## 過去の記録

#### 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

Unique prime factorization and bicentralizer problem for a class of type III factors

### 2015年05月19日(火)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Convex bodies and geometry of some associated Minkowski functionals (日本語)
[ 講演概要 ]
In this talk, we will investigate the construction of so-called Hilbert metric, as well as Funk metric, defined on convex set from a new variational viewpoint. The local and global aspects of the geometry of the resulting Minkowski functionals will be contrasted. As an application, some remarks on the Perron-Frobenius theorem will be made. Part of the project is a joint work with Athanase Papadopoulos (Strasbourg).

#### 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
Anton Evseev 氏 (University of Birmingham)
RoCK blocks, wreath products and KLR algebras (English)
[ 講演概要 ]
The so-called RoCK (or Rouquier) blocks play an important role in representation theory of symmetric groups over a finite field of characteristic $p$, as well as of Hecke algebras at roots of unity. Turner has conjectured that a certain idempotent truncation of a RoCK block is Morita equivalent to the principal block $B_0$ of the wreath product $S_p\wr S_d$ of symmetric groups, where $d$ is the "weight" of the block. The talk will outline a proof of this conjecture, which generalizes a result of Chuang-Kessar proved for $d < p$. The proof uses an isomorphism between a Hecke algebra at a root of unity and a cyclotomic Khovanov-Lauda-Rouquier algebra, the resulting grading on the Hecke algebra and the ideas behind a construction of R-matrices for modules over KLR algebras due to Kang-Kashiwara-Kim.

#### 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

Quiver mutation loops and partition q-series (JAPANESE)
[ 講演概要 ]
Quivers and their mutations are ubiquitous in mathematics and
mathematical physics; they play a key role in cluster algebras,
wall-crossing phenomena, gluing of ideal tetrahedra, etc.
Recently, we introduced a partition q-series for a quiver mutation loop
(a loop in a quiver exchange graph) using the idea of state sum of statistical
mechanics. The partition q-series enjoy some nice properties such
as pentagon move invariance. We also discuss their relation with combinatorial
Donaldson-Thomas invariants, as well as fermionic character formulas of
certain conformal field theories.
This is a joint work with Yuji Terashima.

### 2015年05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) 126号室

On a global estimate of the Diederich–Fornaess index of Levi-flat real hypersurfaces (Japanese)
[ 講演概要 ]
We give yet another proof for a global estimate of the Diederich-Fornaess index of relatively compact domains with Levi-flat boundary, namely, the index must be smaller than or equal to the reciprocal of the dimension of the ambient space. Although the Diederich-Fornaess index is originally defined for relatively compact domains in complex manifolds, our formulation reveals that it makes sense for abstract Levi-flat CR manifolds.

#### 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
Will Donovan 氏 (IPMU)
Twists and braids for general 3-fold flops (English)
[ 講演概要 ]
When a 3-fold contains a floppable rational curve, a theorem of Bridgeland provides a derived equivalence between the 3-fold and its flop. I will discuss recent joint work with Michael Wemyss, showing that these flop functors satisfy Coxeter-type braid relations. Using this result, we construct an action of a braid-type group on the derived category of the 3-fold. This group arises from the topology of a certain simplicial hyperplane arrangement, determined by the local geometry of the curve. I will give examples and explain key elements in the construction, including the noncommutative deformations of curves introduced in our previous work.
[ 講演参考URL ]
http://db.ipmu.jp/member/personal/4007en.html

#### 数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

エラーフリー変換を用いた行列積の高精度計算
(日本語)
[ 講演概要 ]
すべての成分が浮動小数点数である行列の積に関して，数値計算を用いて高信頼な結果を得る手法について研究を行っている．本講演では，HPCの技術者がチューニングをした高速なライブラリを直に使用する高精度行列積アルゴリズムについて紹介したい．アルゴリズムの概要，長所と短所，エラーフリーであることの証明から解説し，区間演算への応用や最近開発できた事後保証型のアルゴリズムについても紹介したい．

#### 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

Central limit theorem for stochastic heat equations in random environments

### 2015年05月14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

Strong instability of standing waves for some nonlinear Schr\"odinger equations (Japanese)
[ 講演概要 ]
デルタ関数をポテンシャルとして含む空間1次元の非線形シュレディンガー方程式を考える．この方程式の定在波解は双曲線関数を用いて具体的に書き表すことができる．そのため，方程式がスケール不変でないにも関わらず，角振動数をパラメータとする定在波解の族のエネルギーや電荷のパラメータ依存性を具体的に計算することができ，定在波解の軌道安定性と不安定性を完全に分類することができる．この講演では，軌道不安定な定在波解の近傍から出発した解が有限時間で爆発するための条件について考察する．このとき，定在波解は強不安定であるというが，今回得られた強不安定性の十分条件と軌道不安定性に関する従来の条件との関係を数値的に調べ，関連する問題を紹介する．

### 2015年05月13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

Controlled topological phases and the bulk-edge correspondence for
topological insulators (English)

### 2015年05月12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

Brakkeの平均曲率流に対する制約条件付きAllen-Cahn方程式の収束について (Japanese)
[ 講演概要 ]
In this talk we consider the Allen-Cahn equation with constraint. In 1994, Chen and Elliott studied the asymptotic behavior of the solution of the Allen-Cahn equation with constraint. They proved that the zero level set of the solution converges to the classical solution of the mean curvature flow under the suitable conditions on initial data. In 1993, Ilmanen proved the existence of the mean curvature flow via the Allen-Cahn equation without constraint in the sense of Brakke. We proved the same conclusion for the Allen-Cahn equation with constraint.

#### トポロジー火曜セミナー

17:30-18:30   数理科学研究科棟(駒場) 056号室
Tea : 17:00-17:30 Common Room

genericな力学系の周期点の個数の増大度 (JAPANESE)
[ 講演概要 ]

その周期軌道の数の増大度は常に高々指数的で，増大度は系の統計的

により，homoclinic接触と呼ばれる複雑な分岐現象が稠密に起きるよ
うな領域においてはgenericな力学系はその周期軌道の数の増大度は

では，弱い双曲性を持ち，homoclinic接触からは離れている「部分双

ろうか．双曲力学系と同様に高々指数的になるだろうか，それとも，
homoclinic 接触とは異なるメカニズムによって，指数的よりも速く
なるだろうか？

には指数的よりも速く増大することを証明した．本講演では，力学

い増大度を引き起こすメカニズムについて，Kaloshinが見つけた
homoclinic接触によるものと講演者たちが見つけたものを対比しつ
つ解説したい．

### 2015年05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) 126号室

Integral Kahler Invariants and the Bergman kernel asymptotics for line bundles
[ 講演概要 ]
On a compact Kahler manifold, one can define global invariants by integrating local invariants of the metric. Assume that a global invariant thus obtained depends only on the Kahler class. Then we show that the integrand can be decomposed into a Chern polynomial (the integrand of a Chern number) and divergences of one forms, which do not contribute to the integral. We apply this decomposition formula to describe the asymptotic expansion of the Bergman kernel for positive line bundles and to show that the CR Q-curvature on a Sasakian manifold is a divergence. This is a joint work with Spyros Alexakis (U Toronto).

#### 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

Phase transitions for controlled Markov chains on infinite graphs (JAPANESE)

#### 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

Deformations of weak Fano varieties (日本語 or English)
[ 講演概要 ]
A smooth projective variety often has obstructed deformations.
Nevertheless, important varieties such as Fano varieties and
Calabi-Yau varieties have unobstructed deformations.
In this talk, I explain about unobstructedness of deformations of weak
Fano varieties, in particular a weak Q-Fano 3-fold.
I also present several examples to show delicateness of this unobstructedness.
[ 講演参考URL ]

### 2015年05月08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

On Perelman type functionals for the Ricci Yang-Mills flow (Japanese)
[ 講演概要 ]
In his works on the Ricci flow, Perelman introduced two functionals with monotonicity
formulas under the Ricci flow. The monotonicity formulas have many remarkable geometric applications. On the other hand, around 2007, Jeffrey Streets and Andrea Young independently and simultaneously introduced a new geometric flow which is called the Ricci Yang-Mills flow. The new flow can be regarded as the Ricci flow coupled with the Yang-Mills
heat flow. In this talk, we will introduce new functionals with monotonicity formulas under the Ricci Yang-Mills flow and discuss its applications.

### 2015年05月07日(木)

#### 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
This seminar will be held on Thursdsay.
Patrick Dehornoy 氏 (Univ. de Caen)
The group of parenthesized braids (ENGLISH)
[ 講演概要 ]
We describe a group B obtained by gluing in a natural way two well-known
groups, namely Artin's braid group B_infty and Thompson's group F. The
elements of B correspond to braid diagrams in which the distances
between the strands are non uniform and some rescaling operators may
change these distances. The group B shares many properties with B_infty:
as the latter, it can be realized as a subgroup of a mapping class
group, namely that of a sphere with a Cantor set removed, and as a group
of automorphisms of a free group. Technically, the key point is the
existence of a self-distributive operation on B.

### 2015年05月02日(土)

#### 調和解析駒場セミナー

13:30-17:00   数理科学研究科棟(駒場) 128号室

Two-weight Morrey norm inequality and the sequential testing
(日本語)
[ 講演概要 ]
In this talk we extend Sawyer's two-weight theory to Morrey spaces and give a characterization of two-weight Morrey norm inequalities for the (general) Hardy-Littlewood maximal operators in terms of the sequential testing due to H\"{a}nninen, Hyt\"{o}nen and Li.
We also introduce the description of the K\"othe dual of Morrey type spaces generated by a basis of measurable functions.
The second topic is based on a joint work with Professors Sawano (Tokyo Metropolitan University) and Masty{\l}o (Adam Mickiewicz University and Institute of Mathematics).

The topology of the dual space of ${\mathcal S}_0$
(日本語)
[ 講演概要 ]
Based on the notation of my Japanese book, I will consider the topology of ${\mathcal S}_0'$, the dual of ${\mathcal S}_0$.
In view of the linear isomorphism ${\mathcal S}_0' \sim {\mathcal S}/{\mathcal P}$, we can consider two different topologies;

1) the weak-* topology
and
2) the quotient topology in ${\mathcal S}/{\mathcal P}$.

We aim to show that these two topologies are the same. This will be an errortum of my Japanese book.
This work is done jointly with Takahiro Noi and Shohei Nakamura in Tokyo Metropolitan University.

### 2015年04月28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

Verify hyperbolicity of 3-manifolds by computer and its applications. (JAPANESE)
[ 講演概要 ]
In this talk I will talk about the program called HIKMOT which
rigorously proves hyperbolicity of a given triangulated 3-manifold. To
prove hyperbolicity of a given triangulated 3-manifold, it suffices to
get a solution of Thurston's gluing equation. We use the notion called
interval arithmetic to overcome two types errors; round-off errors,
and truncated errors. I will also talk about its application to
exceptional surgeries along alternating knots. This talk is based on
joint work with N. Hoffman, K. Ichihara, M. Kashiwagi, S. Oishi, and
A. Takayasu.

#### 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
Bent Orsted 氏 (Aarhus University and the University of Tokyo)
Restricting automorphic forms to geodesic cycles (English)
[ 講演概要 ]
We find estimates for the restriction of automorphic forms on hyperbolic manifolds to compact geodesic cycles in terms of their expansion into eigenfunctions of the Laplacian. Our method resembles earlier work on products of automorphic forms by Bernstein and Reznikov, and it uses Kobayashi's new symmetry-breaking kernels. This is joint work with Jan M\"o{}llers.

### 2015年04月27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

Variational formulas for canonical differentials and application (Japanese)
[ 講演概要 ]
We prove the variational formulas of the second order for $L_1$- and $L_0$-canonical differentials, which with the remarkable contrast are our first example in the case of the deforming non-planar open Riemann surface. As a direct application, we show the rigidity of the Euclidean radius of the moduli disk on open torus under pseudoconvexity. The main part of this talk is a joint work with Masakazu Shiba and Hiroshi Yamaguchi.

#### 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

Lagrangian embeddings of cubic fourfolds containing a plane (日本語)
[ 講演概要 ]
4次元3次超曲面は、複素シンプレクティック多様体の構成、有理性やK3曲面との関係などという観点から研究されている。1985年BeauvilleとDonagiは、4次元3次超曲面上の直線のなすFanoスキームがK3曲面上の2点のHilbertスキームと変形同値な複素シンプレクティック多様体であることを示した。2013年Lehnらは、平面を含まない4次元3次超曲面は8次元複素シンプレクティックにラグランジュ部分多様体として埋め込めることを示した。この8次元複素シンプレクティック多様体は4次元3次超曲面上のねじれ3次曲線全体を考えることにより得られる。

#### 数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

### 2015年04月24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

On K-stability and the volume functions of Q-Fano varieties (JAPANESE)
[ 講演概要 ]
For Fano manifolds X, it is known that X admits K\"ahler-Einstein metrics if and only if the polarized pair
(X, -K_X) is K-polystable. In this talk, I will introduce a new effective stability named "divisorial stability" for Fano manifolds, which is weaker than K-stability and stronger than slope stability along divisors. I will show that:
1. We can easily test divisorial stability via the volume functions.
2. There is a relationship between divisorial stability and the structure property of Okounkov bodies of anti-canonical divisors.
3. For toric Fano manifolds, the existence of K\"ahler-Einstein metrics is equivalent to divisorial semistability.

#### 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.