## 過去の記録

#### 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

[ 講演概要 ]
The main part of this talk is a joint work with my colleagues, M. Abe and S. Hamano. After the solution of Cousin II problem by K. Oka III in 1939, he thought an extra-zero problem in 1945 (his posthumous paper) asking if it is possible to solve an arbitrarily given Cousin II problem adding some extra-zeros whose support is disjoint from the given one. Some special case was affirmatively confirmed in dimension two and a counter-example in dimension three or more was obtained. We will give a complete solution of this problem with examples and to discuss some new questions. An example on a toric variety of which idea is based on K. Stein's paper in 1941 has some special interest and will be discussed. I would like also to discuss some analytic intersections form the viewpoint of Nevanlinna theory.

### 2011年11月04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 ]

このわずか二十年少々の間にも複比に関する新たなそして重要な発見が

いまだに限られているようである.そのような現状について,個人的な

### 2011年11月02日(水)

#### 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

Hypergeometric series and arithmetic-geometric mean over 2-adic fields (JAPANESE)
[ 講演概要 ]
Dwork proved that the Gaussian hypergeometric function on p-adic numbers
can be extended to a function which takes values of the unit roots of
ordinary elliptic curves over a finite field of characteristic p>2.
We present an analogous theory in the case p=2.
As an application, we give a relation between the canonical lift
and the unit root of an elliptic curve over a finite field of
characteristic 2
by using the 2-adic arithmetic-geometric mean.

### 2011年11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

Motivic Milnor fibers and Jordan normal forms of monodromies (JAPANESE)
[ 講演概要 ]
We introduce a method to calculate the equivariant
Hodge-Deligne numbers of toric hypersurfaces.
Then we apply it to motivic Milnor
fibers introduced by Denef-Loeser and study the Jordan
normal forms of the local and global monodromies
of polynomials maps in various situations.
Especially we focus our attention on monodromies
at infinity studied by many people. The results will be
explicitly described by the convexity" of
the Newton polyhedra of polynomials. This is a joint work
with Y. Matsui and A. Esterov.

### 2011年10月31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

Minimal model theory for log surfaces (JAPANESE)
[ 講演概要 ]
We discuss the log minimal model theory for log sur- faces. We show that the log minimal model program, the finite generation of log canonical rings, and the log abundance theorem for log surfaces hold true under assumptions weaker than the usual framework of the log minimal model theory.

#### PDE実解析研究会

13:30-14:30   数理科学研究科棟(駒場) 056号室

Horst Heck
Stationary Weak Solutions of the Navier-Stokes Equations Past an Obstacle (ENGLISH)
[ 講演概要 ]
Consider the stationary Navier-Stokes equations in an exterior smooth domain $\\Omega$. If the flow condition $u_\\infty$ for $u$ at infinity is non-zero and the external force $f\\in \\dot H^{-1}_2(\\Omega)$ is given Leray constructed a weak solution $u\\in \\dot H^1_2(\\Omega)$, the homogeneous Sobolev space, with $u-u_\\infty\\in L^6(\\Omega)$.
We show that if in addition $f\\in \\dot H^{-1}_q(\\Omega)$ for some $q\\in (4/3,4)$ then the weak solution has the property $u-u_\\infty\\in L^{4q/(4-q)}(\\Omega)$.
This additional integrability implies that $u$ satisfies the energy identity. Further consequences are uniqueness results for small $u_\\infty$ and $f$ and continuous dependence of the solution with respect to $u_\\infty$.
The presented results are joint work with Hyunseok Kim and Hideo Kozono.

#### 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

Classification of Moishezon twistor spaces on 4CP^2 (JAPANESE)

### 2011年10月29日(土)

#### 東京無限可積分系セミナー

11:00-14:30   数理科学研究科棟(駒場) 117号室
Alexander Orlov 氏 (Nonlinear Wave Processes Laboratory, Oceanology Institute (Moscow)) 11:00-12:00
CKP Hierarchy, Bosonic Tau Function, Bosonization Formulae﻿ and Orthogonal Polynomials both in Odd and Even Variables
(based on a joint work with Johan van de Leur and Takahiro Shiota) (ENGLISH)
[ 講演概要 ]
We develop the theory of CKP hierarchy introduced in the papers of Kyoto school where the CKP tau function is written as a vacuum expectation value in terms of free bosons. We show that a sort of odd currents naturaly appear. ﻿We consider bosonization formulae which relate bosonic Fock vectors to polynomials in even and odd Grassmannian variables, where both sets play a role of higher times.

van Diejenの$q$差分作用素に対する核関係式と

[ 講演概要 ]
$BC$型のCauchy型核関数がKoornwinderの$q$差分作用素に対して, ある関係式を満たすことが知られている. 本講演ではこの結果を一般化して, 核関数とvan Diejenの$q$差分作用素族との関係を述べる. また,この関係式から現れる2種類の多重$q$超幾何級数の変換公式を紹介する.

### 2011年10月26日(水)

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 000号室

[ 講演概要 ]

ユークリッド距離の二乗の場合に対し,決定論的な解(最適輸送写像)が

また,この事実に関連した,定常時系列モデルを紹介する.

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/04.html

### 2011年10月25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
Andrei Pajitnov 氏 (Univ. de Nantes, Univ. of Tokyo)
Circle-valued Morse theory for complex hyperplane arrangements (ENGLISH)
[ 講演概要 ]
Let A be a complex hyperplane arrangement
in an n-dimensional complex vector space V.
Denote by H the union of the hyperplanes
and by M the complement to H in V.

We develop the real-valued and circle-valued Morse
theory on M. We prove that if A is essential then
M has the homotopy type of a space
obtained from a finite n-dimensional
CW complex fibered over a circle,
by attaching several cells of dimension n.

We compute the Novikov homology of M and show
that its structure is similar to the
homology with generic local coefficients:
it vanishes for all dimensions except n.

This is a joint work with Toshitake Kohno.

#### 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

コホモロジカル誘導の局所化 (ENGLISH)
[ 講演概要 ]
コホモロジカル誘導は(g,K)-加群に対して代数的に定義され、半単純リー群の離散系列表現、主系列表現(のHarish-Chandra加 群)、Zuckerman加群などを生成する。
Borel部分代数の1次元表現からの誘導の場合、誘導された表現は旗多様体のD加群を用いて実現できることが,Hecht, Milicic, Schmid, Wolfにより示されている。

### 2011年10月22日(土)

#### 東京無限可積分系セミナー

13:30-16:00   数理科学研究科棟(駒場) 117号室
Leonid Rybnikov 氏 (IITP, and State University Higher School of Economics,
Department of Mathematics) 13:30-14:30
Quantization of Quasimaps' Spaces (joint work with M. Finkelberg) (ENGLISH)
[ 講演概要 ]
Quasimaps' space Z_d (also known as Drinfeld's Zastava space) is a
remarkable compactification of the space of based degree d maps from
the projective line to the flag variety of type A. The space Z_d has a
natural Poisson structure,
which goes back to Atiyah and Hitchin. We describe
the Quasimaps' space as some quiver variety, and define the
Atiyah-Hitchin Poisson structure in quiver terms.
This gives a natural way to quantize this Poisson structure.
The quantization of the coordinate ring of the Quasimaps' space turns
to be some natural subquotient of the Yangian of type A.
I will also discuss some generalization of this result to the BCD types.
Anton Zabrodin 氏 (
Instituteof Biochemical Physics) 15:00-16:00
Quantum integrable models with elliptic R-matrices
and elliptic hypergeometric series (ENGLISH)
[ 講演概要 ]
Intertwining operators for infinite-dimensional representations of the
Sklyanin algebra with spins l and -l-1 are constructed using the technique of
intertwining vectors for elliptic L-operator. They are expressed in
terms of
elliptic hypergeometric series with operator argument. The intertwining
operators obtained (W-operators) serve as building blocks for the
elliptic R-matrix
which intertwines tensor product of two L-operators taken in
infinite-dimensional
representations of the Sklyanin algebra with arbitrary spin. The
Yang-Baxter equation
for this R-matrix follows from simpler equations of the star-triangle
type for the
W-operators. A natural graphic representation of the objects and
equations involved
in the construction is used.

### 2011年10月20日(木)

#### GCOEセミナー

16:30-18:00   数理科学研究科棟(駒場) 270号室
O. Emanouilov 氏 (Colorado State University)
On reconstruction of Lame coefficients from partial Cauchy data (ENGLISH)
[ 講演概要 ]
For the isotropic Lame system, we prove that if the Lame coefficient ¥mu is a positive constant, then both Lame coefficients can be recovered from the partial Cauchy data.

### 2011年10月19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

Andrei Suslin 氏 (Northwestern University)
K_2 of the biquaternion algebra (ENGLISH)
[ 講演参考URL ]
http://www.ihes.fr/~abbes/SGA/suslin.pdf

### 2011年10月17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

Compact locally homogeneous Kähler manifolds $\Gamma\backslash G/K$ (JAPANESE)

### 2011年10月12日(水)

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 000号室

On Convergence Rate of Multiple Kernel Learning with Various Regularization Types (JAPANESE)
[ 講演概要 ]

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/03.html

### 2011年10月11日(火)

#### 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
Gael Meigniez 氏 (Univ. de Bretagne-Sud, Chuo Univ.)
Making foliations of codimension one,
thirty years after Thurston's works
(ENGLISH)
[ 講演概要 ]
In 1976 Thurston proved that every closed manifold M whose
Euler characteristic is null carries a smooth foliation F of codimension
one. He actually established a h-principle allowing the regularization of
Haefliger structures through homotopy. I shall give some accounts of a new,
simpler proof of Thurston's result, not using Mather's homology equivalence; and also show that this proof allows to make F have dense leaves if dim M is at least 4. The emphasis will be put on the high dimensions.

#### 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

[ 講演概要 ]

により全空間上のスケール不変なTrudinger-Moser型不等式が

2次元で考察し、同方程式の局所解及び大域解の存在を証明する。

### 2011年10月07日(金)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Towards the classification of non-simple $C^*$-algebras of real rank zero (ENGLISH)

### 2011年10月05日(水)

#### 諸分野のための数学研究会

10:00-11:00   数理科学研究科棟(駒場) 056号室

Chun Liu 氏 (University of Tokyo / Pennsylvania State University)
Energetic Variational Approaches for Ionic Fluids (ENGLISH)
[ 講演概要 ]
In this talk, I will present our recent study on the ionic transport through ion channels in cell membranes. Motivated by our earlier work on energetic variational approaches, developed for various complex fluids, especially electrorheological (ER) fluids (Phys. Rev. Lett. 101, 194503 (2008)), we derived/proposed a coupled system for ionic solutions, which takes into account of the solvent water, the diffusion and electro-static interaction of different ions. In particular, I will emphasize on the selectivity effects of the ion channels, under the simplest geometric and molecular structures.

### 2011年10月04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

[ 講演概要 ]

る. Osinにより相対的双曲群の双曲的に埋め込まれた部分群が導入され, 付加的
な代数的性質を持つ相対的擬凸部分群として特徴づけられている. この講演では,

### 2011年09月20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
Clara Loeh 氏 (Univ. Regensburg)
Functorial semi-norms on singular homology (ENGLISH)
[ 講演概要 ]
Functorial semi-norms on singular homology add metric information to
homology classes that is compatible with continuous maps. In particular,
functorial semi-norms give rise to degree theorems for certain classes
of manifolds; an invariant fitting into this context is Gromov's
simplicial volume. On the other hand, knowledge about mapping degrees
allows to construct functorial semi-norms with interesting properties;
for example, so-called inflexible simply connected manifolds give rise
to functorial semi-norms that are non-trivial on certain simply connected
spaces.

### 2011年08月12日(金)

#### GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 370号室
Benny Hon 氏 (Department of Mathematics City University of Hong Kong)
Kernel-based Approximation Methods for Cauchy Problems of Fractional Order Partial Differential Equations (ENGLISH)
[ 講演概要 ]
In this talk we present the recent development of meshless computational methods based on the use of kernel-based functions for solving various inverse and ill-posed problems. Properties of some special kernels such as harmonic kernels; kernels from the construction of fundamental and particular solutions; Green’s functions; and radial basis functions will be discussed. As an illustration, the recent work in using the method of fundamental solutions combined with the Laplace transform and the Tikhonov regularization techniques to solve Cauchy problems of Fractional Order Partial Differential Equations (FOPDEs) will be demonstrated. The main idea is to approximate the unknown solution by a linear combination of fundamental solutions whose singularities are located outside the solution domain. The Laplace transform technique is used to obtain a more accurate numerical approximation of the fundamental solutions and the L-curve method is adopted for searching an optimal regularization parameter in obtaining stable solution from measured data with noises.

### 2011年08月03日(水)

#### 博士論文発表会

10:00-11:15   数理科学研究科棟(駒場) 123号室

Abundance conjecture and canonical bundle formula(アバンダンス予想と標準因子公式) (JAPANESE)

### 2011年07月29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 ]
ジェットスキームや弧空間の概念は 1968年に John F. Nash によって導入された.
このとき彼は弧空間と特異点解消の対応を記述する「Nash 問題」を提起している.