## 過去の記録

#### 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

https://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.
[ 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

https://www.ms.u-tokyo.ac.jp/gcoe/index.html

[ 講演概要 ]

[ 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.

#### 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

### 2011年04月20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

Stochastic power law fluids (JAPANESE)
[ 講演概要 ]
This talk is based in part on a joint work with Yutaka Terasawa.
We consider a SPDE (stochastic partial differential equation) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force.
Here, the extra stress tensor of the fluid is given by a polynomial of degree $p-1$ of the rate of strain tensor, while the colored noise is considered as a random force.
We first investigate the existence and the uniqueness of weak solutions to this SPDE.
We next turn to the special case: $p \\in [1 + {d \\over 2},{2d\\overd-2})$,
where $d$ is the dimension of the space. We prove there that the Galerkin scheme approximates the velocity field in a strong sense. As a consequence, we establish the energy equality for the velocity field.
[ 参考URL ]
http://www.math.kyoto-u.ac.jp/~nobuo/

### 2011年04月18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

Ideal-adic semi-continuity problem for minimal log discrepancies (JAPANESE)
[ 講演概要 ]
De Fernex, Ein and Mustaţă, after Kollár, proved the ideal-adic semi-continuity of log canonicity to obtain Shokurov's ACC conjecture for log canonical thresholds on l.c.i. varieties. I discuss its generalisation to minimal log discrepancies, proposed by Mustaţă.

#### 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

Asymptotic cohomology vanishing and a converse of the Andreotti-Grauert theorem on surface (JAPANESE)

### 2011年04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) 122号室

Amenable actions and crossed products of $C^*$-algebras (JAPANESE)

#### 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
Marek FILA 氏 (Comenius University (Slovakia))
Homoclinic and heteroclinic orbits for a semilinear parabolic equation (ENGLISH)
[ 講演概要 ]
We study the existence of connecting orbits for the Fujita equation

u_t=\\Delta u+u^p

with a critical or supercritical exponent $p$. For certain ranges of the exponent we prove the existence of heteroclinic connections from positive steady states to zero and the existence of a homoclinic orbit with respect to zero. This is a joint work with Eiji Yanagida.

### 2011年04月13日(水)

#### 関数解析セミナー

15:00-17:00   数理科学研究科棟(駒場) 128号室
Alexander Pushnitski 氏 (King's College, London)
Spectral theory for functions of self-adjoint operators (ENGLISH)
[ 講演概要 ]
Let A, B be self-adjoint operators such that the standard assumptions of smooth scattering theory for the pair A, B are satisfied. The spectral theory of the operators of the type f(A)-f(B) will be discussed, with a particular attention to the case of discontinuous functions f. It turns out that the spectrum of f(A)-f(B) can often be explicitly described in terms of the spectrum of the scattering matrix for the pair A,B. This is joint work with D.Yafaev.

### 2011年04月12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

On diffeomorphisms over non-orientable surfaces embedded in the 4-sphere (JAPANESE)
[ 講演概要 ]
4次元球面内に標準的に埋め込まれた向き付け可能曲面上の

### 2011年04月11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

レゾルベントの代数解析と行列の exact なスペクトル分解アルゴリズム (JAPANESE)

### 2011年03月31日(木)

#### 講演会

13:00-14:00   数理科学研究科棟(駒場) 118号室

Alain Joye 氏 (Univ. Grenoble)
Dynamical localization for unitary Anderson models (JAPANESE)

#### 講演会

14:30-15:30   数理科学研究科棟(駒場) 118号室

Gerard Ben Arous 氏 (Courant Institute, New York Univ.)
Stable limits for biased random walks on random trees (JAPANESE)
[ 講演概要 ]
It is well know that transport in random media can be hampered by dead-end regions and that the velocity can even vanish for strong drifts. We study this phenomenon in great detail for random trees. That is, we study the behavior of biased random walks on supercritical random trees with leaves, in the sub-ballistic regime. When the drift is strong enough it is well known that trapping in the dead-ends of the tree, causes the velocity to vanish. We study the behavior of the walk in this regime, and in particular find the exponents for the mean displacement and the time to reach a given large distance. We also establish a scaling limit result in the case where the drift are random and a non-lattice condition is satisfied. (Joint work with Alexander Fribergh, Alan Hammond, Nina Gantert)

### 2011年03月22日(火)

#### 講演会

14:00-15:00   数理科学研究科棟(駒場) 128号室

Amir Dembo 氏 (Stanford Univ.)
Potts models and Bethe states on sparse random graphs (JAPANESE)
[ 講演概要 ]
Theoretical models of disordered materials lead to challenging mathematical problems with applications to random combinatorial problems and coding theory. The underlying mathematical structure is that of many discrete variables that are strongly interacting according to a mean field model determined by a random sparse graph. Focusing on ferromagnetic Potts measures on random finite graphs that converge locally to trees we validate the `cavity' prediction for the limiting free energy per spin and show that local marginals are approximated well by the belief propagation algorithm. This is a concrete example of the more general approximation by Bethe measures, namely, the local convergence of the Boltzmann distribution on the original graph to the Boltzmann distribution on an appropriate infinite random tree (this talk is based on a joint work with Andrea Montanari and Nike Sun).