## 過去の記録

### 2012年05月30日(水)

#### 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
Valentina Di Proietto 氏 (東京大学数理科学研究科)
Kernel of the monodromy operator for semistable curves (ENGLISH)
[ 講演概要 ]
For a semistable curve, we study the action of the monodromy operator on the first log-crystalline cohomology group. In particular we examine the relation between the kernel of the monodromy operator and the first rigid cohomology group, in the case of trivial coefficients, giving a new proof of a theorem of B. Chiarellotto and in the case of certain unipotent F-isocrystals as coefficients.
This is a joint work in progress with B. Chiarellotto, R. Coleman and A. Iovita.

#### 講演会

14:50-16:20   数理科学研究科棟(駒場) 123号室
This is the fourth of four lectures planned on 5/25, 5/28, 5/29 and 5/30.
Harald Niederreiter 氏 (RICAM, Austrian Academy of Sciences)
Low-discrepancy sequences and algebraic curves over finite fields (III) (ENGLISH)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

### 2012年05月29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

Triple linking numbers and triple point numbers
of torus-covering $T^2$-links
(JAPANESE)
[ 講演概要 ]
The triple linking number of an oriented surface link was defined as an
torus-covering $T^2$-link $\\mathcal{S}_m(a,b)$ is a surface link in the
form of an unbranched covering over the standard torus, determined from
two commutative $m$-braids $a$ and $b$.
In this talk, we consider $\\mathcal{S}_m(a,b)$ when $a$, $b$ are pure
$m$-braids ($m \\geq 3$), which is a surface link with $m$-components. We
present the triple linking number of $\\mathcal{S}_m(a,b)$ by using the
linking numbers of the closures of $a$ and $b$. This gives a lower bound
of the triple point number. In some cases, we can determine the triple
point numbers, each of which is a multiple of four.

#### GCOEレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (CNRS, Orsay)
Random walk on reductive groups. (ENGLISH)
[ 講演概要 ]
The asymptotic behavior of the sum of real numbers chosen independantly with same probability law is controled by many classical theorems: Law of Large Numbers, Central Limit Theorem, Law of Iterated Logarithm, Local Limit Theorem, Large deviation Principle, 0-1 Law,... In these introductory talks I will recall these classical results and explain their analogs for products of matrices chosen independantly with same probability law, when the action of the support of the law is semisimple. We will see that the dynamics of the corresponding action on the flag variety is a crucial tool for studying these non-commutative random walks.

#### 講演会

14:50-16:20   数理科学研究科棟(駒場) 123号室
This is the third of four lectures; the first is the colloquium on May 25th(Fri) 16:30--17:30 at 002 and the second is on May 28th(Mon).
Harald Niederreiter 氏 (RICAM, Austrian Academy of Sciences)
Low-discrepancy sequences and algebraic curves over finite fields (II) (ENGLISH)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

### 2012年05月28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

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

・$\mu$-constant-deformation の Tjurina 数
・対数的ベクトル場の構造と構成法
・ニュートン非退化な超曲面に対する Kouchnirenko の公式
について述べる.

#### 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
Mihnea Popa 氏 (University of Illinois at Chicago)
Generic vanishing and linearity via Hodge modules (ENGLISH)
[ 講演概要 ]
I will explain joint work with Christian Schnell, in which we extend the fundamental results of generic vanishing theory (for instance for the canonical bundle of a smooth projective variety) to bundles of holomorphic forms and to rank one local systems, where parts of the theory have eluded previous efforts. To achiever this, we bring all of the old and new results under the same roof by enlarging the scope of generic vanishing theory to the study of filtered D-modules associated to mixed Hodge modules. Besides Saito's vanishing and direct image theorems for Hodge modules, an important input is the Laumon-Rothstein Fourier transform for bundles with integrable connection.

#### 講演会

14:50-16:20   数理科学研究科棟(駒場) 123号室
This is the second of four lectures; the first is the colloquium on May 25th(Fri) 16:30--17:30 at 002.
Harald Niederreiter 氏 (RICAM, Austrian Academy of Sciences)
Low-discrepancy sequences and algebraic curves over finite fields (I) (ENGLISH)
[ 講演概要 ]
This is the second of the four lectures. The first one is Colloquium talk on May 25th 16:30--17:30 at 002.

Abstract from Colloquium:
Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo
methods in computational mathematics. QMC methods employ evenly distributed
low-discrepancy sequences instead of the random samples used in Monte Carlo methods.
For many types of computational problems, QMC methods are more efficient than
Monte Carlo methods. After a general introduction to QMC methods, the talk focuses
on the problem of constructing low-discrepancy sequences which has fascinating links
with subjects such as finite fields, error-correcting codes, and algebraic curves.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

### 2012年05月26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
このセミナーは,月に1度程度,不定期に開催されます.

The Takagi function - a survey (JAPANESE)
[ 講演概要 ]
More than a century has passed since Takagi published his simple example of a continuous but nowhere differentiable function,
yet Takagi's function -- as it is now commonly referred
to despite repeated rediscovery
by mathematicians in the West -- continues to inspire, fascinate and puzzle researchers as never before.
In this talk, I will give not only an overview of the history and known characteristics of the function,
but also discuss some of the fascinating applications it has found -- some quite recently! -- in such diverse areas of mathematics as number theory, combinatorics, and analysis.

Dyadic, classical and martingale harmonic analysis II (JAPANESE)
[ 講演概要 ]
In a filtered measure space, we investigate the characterization of weights for which positive operators and maximal operators are bounded.

For this, a refinement of Carleson embedding theorem is introduced in this setting. Sawyer type characterization of weights for which a two-weight norm inequality for a generalized Doob's maximal operator holds is established by an application of our Carleson embedding theorem. If time permits, we would like to mention Hyt\\"onen-P\\'erez type sharp one-weight estimate of Doob's
maximal operator which is derived from our two-weight characterization.
This talk is based on a joint work with Professor Hitoshi Tanaka
(The University of Tokyo).

### 2012年05月25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)。

Harald Niederreiter 氏 (RICAM, Austrian Academy of Sciences)
Quasi-Monte Carlo methods: deterministic is often better than random (ENGLISH)
[ 講演概要 ]
Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo methods in computational mathematics. QMC methods employ evenly distributed low-discrepancy sequences instead of the random samples used in Monte Carlo methods. For many types of computational problems, QMC methods are more efficient than Monte Carlo methods. After a general introduction to QMC methods, the talk focuses on the problem of constructing low-discrepancy sequences which has fascinating links with subjects such as finite fields, error-correcting codes, and algebraic curves.

This talk also serves as the first talk of the four lecture series. The other three are on 5/28, 5/29, 5/30, 14:50-16:20 at room 123.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

#### GCOEレクチャーズ

14:00-15:30   数理科学研究科棟(駒場) 118号室
Mihnea Popa 氏 (University of Illinois at Chicago)
Generic vanishing theory and connections with derived categories (ENGLISH)
[ 講演概要 ]
I will give a basic introduction to the main results regarding the cohomology of deformations of the canonical bundle, and explain a connection with certain t-structures on the derived categories of Picard varieties. (This will also serve as an introduction for the talk at AG seminar on 5/28, 15:30-17:00.)

### 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

http://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 ]
http://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).