## 過去の記録

#### 数理人口学・数理生物学セミナー

14:40-16:10   数理科学研究科棟(駒場) 052号室

[ 講演概要 ]

はない.そこで本研究では,individual based modelに東京都市圏パーソント
リップ調査を組み合わせることにより感染拡大モデルを構築し,数値シミュレー
ションによって外出規制および施設閉鎖の効果を検討した.外出規制に関して
は,規制日数が12日以上と長い場合には効果が大きいことがわかった.また,施

わらないものの,累積罹患率は低下することがわかった.

### 2010年01月19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

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

Entire Cyclic Cohomology of Noncommutative Spheres

#### トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム

Localization via group action and its application to
the period condition of algebraic minimal surfaces
[ 講演概要 ]
The optimal estimate for the number of exceptional
values of the Gauss map of algebraic minimal surfaces is a long
standing problem. In this lecture, I will introduce new ideas
toward the solution of this problem. The collective Cohn-Vossen
inequality" is the key idea. From this we have effective
Nevanlinna's lemma on logarithmic derivative for a certain class
of meromorphic functions on the disk. On the other hand, we can
construct a family holomorphic functions on the disk from the
Weierstrass data of the algebraic minimal surface under
consideration, which encodes the period condition.
Applying effective Lemma on logarithmic derivative to these
functions, we can extract an intriguing inequality.

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 118号室

Fractional Evolution Equations and Applications 1
[ 講演概要 ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.

Motivation: Continuous time random walk (CTRW) process
Fractional differential equations in time and Mittag-Leffler functions

### 2010年01月18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

スプライス商特異点について

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室
Anne-Sophie Kaloghiros 氏 (RIMS)
The divisor class group of terminal Gorenstein Fano 3-folds and rationality questions
[ 講演概要 ]
Let Y be a quartic hypersurface in CP^4 with mild singularities, e.g. no worse than ordinary double points.
If Y contains a surface that is not a hyperplane section, Y is not Q-factorial and the divisor class group of Y, Cl Y, contains divisors that are not Cartier. However, the rank of Cl Y is bounded.

In this talk, I will show that in most cases, it is possible to describe explicitly the divisor class group Cl Y by running a Minimal Model Program (MMP) on X, a small Q-factorialisation of Y. In this case, the generators of Cl Y/ Pic Y are topological traces " of K-negative extremal contractions on X.
This has surprising consequences: it is possible to conclude that a number of families of non-factorial quartic 3-folds are rational.
In particular, I give some examples of rational quartic hypersurfaces Y_4\\subset CP^4 with rk Cl Y=2 and show that when the divisor class group of Y has sufficiently high rank, Y is always rational.

### 2010年01月15日(金)

#### GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 117号室

### 2010年01月14日(木)

#### 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
Marius Junge 氏 (Univ. Illinois, Urbana-Champaign)
Applications of operator algebras in Quantum information theory

### 2010年01月13日(水)

#### 講演会

16:45-17:45   数理科学研究科棟(駒場) 128号室
Felix Rubin 氏 (Zurich 大学)
Scaled limit for the largest eigenvalue from the generalized Cauchy ensemble

#### 講演会

15:30-16:30   数理科学研究科棟(駒場) 128号室
Michael Allman 氏 (Warwick 大学)
Breaking the chain: slow versus fast pulling

### 2010年01月12日(火)

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100112nishioka

#### トポロジー火曜セミナー

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

Index problem for generically-wild homoclinic classes in dimension three
[ 講演概要 ]
In the sphere of non-hyperbolic differentiable dynamical systems, one can construct an example of a homolinic class which does not admit any kind of dominated splittings (a weak form of hyperbolicity) in a robust way. In this talk, we discuss the index (dimension of the unstable manifold) of the periodic points inside such homoclinic classes from a $C^1$-generic viewpoint.

On a generalized suspension theorem for directed Fukaya categories
[ 講演概要 ]
The directed Fukaya category $\\mathrm{Fuk} W$ of exact Lefschetz
fibration $W : X \\to \\mathbb{C}$ proposed by Kontsevich is a
categorification of the Milnor lattice of $W$. This is defined as the
directed $A_\\infty$-category $\\mathrm{Fuk} W = \\mathrm{Fuk}^\\to \\mathbb{V}$ generated by a distinguished basis $\\mathbb{V}$ of
vanishing cycles.

Recently Seidel has proved that this is stable under the suspension $W + u^2$ as a consequence of his foundational work on the directed
Fukaya category. We generalize his suspension theorem to the $W + u^d$
case by considering partial tensor product $\\mathrm{Fuk} W \\otimes' \\mathcal{A}_{d-1}$, where $\\mathcal{A}_{d-1}$ is the category
corresponding to the $A_n$-type quiver. This also generalizes a recent
work by the author with Kazushi Ueda.

### 2010年01月08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) 123号室
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)

[ 講演概要 ]

### 2010年01月07日(木)

#### 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
Luc Rey-Bellet 氏 (Univ. Massachusetts)
Large deviations, Billiards, and Non-equilibrium Statistical Mechanics

#### GCOEセミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
LucRey-Bellet 氏 (Univ. Massachusetts)
Large deviations, Billiards, and Non-equilibrium Statistical Mechanics
[ 講演概要 ]
Large deviations have applications in many aspects of statistical mechanics. New applications for the steady states of non-equilibrium statistical mechanics have emerged during the past ten years and these applications deal with the fluctuations of the entropy production. After discussing some general aspects of entropy production we turn to concrete examples, in particular billiards with and without external forces and discuss large deviations theorems for such systems.

### 2010年01月05日(火)

#### トポロジー火曜セミナー

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

The volume growth of hyperkaehler manifolds of type $A_{\\infty}$
[ 講演概要 ]
Hyperkaehler manifolds of type $A_{\\infty}$ were constructed due to Anderson-Kronheimer-LeBrun and Goto. These manifolds are 4-demensional, noncompact and their homology groups are infinitely generated. We focus on the volume growth of these hyperkaehler metrics. Here, the volume growth is asymptotic behavior of the volume of a ball of radius $r0$ with the center fixed. There are known examples of hyperkaehler manifolds whose volume growth is $r^4$ (ALE space) or $r^3$ (Taub-NUT space). In this talk we show that there exists a hyperkaehler manifold of type $A_{\\infty}$ whose volume growth is $r^c$ for a given $3 松尾 信一郎 氏 (東京大学大学院数理科学研究科) 17:30-18:30 On the Runge theorem for instantons [ 講演概要 ] A classical theorem of Runge in complex analysis asserts that a meromorphic function on a domain in the Riemann sphere can be approximated, over compact subsets, by rational functions, that is, meromorphic functions on the Riemann sphere. This theorem can be paraphrased by saying that any solution of the Cauchy-Riemann equations on a domain in the Riemann sphere can be approximated, over compact subsets, by global solutions. In this talk we will present an analogous result in which the Cauchy-Riemann equations on Riemann surfaces are replaced by the Yang-Mills instanton equations on oriented 4-manifolds. We will also mention that the Runge theorem for instantons can be applied to develop Yang-Mills gauge theory on open 4-manifolds. ### 2009年12月25日(金) #### 講演会 17:00-18:00 数理科学研究科棟(駒場) 370号室 Academician T. Sh. Kalmenov 氏 (Research Centre of Physics and Mathematics Almaty, Kazakhstan) A criterion for the strong solvability of the mixed Cauchy problem for the Laplace equation ### 2009年12月24日(木) #### 数理人口学・数理生物学セミナー 16:00-17:30 数理科学研究科棟(駒場) 123号室 堀内 四郎 氏 (The City University of New York, Hunter College) Decomposition分析:趨勢データ分析の新しい枠組とアプローチ [ 講演概要 ] A demographic measure is often expressed as a deterministic or stochastic function of multiple variables (covariates), and a general problem (the decomposition problem) is to assess contributions of individual covariates to a difference in the demographic measure (dependent variable) between two populations. We propose a method of decomposition analysis based on an assumption that covariates change continuously along an actual or hypothetical dimension. This assumption leads to a general model that logically justifi es the additivity of covariate effects and the elimination of interaction terms, even if the dependent variable itself is a nonadditive function. A comparison with earlier methods illustrates other practical advantages of the method: in addition to an absence of residuals or interaction terms, the method can easily handle a large number of covariates and does not require a logically meaningful ordering of covariates. Two empirical examples show that the method can be applied fl exibly to a wide variety of decomposition problems. [ 講演参考URL ] http://shiro_horiuchi.homestead.com/homepage.html ### 2009年12月22日(火) #### Lie群論・表現論セミナー 16:30-18:00 数理科学研究科棟(駒場) 126号室 西山享 氏 (青山学院大学) 既約表現の隨伴多様体は余次元1で連結か?--- 証明の破綻とその背景 [ 講演概要 ] 既約 Harish-Chandra$ (g, K) $加群の原始イデアルの隨伴多様体が既約であって、ただ一つの冪零隨伴軌道$ O^G $の閉包になることはよく知られている(Joseph, Borho)。 一方、HC加群の隨伴多様体は必ずしも既約でないが、その既約成分は$ O^G $の$ K $-等質ラグランジュ部分多様体の閉包になる。 それらの既約成分は余次元1で連結であることをいくつかの集会で報告したが、その証明には初等的な誤りがあった。セミナーでは、証明の元になった Vogan の定理の紹介(もちろん間違っていない)と、それを拡張する際になぜ証明が破綻するかについてお話しする。(今のところ証明修復の目処は立っていない。) [ 講演参考URL ] https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html #### 作用素環セミナー 14:40-18:00 数理科学研究科棟(駒場) 128号室 谷本溶 氏 (Univ. Roma Tor Vergata'') 14:40-16:10 Symmetric representations of the group of diffeomorphisms of$\\mathbb R\$
David Kerr 氏 (Texas A&M Univ.) 16:30-18:00
Topological entropy for actions of sofic groups

#### 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

Relative DG-category, mixed elliptic motives and elliptic polylog
[ 講演概要 ]
We consider a full subcategory of
mixed motives generated by an elliptic curve
over a field, which is called the category of
mixed elliptic motives. We introduce a DG
Hopf algebra such that the categroy of
mixed elliptic motives is equal to that of
comodules over it. For the construction, we
use the notion of relative DG-category with
respect to GL(2). As an application, we construct
an mixed elliptic motif associated to
the elliptic polylog. It is a joint work with
Kenichiro Kimura.

#### 東京無限可積分系セミナー

10:00-14:00   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

Y. Avishai 氏 (Ben Gurion University) 13:00-14:00
Laplacian on graphs: Examples from physics
[ 講演概要 ]
When the Laplacian operator is written as a second order difference operator the physicists refer to it as a tight-binding model. In two dimensions the eigenvalue problem connects the function at a given point to the sum of its values on its nearest neighbors. In numerous physical problems, some of the coefficients are multiplied by phase factors. This problem is amazingly rich and the pattern of eigenvalues E(φ) has a fractal nature known as the Hofstadter butterfly.
I will discuss some of these models and especially concentrate on two problems, which I solved recently, where the vertices of the graphs are located on the sphere S2. The first one corresponds to the famous problem of the Dirac magnetic monopole, while in the second one, the eigenfunctions are two component vectors and the phase factors are replaced by unitary 2x2 matrices. This is relevant to the spin-orbit problem in Physics. In both cases the solutions can be obtained in closed form, and exhibit a beautiful symmetry pattern. Their elucidation requires some special techniques in graph theory. Quite surprisingly, the spectra of the two systems coincide at one symmetry point.

### 2009年12月21日(月)

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室

Ampleness of two-sided tilting complexes
[ 講演概要 ]
From the view point of noncommutative algebraic geometry (NCAG),
a two-sided tilting complex is an analog of a line bundle.
In this talk we introduce the notion of ampleness for two-sided
tilting complexes over finite dimensional algebras.
From the view point of NCAG, the Serre functors are considered to be
shifted canonical bundles. We show by examples that the property
of shifted canonical bundle captures some representation theoretic
property of algebras.

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 128号室
Thomas Simon 氏 (Universite de Lille 1)
Absolute continuity of Ornstein-Uhlenbeck processes
[ 講演概要 ]
Let X be a multidimensional Ornstein-Uhlenbeck process, solution to the S.D.E.

dX = AX + dB

where A is a real nxn matrix and B a Lévy process. We show that when A is non-singular, the law of X_1 is absolutely continuous if and only if the jumping measure of B fulfils a certain geometric condition with respect to A and the Gaussian part of B, which we call the exhaustion property. This optimal criterion is much weaker than for B, which might be very singular and genuinely one-dimensional. The proof uses a certain time derivation procedure and basic arguments from controllability theory.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/13.html