## 過去の記録

### 2011年05月26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

Obstacle problem of Navier-Stokes equations in thermohydraulics (JAPANESE)
[ 講演概要 ]
In this talk, we consider the well-posedness of a variational inequality for the Navier-Stokes equations in 2 or 3 space dimension with time dependent constraints. This problem is motivated by an initial-boundary value problem for a thermohydraulics model. The velocity field is constrained by a prescribed function,
depending on the space and time variables, so this is called the obstacle problem. The abstract theory of nonlinear evolution equations governed by subdifferentials of time dependent convex functionals is quite useful for showing their well-posedness. In their mathematical treatment one of the key is to specify the class of time-dependence of convex functionals. We shall discuss the existence and uniqueness questions for Navier-Stokes variational inequalities, in which a bounded constraint is imposed on the velocity field, in higher space dimensions. Especially, the uniqueness of a solution is due to the advantage of the prescribed constraint to the velocity fields.

### 2011年05月25日(水)

#### 代数学コロキウム

17:00-18:00   数理科学研究科棟(駒場) 056号室

On good reduction of some K3 surfaces (JAPANESE)
[ 講演概要 ]

X の l 進エタールコホモロジーから定まるガロア表現は不分岐表現となる
(ここで l は K の剰余体の標数と異なる素数).
では逆に,このガロア表現が不分岐ならば良い還元をもつか …(*)
という問題を考えると,
X がアーベル多様体ならば (*) は成り立つ(Serre--Tate)が,

そこで,(*) が成り立つような多様体のクラスを探すことを考える.
この講演では,ある種の K3 曲面について (*) をやや弱めた主張が成り立つことを紹介する.

### 2011年05月24日(火)

#### 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 ]

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

#### 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 Stratifications for Line Arrangements (JAPANESE)
[ 講演概要 ]
The homotopy type of complements of complex
hyperplane arrangements have a special property,
so called minimality (Dimca-Papadima and Randell,
around 2000). Since then several approaches based
on (continuous, discrete) Morse theory have appeared.
In this talk, we introduce the "dual" object, which we
call minimal stratification for real two dimensional cases.
A merit is that the minimal stratification can be explicitly
described in terms of semi-algebraic sets.
We also see associated presentation of the fundamental group.

#### 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

Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds (JAPANESE)
[ 講演概要 ]
If a homogeneous space $G/H$ is acted properly discontinuously
upon by a subgroup $\\Gamma$ of $G$ via the left action, the quotient space $\\Gamma \\backslash G/H$ is called a
Clifford--Klein form. In 1962, E. Calabi and L. Markus proved that there is no infinite subgroup of the Lorentz group $O(n+1, 1)$ whose left action on the de Sitter space $O(n+1, 1)/O(n, 1)$ is properly discontinuous.
It follows that a compact Clifford--Klein form of the de Sitter space never exists.
In this talk, we present a new extension of the theorem of E. Calabi and L. Markus to a certain class of Lorentzian manifolds that are not necessarily homogeneous.

#### 博士論文発表会

13:15-14:30   数理科学研究科棟(駒場) 128号室

マルチンゲール理論およびその数理ファイナンスへの応用に関する幾つかの性質 (JAPANESE)

### 2011年05月23日(月)

#### 代数幾何学セミナー

17:00-18:30   数理科学研究科棟(駒場) 126号室

Alpha invariant and K-stability of Fano varieties (JAPANESE)
[ 講演概要 ]
From the results of Tian, it is proved that the lower bounds of alpha invariant implies K-stability of Fano manifolds via the existence of Kähler-Einstein metrics. In this talk, I will give a direct proof of this relation in algebro-geometric way without using Kähler-Einstein metrics. This is joint work with Yuji Odaka (RIMS).

### 2011年05月19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

[ 講演概要 ]

### 2011年05月18日(水)

#### 諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

[ 講演参考URL ]
http://info.ms.u-tokyo.ac.jp/seminar/mathvar/future.html

#### 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

On the linear independence of values of some Dirichlet series (JAPANESE)
[ 講演概要 ]

2000年にT.Rivoalにより証明されており,今回の結果はその一般化に相当する.

### 2011年05月17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

Quandle colorings with non-commutative flows (JAPANESE)
[ 講演概要 ]
This is a joint work with Masahide Iwakiri, Yeonhee Jang and Kanako Oshiro.
We introduce quandle coloring invariants and quandle cocycle invariants
with non-commutative flows for knots, spatial graphs, handlebody-knots,
where a handlebody-knot is a handlebody embedded in the $3$-sphere.
Two handlebody-knots are equivalent if one can be transformed into the
other by an isotopy of $S^3$.
The quandle coloring (resp. cocycle) invariant is a twisted'' quandle
coloring (resp. cocycle) invariant.

### 2011年05月16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

#### 代数幾何学セミナー

17:00-18:30   数理科学研究科棟(駒場) 126号室

On images of Mori dream spaces (JAPANESE)
[ 講演概要 ]
Mori dream space (MDS), introduced by Y. Hu and S. Keel, is a class of varieties whose geometry can be controlled via the VGIT of the Cox ring. It is a generalization of both toric varieties and log Fano varieties.

The purpose of this talk is to study the image of a morphism from a MDS.
Firstly I prove that such an image again is a MDS.
Secondly I introduce a fan structure on the effective cone of a MDS and show that the fan of the image coincides with the restriction of that of the source.

This fan encodes some information of the Zariski decompositions, which turns out to be equivalent to the information of the GIT equivalence. In toric case, this fan coincides with the so called GKZ decomposition.

The point is that these results can be clearly explained via the VGIT description for MDS.

If I have time, I touch on generalizations and an application to the Shokurov polytopes.

### 2011年05月11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
Michel Raynaud 氏 (Universite Paris-Sud)
Permanence following Temkin (ENGLISH)
[ 講演概要 ]
When one proceeds to a specialization, the good properties of algebraic equations may be destroyed. Starting with a bad specialization, one can try to improve it by performing modifications under control. If, at the end of the process, the initial good properties are preserved, one speaks of permanence. I shall give old and new examples of permanence. The new one concerns the relative semi-stable reduction of curves recently proved by Temkin.

(本講演は「東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とIHESとの双方向同時中継で行います。)

### 2011年05月10日(火)

#### 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 ]

(1) 全ての保存量 (Hamiltonian,運動量,角運動量,重心の位置)を保つ;
(2) Lagrange 正三角形解,8 の字解,Broucke の発見した周期解などの力学的に安定な解軌道を数値的に再現する;
(3) Lagrange 平衡解の存在を解析的に示すことができる;
(4) Lagrange 平衡解の線形安定性が元の 3 体問題のそれと高精度で一致する.
[ 講演参考URL ]
http://www.infsup.jp/utnas/

#### 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

Isotated points in the space of group left orderings (JAPANESE)
[ 講演概要 ]
The set of all left orderings of a group G admits a natural
topology. In general the space of left orderings is homeomorphic to the
union of Cantor set and finitely many isolated points. In this talk I
will give a new method to construct left orderings corresponding to
isolated points, and will explain how such isolated orderings reflect
the structures of groups.

### 2011年05月09日(月)

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

Fourier--Mukai partners of elliptic ruled surfaces (JAPANESE)
[ 講演概要 ]
Atiyah classifies vector bundles on elliptic curves E over an algebraically closed field of any characteristic. On the other hand, a rank 2 vector bundle on E defines a surface S with P^1-bundle structure on E.
We study when S has an elliptic fibration according to the Atiyah's classification. As its application, we determines the set of Fourier--Mukai partners of elliptic ruled surfaces over the complex number field.

#### 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

Order of meromorphic maps and rationality of the image space (JAPANESE)

### 2011年05月02日(月)

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

Projective varieties admitting an embedding with Gauss map of rank zero (JAPANESE)
[ 講演概要 ]

「ある埋込み $¥iota: X ¥hookrightarrow ¥mathbb{P}^M$ が存在し,そのガウス写像 $X ¥dashrightarrow G(¥dim(X), ¥mathbb{P}^M)$ の一般点での階数が零となる.」

### 2011年04月27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

Sturm の定理の Hilbert 保型形式に対する類似 (JAPANESE)
[ 講演概要 ]
Sturm は重さ$k$, レベル$\\Gamma_1(N)$ のmod $\\ell$ 正則楕円保型形式が最初
の$(k/12)[\\Gamma_1(1):\\Gamma_1(N)]$ までの mod $\\ell$ Fourier 係数で決ま
ることを示した.

### 2011年04月26日(火)

#### 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 ]

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

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同です。いつもと場所が違います

Topological Blow-up (JAPANESE)
[ 講演概要 ]
Suppose that a Lie group $G$ acts on a manifold
$M$. The quotient space $X:=G\\backslash M$ is locally compact,
but not Hausdorff in general. Our aim is to understand
such a non-Hausdorff space $X$.
The space $X$ has the crack $S$. Rougly speaking, $S$ is
the causal subset of non-Hausdorffness of $X$, and especially
$X\\setminus S$ is Hausdorff.

We introduce the concept of topological blow-up' as a repair'
of the crack. The repaired' space $\\tilde{X}$ is
locally compact and Hausdorff space containing $X\\setminus S$
as its open subset. Moreover, the original space $X$ can be
recovered from the pair of $(\\tilde{X}, S)$.

#### 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, Lie群論・表現論セミナーと合同

Topological Blow-up (JAPANESE)
[ 講演概要 ]
Suppose that a Lie group $G$ acts on a manifold
$M$. The quotient space $X:=G\\backslash M$ is locally compact,
but not Hausdorff in general. Our aim is to understand
such a non-Hausdorff space $X$.
The space $X$ has the crack $S$. Roughly speaking, $S$ is
the causal subset of non-Hausdorffness of $X$, and especially
$X\\setminus S$ is Hausdorff.

We introduce the concept of topological blow-up' as a repair'
of the crack. The repaired' space $\\tilde{X}$ is
locally compact and Hausdorff space containing $X\\setminus S$
as its open subset. Moreover, the original space $X$ can be
recovered from the pair of $(\\tilde{X}, S)$.

#### 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

On the system of fifth-order differential equations which describes surfaces containing six continuous families of circles (JAPANESE)

### 2011年04月25日(月)

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

Mirror symmetry and projective geometry of Reye congruences (JAPANESE)
[ 講演概要 ]
This is a joint work with Shinobu Hosono.
It is well-known that the projective dual of the second Veronese variety v_2(P^n) is the symmetric determinantal hypersurface H. However, in the context of homological projective duality after Kuznetsov, it is natural to consider that the Chow^2 P^n and H are dual (note that Chow^2 P^n is the secant variety of v_2(P^n)).
Though we did not yet formulate what this duality exactly means in full generality, we show some results in this context for the values n¥leq 4.
For example, let n=4. We consider Chow^2 P^4 in P(S^2 V) and H in P(S^2 V^*), where V is the vector space such that P^4 =P(V). Take a general 4-plane P in
P(S^2 V^*) and let P' be the orthogonal space to P in P(S^2 V). Then X:=Chow^2 P^4 ¥cap P' is a smooth Calabi-Yau 3-fold, and there exists a natural double cover Y -> H¥cap P with a smooth Calabi-Yau 3-fold Y. It is easy to check
that X and Y are not birational each other.
Our main result asserts the derived equivalence of X and Y. This derived equivalence is given by the Fourier Mukai functor D(X)-> D(Y) whose kernel is the ideal sheaf in X×Y of a flat family of curves on Y parameterized by X.
Curves on Y in this family have degree 5 and arithmetic genus 3, and these have a nice interpretation by a BPS number of Y. The proof of the derived equivalence is slightly involved so I explain a similar result in the case where n=3. In this case, we obtain a fully faithful functor from D(X)-> D(Y), where X is a so called the Reye congruence Enriques surface and Y is the 'big resolution' of the Artin-Mumford quartic double solid.