garside monoid.
To understand the elliptic Artin groups, which are the fundamental
groups of the complement of discriminant divisors of the semi-versal
deformation of the simply elliptic singularities E_6~, E_7~ and E_8~,
we need to consider another generalization of Artin groups.
In this talk, we will study the presentations of fundamental groups
of the complement of complexified real affine line arrangements
and consider the associated monoids.
It turns out that, in some cases, they are not Garside monoids.
Nevertheless, we will show that they satisfy the cancellation condition
and carry certain particular elements similar to the fundamental elements
in Artin monoids.
As a result, we will show that the word problem can be solved
and the center of them are determined.

#### 数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室

https://www.ms.u-tokyo.ac.jp/gcoe/index.html

[ 講演概要 ]

「 Step 1 : 流体粒子の仮の位置を計算する陽解法 Step 」と

「 Step 2 : 陽解法で計算された粒子配置に基づいて Poisson 方程式から圧力分布を計算し粒子の位置を更新する半陰解法 Step 」

と、2つの Step を交互に繰り返すアルゴリズムが広く採用されている。ところが、この時間発展スキームで計算される圧力は時間的にも空間的にも振動してしまうという欠点が、幾つかの研究で報告されている。 この圧力振動問題の理由を、上記の時間発展スキームを 数学的に定式化し直すプロセスを通じて明らかにしながら、粒子法の今後の改善に関して考察を行う。なお本講演は、神奈川工科大学における服部元史(情報メディア学科)、藤井みゆき(情報教育研究センター)、田辺誠(機械工学科)の共同研究の成果である。
[ 講演参考URL ]
http://www.infsup.jp/utnas/

#### 講演会

14:40-16:10   数理科学研究科棟(駒場) 470号室

[ 講演概要 ]

この講演では、その類似性について、ストリング・トポロジーを中心に概観したいと思います。

### 2012年05月07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

The second metric variation of the total $Q$-curvature in conformal geometry (JAPANESE)
[ 講演概要 ]
Branson's $Q$-curvature of even-dimensional compact conformal manifolds integrates to a global conformal invariant called the total $Q$-curvature. While it is topological in two dimensions and is essentially the Weyl action in four dimensions, in the higher dimensional cases its geometric meaning remains mysterious. Graham and Hirachi have shown that the first metric variation of the total $Q$-curvature coincides with the Fefferman-Graham obstruction tensor. In this talk, the second variational formula will be presented, and it will be made explicit especially for conformally Einstein manifolds. The positivity of the second variation will be discussed in connection with the smallest eigenvalue of the Lichnerowicz Laplacian.

#### 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

Algebro-geometric characterization of Cayley polytopes (JAPANESE)
[ 講演概要 ]
A lattice polytope is called a Cayley polytope if it is "small" in some
sense.
In this talk, I will explain an algebro-geometric characterization of
Cayley polytopes
by considering whether or not the corresponding polarized toric
varieties are covered by lines, planes, etc.

We can apply this characterization to the study of Seshadri constants,
which are invariants measuring the positivity of ample line bundles.
That is, we can obtain an explicit description of a polarized toric
variety whose Seshadri constant is one.

#### GCOEセミナー

14:30-16:00   数理科学研究科棟(駒場) 370号室

Distributional behaviors of time-averaged observables in anomalous diffusions (subdiffusion and superdiffusion) (ENGLISH)
[ 講演概要 ]
In anomalous diffusions attributed to a power-law distribution,
time-averaged observables such as diffusion coefficient and velocity of drift are intrinsically random. Anomalous diffusion is ubiquitous phenomenon not only in material science but also in biological transports, which is characterized by a non-linear growth of the mean square displacement (MSD).
(subdiffusion: sublinear growth, super diffusion: superlinear growth).
It has been known that there are three different mechanisms generating subdiffusion. One of them is a power-law distribution in the trapping-time distribution. Such anomalous diffusion is modeled by the continuous time random walk (CTRW). In CTRW, the time-averaged MSD grows linearly with time whereas the ensemble-averaged MSD does not. Using renewal theory, I show that diffusion coefficients obtained by single trajectories converge in distribution. The distribution is the Mittag-Leffler (or inverse Levy) distribution [1,2].
In superdiffusion, there are three different mechanisms. One stems from positive correlations in random walks; the second from persistent motions in random walks, called Levy walk; the third from very long jumps in random walks, called Levy flight.
If the persistent time distribution obeys a power law with divergent mean in Levy walks, the MSD grows as t^2 whereas the mean of positions is zero. When an external bias is added in Levy walks, the response to bias (velocity of drift) appears in the distribution, which is what we term a distributional response [3]. The distribution is the generalized arcsine distribution.
These distributional behaviors open a new window to dealing with the average (ensemble or time average) in single particle tracking experiments.

[1] Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008).
[2] T. Miyaguchi and T. Akimoto, Phys. Rev. E 83, 031926 (2011).
[3] T. Akimoto, Phys. Rev. Lett. 108, 164101 (2012)

### 2012年05月02日(水)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

A measurable group theoretic solution to von Neumann's Problem (after Gaboriau and Lyons) (JAPANESE)

### 2012年05月01日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

Minimal models, formality and hard Lefschetz property of
solvmanifolds with local systems (JAPANESE)
[ 講演概要 ]
For a simply connected solvable Lie group G with a
cocompact discrete subgroup {\\Gamma}, we consider the space of
differential forms on the solvmanifold G/{\\Gamma} with values in certain
flat bundle so that this space has a structure of a differential graded
algebra(DGA). We construct Sullivan's minimal model of this DGA. This
result is an extension of Nomizu's theorem for ordinary coefficients in
the nilpotent case. By using this result, we refine Hasegawa's result of
formality of nilmanifolds and Benson-Gordon's result of hard Lefschetz
properties of nilmanifolds.

### 2012年04月27日(金)

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 006号室

[ 講演概要 ]

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/02.html

### 2012年04月25日(水)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Bost-Connes system and class field theory (JAPANESE)