## 過去の記録

### 2014年12月08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

### 2014年12月04日(木)

#### 幾何コロキウム

17:00-18:30   数理科学研究科棟(駒場) 123号室

### 2014年12月03日(水)

#### 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

Central property (T) for $SU_q(2n+1)$ (English)

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 128号室
Xavier Cabre 氏 (ICREA and UPC, Barcelona)
New isoperimetric inequalities with densities, part II: Detailed proofs and related works (ENGLISH)
[ 講演概要 ]
This is a sequel to the Tuesday Analysis Seminar on December 2 by the same speaker.
In joint works with X. Ros-Oton and J. Serra, the study of the regularity of stable solutions to reaction-diffusion problems has led us to certain Sobolev and isoperimetric inequalities with weights. We will present our results in these new isoperimetric inequalities with the best constant, that we establish via the ABP method.
More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (or densities) in open convex cones of R^n. Our results apply to all nonnegative homogeneous weights satisfying a concavity condition in the cone. Surprisingly, even that our weights are not radially symmetric, Euclidean balls centered at the origin (intersected with the cone) minimize the weighted isoperimetric quotient. As a particular case of our results, we provide with new proofs of classical results such as the Wulff inequality and the isoperimetric inequality in convex cones of Lions and Pacella. Furthermore, we also study the anisotropic isoperimetric problem for the same class of weights and we prove that the Wulff shape always minimizes the anisotropic weighted perimeter under the weighted volume constraint.

#### 数理人口学・数理生物学セミナー

14:50-16:20   数理科学研究科棟(駒場) 122号室

(JAPANESE)
[ 講演概要 ]
Busenberg et al. (1991) では、非線形偏微分方程式系として記述されるある年

### 2014年12月02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 Common Room

The Atiyah-Segal completion theorem in noncommutative topology (JAPANESE)
[ 講演概要 ]
C*環の位相的な性質を扱う"非可換"トポロジーの理論を用
いて，Atiyah-Segal completion theoremに新しい視点を導入する．ここで，R.
MeyerとR. Nestらによって発展したKasparov categoryの三角圏としてのホモロ
ジー代数が中心的な役割を果たす．また，これは系として同変Kホモロジーや捩
れK理論に対するAtiyah-Segal型のcompletion theoremを含む．これは荒野悠輝

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Remark on single exponential bound of the vorticity gradient for the two-dimensional Euler flow around a corner (JAPANESE)
[ 講演概要 ]
In this talk, the two dimensional Euler flow under a simple symmetry condition with hyperbolic structure in a unit square $D=\{(x_{1}, x_{2}): 0 < x_{1} + x_{2} < \sqrt{2},\ 0<-x_{1} + x_{2} < \sqrt{2}\}$ is considered.
It is shown that the Lipschitz estimate of the vorticity on the boundary is at most single exponential growth near the stagnation point.
(Joint work with Tsuyoshi Yoneda and Hideyuki Miura.)

#### 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
Xavier Cabre 氏 (ICREA and UPC, Barcelona)
New isoperimetric inequalities with densities arising in reaction-diffusion problems (English)
[ 講演概要 ]
In joint works with X. Ros-Oton and J. Serra, the study of the
regularity of stable solutions to reaction-diffusion problems
has led us to certain Sobolev and isoperimetric inequalities
with weights.  We will present our results in these new
isoperimetric inequalities with the best constant, that we
establish via the ABP method.  More precisely, we obtain
a new family of sharp isoperimetric inequalities with weights
(or densities) in open convex cones of R^n. Our results apply
to all nonnegative homogeneous weights satisfying a concavity
condition in the cone. Surprisingly, even that our weights are
not radially symmetric, Euclidean balls centered at the origin
(intersected with the cone) minimize the weighted isoperimetric
quotient. As a particular case of our results, we provide with
new proofs of classical results such as the Wulff inequality and
the isoperimetric inequality in convex cones of Lions and Pacella.
Furthermore, we also study the anisotropic isoperimetric problem
for the same class of weights and we prove that the Wulff shape
always minimizes the anisotropic weighted perimeter under the
weighted volume constraint.

### 2014年12月01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

Effective and noneffective extension theorems (Japanese)
[ 講演概要 ]
As an effective extension theorem, I will review the sharp $L^2$ extension theorem explaining the ideas of its proofs due to Blocki and Guan-Zhou. A new proof using the Poincare metric with be given, too. As a noneffective extension theorem, I will talk about an extension theorem from semipositive divisors. It is obtained as an application of an isomorphism theorem which is essentially contained in my master thesis.

#### 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
Malte Wandel 氏 (RIMS)
Induced Automorphisms on Hyperkaehler Manifolds (ENGLISH)
[ 講演概要 ]
in this talk I want to report on a joint project with Giovanni Mongardi (Milano). We study automorphisms of hyperkaehler manifolds. All known deformation classes of these manifolds contain moduli spaces of stable sheaves on surfaces. If the underlying surface admits a non-trivial automorphism, it is often possible to transfer this automorphism to a moduli space of sheaves. In this way we obtain a big class of interesting examples of automorphisms of hyperkaehler manifolds. I will present a criterion to 'detect' automorphisms in this class and discuss several applications for the classification of automorphisms of manifolds of K3^[n]- and kummer n-type. If time permits I will try to talk about generalisations to O'Grady's sporadic examples.

#### 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

Poisson方程式に対する一般化粒子法の誤差評価 (日本語)
[ 講演概要 ]
SPH法やMPS法に代表される粒子法は, 津波のような移動境界流れに対する数値計算手法の一つとして, 現在幅広く利用されている. 一方で, 近似解の誤差評価といった粒子法の数学的正当化は, 我々の知る限り十分に行われているとは言えない.
そこで我々は, 誤差評価の第一ステップとして, Poisson方程式に対するある一般化粒子法を導入し, その誤差評価を行った. 提案する粒子法は, SPH法やMPS法を含む, より広いクラスの粒子法を記述することが可能である. 本講演では, 粒子分布の正則性と接続性を導入し, これらの性質を持った粒子分布の下で, 近似解の誤差が重み関数の影響半径に関して2次収束することを示す. 我々の誤差評価では, 従来は工学的な経験則に基づいていた 参照関数の選択や粒子数と影響半径の組合わせの選択などに, 数学的に正当化されたある十分条件を与えていることが重要である.
[ 講演参考URL ]
http://www.infsup.jp/utnas/

### 2014年11月28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

Estimating the reproduction numbers of emerging infectious diseases: Case studies of Ebola and dengue (JAPANESE)
[ 講演概要 ]
The basic and effective reproduction numbers offer epidemiological
insights into the growth of generations of infectious disease cases,
informing the required control effort. Recently, the renewal process
model has appeared to be a usefu tool for quantifying the reproduction
numbers in real-time using only case data. Here I present methods,
results and pitfalls of the use of renewal process model, presenting
recent case studies of Ebola virus disease epidemic in West Africa and a
massive epidemic of dengue fever in the summer of Japan 2014.
[ 講演参考URL ]
http://www.ghp.m.u-tokyo.ac.jp/profile/staff/hnishiura/

### 2014年11月26日(水)

#### 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
Yi-Zhi Huang 氏 (Rutgers Univ.)
A program to construct and study conformal field theories (ENGLISH)

#### 講演会

16:00-17:00   数理科学研究科棟(駒場) 123号室
Mykhaylo Shkolnikov 氏 (Princeton University)
Intertwinings, wave equations and beta ensembles (ENGLISH)
[ 講演概要 ]
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to wave equations and more general hyperbolic partial differential equations. The talk will be devoted to this recent development, as well as an algebraic perspective on intertwinings which, in particular, gives rise to a novel intertwining in beta random matrix theory. Based on joint works with Vadim Gorin and Soumik Pal.

#### 統計数学セミナー

16:30-17:40   数理科学研究科棟(駒場) 052号室

Sparse and robust linear regression: Iterative algorithm and its statistical convergence

[ 講演概要 ]

### 2014年11月25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) 128号室

Stationary scattering theory on manifold with ends (JAPANESE)

#### 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 Common Room

Quandle knot invariants and applications (JAPANESE)
[ 講演概要 ]
A quandles is an algebraic structure closely related to knots. Homology theories of
quandles have been defined, and their cocycles are used to construct invariants for
classical knots, spatial graphs and knotted surfaces. In this talk, an overview is given
for quandle cocycle invariants and their applications to geometric properties of knots.
The current status of computations, recent developments and open problems will also
be discussed.

#### Kavli IPMU Komaba Seminar

10:30-11:30   数理科学研究科棟(駒場) 128号室
Naichung Conan Leung 氏 (The Chinese University of Hong Kong)
Donaldson-Thomas theory for Calabi-Yau fourfolds.
(ENGLISH)
[ 講演概要 ]
Donaldson-Thomas theory for Calabi-Yau threefolds is a
complexification of Chern-Simons theory. In this talk I will discuss
my joint work with Cao on the complexification of Donaldson theory.
This work is supported by a RGC grant of HK Government.

### 2014年11月22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
Denny Hakim 氏 (首都大学東京) 13:30-14:30
On the Inclusion of Generalized Morrey Spaces and the Boundedness of the Generalized Fractional Maximal Operators (ENGLISH)
[ 講演概要 ]
In this talk, we shall prove a necessary and sufficient condition for an inclusion property of generalized Morrey spaces. We use this property in our proof of the boundedness of the generalized fractional maximal operators on these spaces. Our result also cover the generalized weak Morrey spaces.
This research is a joint work with Y. Sawano, H. Gunawan, K.M. Limanta and A.A. Masta.
Tamara Tararykova 氏 (Cardiff University / Eurasian National University) 14:45-15:45
Hardy-type inequality for 0 < p < 1 and hypodecreasing functions (ENGLISH)
[ 講演概要 ]
T.B.A.
Victor Burenkov 氏 (Cardift School of Mathematics / Peoples' Friendship University of Russia / Steklov Institute of Mathematics) 16:00-17:00
Sharp spectral stability estimate for uniformly elliptic differential operators (EMGLISH)
[ 講演概要 ]
T.B.A.

### 2014年11月21日(金)

#### 作用素環セミナー

15:00-17:00   数理科学研究科棟(駒場) 126号室

Haagerupのbicentralizer論文の紹介 (English)

### 2014年11月20日(木)

#### 作用素環セミナー

13:00-15:00   数理科学研究科棟(駒場) 128号室

Haagerupのbicentralizer論文の紹介 (English)

#### 東京無限可積分系セミナー

15:00-18:30   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

[ 講演概要 ]

また証明に用いた写像の性質を調べることで恒等式の側での精密化を行う.

### 2014年11月19日(水)

#### 作用素環セミナー

13:00-15:00   数理科学研究科棟(駒場) 126号室

Haagerupのbicentralizer論文の紹介 (English)

#### 代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室
Fabien Pazuki 氏 (Univ Bordeaux and Univ Copenhagen)
Bad reduction of curves with CM jacobians (English)
[ 講演概要 ]
An abelian variety defined over a number field and having complex multiplication (CM) has potentially good reduction everywhere. If a curve of positive genus which is defined over a number field has good reduction at a given finite place, then so does its jacobian variety. However, the converse statement is false already in the genus 2 case, as can be seen in the entry $[I_0-I_0-m]$ in Namikawa and Ueno's classification table of fibres in pencils of curves of genus 2. In this joint work with Philipp Habegger, our main result states that this phenomenon prevails for certain families of curves.

We prove the following result: Let F be a real quadratic number field. Up to isomorphisms there are only finitely many curves C of genus 2 defined over $\overline{\mathbb{Q}}$ with good reduction everywhere and such that the jacobian Jac(C) has CM by the maximal order of a quartic, cyclic, totally imaginary number field containing F. Hence such a curve will almost always have stable bad reduction at some prime whereas its jacobian has good reduction everywhere. A remark is that one can exhibit an infinite family of genus 2 curves with CM jacobian such that the endomorphism ring is the ring of algebraic integers in a cyclic extension of $\mathbb{Q}$ of degree 4 that contains $\mathbb{Q}(\sqrt{5})$, for example.

#### 数理人口学・数理生物学セミナー

14:50-16:20   数理科学研究科棟(駒場) 122号室