## 過去の記録

#### 談話会・数理科学講演会

16:50-17:50   数理科学研究科棟(駒場) 123号室
Bent Oersted 氏 (Aarhus University and University of Tokyo)
Rigidity of conformal functionals on spheres (ENGLISH)
[ 講演概要 ]
On a compact smooth manifold one may construct a Riemannian metric in many different ways. Each metric gives rise to natural elliptic operators such as the Laplace-Beltrami operator and corresponding spectral invariants, e.g. the eigenvalues, the trace of the heat semigroup, and the zeta function. In
this lecture we shall consider such functionals on the space of metrics on the sphere, combining conformal differential geometry and representation theory of semisimple Lie groups to obtain results about local extremal properties of special functionals. This is based on joint work with Niels Martin Moeller.

### 2015年04月23日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室
Bernold Fiedler 氏 (ベルリン自由大学)
The importance of being just late (ENGLISH)
[ 講演概要 ]
Delays are a ubiquitous nuisance in control. Delays increase finite-dimensional phase spaces to become infinite-dimensional. But, are delays all that bad?

Following an idea of Pyragas, we attempt noninvasive and model-independent stabilization of unstable p-periodic phenomena $u(t)$ by a friendly delay $r$ . Our feedback only evaluates differences $u(t-r)-u(t)$. When the time delay $r$ is chosen to be an integer multiple $np$ of the minimal period $p$, the difference and the feedback vanish alike: the control strategy becomes noninvasive on the target periodic orbit.

We survey promise and limitations of this idea, including applications and an example of delay control of delay equations.

The results are joint work with P. Hoevel, W. Just, I. Schneider, E. Schoell, H.-J. Wuensche, S. Yanchuk, and others. See also

http://dynamics.mi.fu-berlin.de/

#### 東京無限可積分系セミナー

17:00-18:30   数理科学研究科棟(駒場) 002号室

Parabolic analogue of periodic Kazhdan-Lusztig polynomials (JAPANESE)
[ 講演概要 ]
We construct a parabolic analogue of so-called periodic modules, which are modules over the Hecke algebra
associated with an affine Weyl group.
These modules have a basis similar to Kazhdan-Lusztig basis.
Our construction enables us to see the relation between (ordinary)periodic KL-polynomials and parabolic ones.

### 2015年04月22日(水)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 122号室

Construction of minimal skew products of amenable minimal dynamical systems

### 2015年04月21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) 126号室

[ 講演概要 ]
We introduce the ring of differential operators with constant coefficients and commensurate time lags (we use the terminology D$\Delta$ operators from now) initially defined by H. Gl\"using-L\"ur\ss en for ordinary $D\Delta$ operators and observe that various function modules enjoy good cohomological properties over this ring. %After revising the notion of the residue current in the spirit of M. Andersson and E. Wulcan, we introduce the multidimensional version of the ring D$\Delta$ operators.
Combining this ring theoretic observation with the integral representation technique developed by M. Andersson, we solve a certain type of division with bounds. In the last chapter, we prove the injectivity property of various function modules over this ring as well as spectral synthesis type theorems for $D\Delta$ equations.

#### 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 : 16:30-17:00 Common Room

Orbit equivalence relations arising from Baumslag-Solitar groups (JAPANESE)
[ 講演概要 ]
This talk is about measure-preserving actions of countable groups on probability
measure spaces and their orbit structure. Two such actions are called orbit equivalent
if there exists an isomorphism between the spaces preserving orbits. In this talk, I focus
on actions of Baumslag-Solitar groups that have two generators, a and t, with the relation
ta^p=a^qt, where p and q are given integers. This group is well studied in combinatorial
and geometric group theory. Whether Baumslag-Solitar groups with different p and q can
have orbit-equivalent actions is still a big open problem. I will discuss invariants under
orbit equivalence, motivating background and some results toward this problem.

#### Lie群論・表現論セミナー

17:00-18:30   数理科学研究科棟(駒場) 122号室

ベクトル値正則離散系列表現のノルム計算と解析接続 (English)
[ 講演概要 ]

### 2015年04月20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

Weighted Laplacians on real and complex complete metric measure spaces (Japanese)
[ 講演概要 ]
We compare the weighted Laplacians on real and complex (K¥"ahler) metric measure spaces. In the compact case K¥"ahler metric measure spaces are considered on Fano manifolds for the study of K¥"ahler Ricci solitons while real metric measure spaces are considered with Bakry-¥'Emery Ricci tensor. There are twisted Laplacians which are useful in both cases but look alike each other. We see that if we consider noncompact complete manifolds significant differences appear.

#### 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 ]

マルチンゲール性などの時間軸方向のσ加法族の性質を仮定せずに成り立つ時間一様な

という問題である．この例のような増加過程の場合は教科書にある各時刻での確率変数の
４次モーメント有界条件だけで一様概収束を得る．マルコフ性等の時間軸方向の良い性質を

#### 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

Fano 5-folds with nef tangent bundles (日本語)
[ 講演概要 ]
Campana と Peternell は, ネフな接束をもつ Fano 多様体は有理等質多様体で
あると予想した.

とが示されている.

によって場合分けすることができて, 趙・宮岡・Shepherd-Barron, 宮岡, Hwang,
Mok らの結果から, 5 次元の場合には, 擬指数が 4 であるときを除けば有理等

その結果として 5 次元のときには Campana と Peternell の予想が正しいこと
が従う.

### 2015年04月17日(金)

#### 幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 126号室

ブロディ曲線の成す力学系の平均次元 (日本語)
[ 講演概要 ]

### 2015年04月15日(水)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 122号室
Juan Orendain 氏 (UNAM/Univ. Tokyo)
On the tricategory of coordinate free conformal nets
(English)

#### 数理人口学・数理生物学セミナー

14:55-16:40   数理科学研究科棟(駒場) 128演習室号室

(JAPANESE)
[ 講演概要 ]

が歴然としているのは、成熟年齢やサイズなど個体の持つ生活史の特性が、双方
とも異なる事に起因すると考えられている．しかし、それら個体の特性が個体群

ズ構造、両方を考慮した構造人口模型を考える．具体的には、人口規模の増大が

また、この種をあるサイズに達したときに繁殖する一回繁殖生物と仮定する．こ
れらの仮定から生成された構造人口模型の定常状態を環境収容力と考え、サイズ
の成長率の分散（個体差）が環境収容力とそこでの個体群構造への影響を解析し
たい．

### 2015年04月14日(火)

#### 諸分野のための数学研究会

13:30-14:30   数理科学研究科棟(駒場) 056号室
※ 通常の時間と異なります。

[ 講演概要 ]

また、ミクロな気液二相流や微粒子が分散した懸濁液の蒸発プロセス等、工学的に重要であり、また現象としても興味深い事例を時間の許す限り紹介する。

#### 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 : 16:30-17:00 Common Room

Pin(2)-monopole invariants for 4-manifolds (JAPANESE)
[ 講演概要 ]
The Pin(2)-monopole equations are a variant of the Seiberg-Witten equations
which can be considered as a real version of the SW equations. A Pin(2)-mono
pole version of the Seiberg-Witten invariants is defined, and a special feature of
this is that the Pin(2)-monopole invariant can be nontrivial even when all of
the Donaldson and Seiberg-Witten invariants vanish. As an application, we
construct a new series of exotic 4-manifolds.

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

[ 講演概要 ]
With the aim of uniform treatment of multiplicity-free representations of Lie groups, T. Kobayashi introduced the theory of visible actions on complex manifolds.

In this talk we consider visible actions of a compact real form U of a connected complex reductive algebraic group G on G-spherical varieties. Here a complex G-variety X is said to be spherical if a Borel subgroup of G has an open orbit on X. The sphericity implies the multiplicity-freeness property of the space of polynomials on X. Our main result gives an abstract proof for the visibility of U-actions. As a corollary, we obtain an alternative proof for the visibility of U-actions on linear multiplicity-free spaces, which was earlier proved by A. Sasaki (2009, 2011), and the visibility of U-actions on generalized flag varieties, earlier proved by Kobayashi (2007) and T- (2013, 2014).

### 2015年04月13日(月)

#### 東京確率論セミナー

16:50-17:50   数理科学研究科棟(駒場) 128号室
Hans Rudolf Kuensch 氏 (ETH Zurich)
Modern Monte Carlo methods -- Some examples and open questions (ENGLISH)
[ 講演概要 ]
Probability and statistics once had strong relations, but in recent years the two fields have moved into opposite directions. Despite this, I believe that both fields would profit if they continued to interact. Monte Carlo methods are one topic that is of interest to both probability and statistics: Statisticians use advanced Monte Carlo methods, and analyzing these methods is a challenge for probabilists. I will illustrate this, using as examples rare event estimation by sample splitting, approximate Bayesian computation and Monte Carlo filters.

#### 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

Campana's Multiplicity and Integral Points on P^2 (English)
[ 講演概要 ]
We analyze when the complements of (possibly reducible) curves in P^2 have Zariski-dense integral points. The analysis utilizes the structure theories for affine surfaces based on logarithmic Kodaira dimension. When the log Kodaira dimension is one, an important role is played by Campana's multiplicity divisors for fibrations, but there are some subtleties. This is a joint work with Aaron Levin (Michigan State).

#### 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
Frédéric Campana 氏 (Université de Lorraine)
An orbifold version of Miyaoka's semi-positivity theorem and applications (English)
[ 講演概要 ]
This orbifold' version of Miyaoka's theorem says that if (X,D)
is a projective log-canonical pair with K_X+D pseudo-effective,
then its 'cotangent' sheaf $¥Omega^1(X,D)$ is generically semi-positive.
The definitions will be given. The original proof of Miyaoka, which
mixes
char 0 and char p>0 arguments could not be adapted. Our proof is in char
0 only.

A first consequence is when (X,D) is log-smooth with reduced boudary D,
in which case the cotangent sheaf is the classical Log-cotangent sheaf:
if some tensor power of $¥omega^1_X(log(D))$ contains a 'big' line
bundle, then K_X+D is 'big' too. This implies, together with work of
Viehweg-Zuo,
the hyperbolicity conjecture' of Shafarevich-Viehweg.

The preceding is joint work with Mihai Paun.

A second application (joint work with E. Amerik) shows that if D is a
non-uniruled smooth divisor in aprojective hyperkaehler manifold with
symplectic form s,
then its characteristic foliation is algebraic only if X is a K3 surface.
This was shown previously bt Hwang-Viehweg assuming D to be of general
type. This result has some further consequences.

### 2015年04月10日(金)

#### 統計数学セミナー

14:50-16:00   数理科学研究科棟(駒場) 128号室
Yacine Ait-Sahalia 氏 (Princeton University)
Principal Component Analysis of High Frequency Data (joint with Dacheng Xiu)
[ 講演概要 ]
We develop a methodology to conduct principal component analysis of high frequency financial data. The procedure involves estimation of realized eigenvalues, realized eigenvectors, and realized principal components and we provide the asymptotic distribution of these estimators. Empirically, we study the components of the constituents of Dow Jones Industrial Average Index, in a high frequency version, with jumps, of the Fama-French analysis. Our findings show that, excluding jump variation, three Brownian factors explain between 50 and 60% of continuous variation of the stock returns. Their explanatory power varies over time. During crises, the first principal component becomes increasingly dominant, explaining up to 70% of the variation on its own, a clear sign of systemic risk.

### 2015年04月08日(水)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 122号室

On treeable equivalence relations arising from the Baumslag-Solitar groups
(English)

#### 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

Integrality of $p$-adic multiple zeta values and application to finite multiple zeta values.
(English)
[ 講演概要 ]
I will give a proof of an integrality of p-adic multiple zeta values. I would also like to explain how it can be applied to give an upper bound of the dimension of finite multiple zeta values.
(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.)

### 2015年04月07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 : 16:30-17:00 Common Room

Potential functions for Grassmannians (JAPANESE)
[ 講演概要 ]
Potential functions are Floer-theoretic invariants
obtained by counting Maslov index 2 disks
with Lagrangian boundary conditions.
In the talk, we will discuss our joint work
with Yanki Lekili and Yuichi Nohara
on Lagrangian torus fibrations on the Grassmannian
of 2-planes in an n-space,
the potential functions of their Lagrangian torus fibers,
and their relation with mirror symmetry for Grassmannians.

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
Bent Orsted 氏 (Aarhus University)
Branching laws and elliptic boundary value problems
(English)
[ 講演概要 ]
Classically the Poisson transform relates harmonic functions in the complex upper half plane to their boundary values on the real axis. In some recent work by Caffarelli et al. some new generalizations of this appears in connection with the fractional Laplacian. In this lecture we
shall explain how the symmetry-breaking operators introduced by T. Kobayashi for studying branching laws may shed new light on the situation for elliptic boundary value problems. This is based on joint work with J. M\"o{}llers and G. Zhang.

### 2015年04月06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

Analytic torsion for K3 surfaces with involution (Japanese)
[ 講演概要 ]
In 2004, I introduced a holomorphic torsion invariant for 2-elementary K3 surfaces, i.e., K3 surfaces with involution. In the talk, I will report a recent progress in this invariant. Namely, for all possible deformation types, the holomorphic torsion invariant viewed as a function on the moduli space, is expressed as the product of an explicit Borcherds lift and an explicit Siegel modular form. If time permits, I will interpret the result in terms of the BCOV invariant, i.e., the genus-one string amplitude in B-model, for Calabi-Yau threefolds of Borcea-Voisin. This is a joint work with Shouhei Ma.