## 過去の記録

#### 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
Abel Klein 氏 (UC Irvine)
Quantitative unique continuation principle, local behavior of solutions, and bounds on the density of states for Schr\\"odinger operators (ENGLISH)
[ 講演概要 ]
We establish bounds on the density of states measure for Schr\\"odinger operators. These are deterministic results that do not require the existence of the density of states measure, or, equivalently, of the integrated density of states. The results are stated in terms of a density of states outer-measure'' that always exists, and provides an upper bound for the density of states measure when it exists. We prove log-H\\"older continuity for this density of states outer-measure in one, two, and three dimensions for Schr\\"odinger operators, and in any dimension for discrete Schr\\"odinger operators. Our proofs use a quantitative unique continuation principle and the local behavior of approximate solutions of the stationary Schr\\"odinger equation.
(Joint work with Jean Bourgain.)
References: Jean Bourgain and Abel Klein: Bounds on the density of states for Schr\\"odinger operators. Invent. Math. 194, 41-72 (2013).

### 2013年12月09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

Donaldson-Tian-Yau 予想と K-安定性について (JAPANESE)
[ 講演概要 ]

#### 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

On birationally tririgid Q-Fano threefolds (JAPANESE)
[ 講演概要 ]
I will talk about birational geometry of Q-Fano threefolds. A Mori
fiber space birational to a given Q-Fano threefold is called a birational Mori fiber structure of the threefold. The existence of Q-Fano threefolds with a unique birational Mori fiber structure (resp. with two birational Mori fiber structures) is known. In this talk I will give an example of Q-Fano threefolds with three birational Mori fiber structures and also discuss about the behavior of birational Mori fiber structures in a family.

### 2013年12月06日(金)

#### 幾何コロキウム

17:00-18:00   数理科学研究科棟(駒場) 123号室

[ 講演概要 ]

#### FMSPレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 118号室
Simon Gindikin 氏 (Rutgers University)
Horospheres: geometry and analysis (II) (ENGLISH)
[ 講演概要 ]
About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gindikin.pdf

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 002号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

[ 講演概要 ]
GL(n) に対する局所 Langlands 対応とその幾何学的実現は,Harris-Taylor によって,保型表現の大域的な議論を用いて証明された.しかし,対応が実現される幾何学的な仕組みについては,未だ十分に理解されているとは言い難い.

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 002号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

[ 講演概要 ]
GL(n) に対する局所 Langlands 対応とその幾何学的実現は,Harris-Taylor によって,保型表現の大域的な議論を用いて証明された.しかし,対応が実現される幾何学的な仕組みについては,未だ十分に理解されているとは言い難い.本講演では,幾何学的実現に対する,Lubin-Tate パーフェクトイド空間を用いたアプローチについて紹介する.

### 2013年12月05日(木)

#### 幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 122号室

Variational characterizations of exact solutions of the Einstein equation (JAPANESE)
[ 講演概要 ]
There are a set of well-known exact solutions to the Einstein equation. The most important one is the Schwarzschild metric, and it models a Ricci-flat space-time, which is asymptotically flat. In addition, there are the Reissner-Nordstrom metric and the Majumdar-Papapetrou metric, which satisfy the Einstein-Maxwell equation, instead of the vacuum Einstein equation. In a jointwork with Marcus Khuri and Gilbert Weinstein, it is shown that those metrics are characterized as the equality
cases of a set of so-called Penrose-type inequalities. The method of proof is a
conformal deformation of Riemannian metrics defined on the space-like slice of the space-time.

### 2013年12月04日(水)

#### 統計数学セミナー

13:30-14:40   数理科学研究科棟(駒場) 052号室

[ 講演概要 ]

[ 講演参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/09.html

#### FMSPレクチャーズ

15:00-16:30   数理科学研究科棟(駒場) 128号室
Simon Gindikin 氏 (Rutgers University)
Horospheres: geometry and analysis (I) (ENGLISH)
[ 講演概要 ]
About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gindikin.pdf

### 2013年12月03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: 16:30 - 17:00 コモンルーム
Bruno Martelli 氏 (Univ. di Pisa)
Hyperbolic four-manifolds with one cusp (cancelled) (JAPANESE)
[ 講演概要 ]
(joint work with A. Kolpakov)

We introduce a simple algorithm which transforms every
four-dimensional cubulation into a cusped finite-volume hyperbolic
four-manifold. Combinatorially distinct cubulations give rise to
topologically distinct manifolds. Using this algorithm we construct
the first examples of finite-volume hyperbolic four-manifolds with one
cusp. More generally, we show that the number of k-cusped hyperbolic
four-manifolds with volume smaller than V grows like C^{V log V} for
any fixed k. As a corollary, we deduce that the 3-torus bounds
geometrically a hyperbolic manifold.

#### FMSPレクチャーズ

13:00-14:30   数理科学研究科棟(駒場) 126号室

Erwin Bolthausen 氏 (University of Zurich)
Random walks in random environments (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf

### 2013年12月02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
Anne-Katrin Herbig 氏 (名古屋大学)
A smoothing property of the Bergman projection (ENGLISH)
[ 講演概要 ]
Let $D$ be a bounded domain with smooth boundary in complex space of dimension $n$. Suppose its Bergman projection $B$ maps the Sobolev space of order $k$ continuously into the one of order $m$. Then the following smoothing result holds: the full Sobolev norm of $Bf$ of order $k$ is controlled by $L^2$-derivatives of $f$ taken along a single, distinguished direction (of order up to $m$). This talk is based on joint work with J. D. McNeal and E. J. Straube.

### 2013年11月29日(金)

#### FMSPレクチャーズ

10:40-12:10   数理科学研究科棟(駒場) 126号室

Erwin Bolthausen 氏 (University of Zurich)
Random walks in random environments (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf

#### FMSPレクチャーズ

14:50-16:20   数理科学研究科棟(駒場) 126号室

Erwin Bolthausen 氏 (University of Zurich)
Random walks in random environments (ENGLISH)
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf

### 2013年11月28日(木)

#### 幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 122号室

[ 講演概要 ]
スカラー曲率函数に対する逆問題は微分幾何における基本問題である.すなわち,閉多様体に滑らかな函数が与えられたとき,その函数をスカラー曲率とする計量の存在を問う.この問題はKazdan-Warnerにより解決した.

#### GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 470号室
Oleg Emanouilov 氏 (Colorado State Univ.)
Inverse problem for the Maxwell equations (ENGLISH)
[ 講演概要 ]
We consider an analog of Caderon's problem for the system of Maxwell equations in a cylindrical domain.
Under some geometrical assumptions on domain we show that from the partial data one can recover the complete set of parameters.

### 2013年11月27日(水)

#### 統計数学セミナー

13:30-14:40   数理科学研究科棟(駒場) 052号室

Density of solutions to stochastic functional differential equations (JAPANESE)
[ 講演概要 ]

[ 講演参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/08.html

### 2013年11月26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 ]
Sは有理楕円曲面とする.Sの生成ファイバーは
1変数有理函数体上の楕円曲線であり,楕円曲線の

C_2を構成することできる.本講演では,このアイ
デアに基づいて得られるある7次のline-conic
arrangementsについて解説する.

#### 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

Huaxiong Huang 氏 (York University)
An immersed boundary method for mass transfer across permeable moving interfaces (ENGLISH)
[ 講演概要 ]
In this talk, we present an immersed boundary method for mass transfer across permeable deformable moving interfaces interacting with the surrounding fluids. One of the key features of our method is the introduction of the mass flux as an independent variable, governed by a non-standard vector transport equation. The flux equation, coupled with the mass transport and the fluid flow equations, allows for a natural implementation of an immersed boundary algorithm when the flux across the interfaces is proportional to the jump in concentration. As an example, the oxygen transfer from red blood cells in a capillary to its wall is used to illustrate the applicability of the proposed method. We show that our method is capable of handling multi-physics problems involving fluid- structure interaction with multiple deformable moving interfaces and (interfacial) mass transfer simultaneously.
This is joint work with X. Gong and Z. Gong.

#### 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

Global Strichartz estimates for Schr\\"odinger equations with long range metrics (JAPANESE)
[ 講演概要 ]
We consider Schr\\"odinger equations on the asymptotically Euclidean space
with the long-range condition on the metric.
We show that if the high energy resolvent has at most polynomial growth with respect to the energy,
then global-in-time Strichartz estimates, outside a large compact set, hold.
Under the non-trapping condition we also discuss global-in-space Strichartz estimates.
This talk is based on a joint work with J.-M. Bouclet (Toulouse University).

### 2013年11月25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 hyperkaehler metrics on holomorphic cotangent bundles on complex reductive Lie groups (JAPANESE)
[ 講演概要 ]
There exists a complete hyperkaehler metric on the holomorphic cotangent bundle on each complex reductive Lie group. It was constructed by Kronheimer, using hyperkaehler quotient method. In this talk I explain how to describe the Kaehler potentials of these metrics.

#### 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 singular metrics of some line bundles with infinitely generated section rings (JAPANESE)
[ 講演概要 ]
We consider Hermitian metrics of pseudo-effective line bundles on smooth
projective varieties defined over $\\mathbb{C}$.
Especially we are interested in (possibly singular) Hermitian metrics
with semi-positive curvatures when the section rings are not finitely generated.
We study where and how minimal singular metrics, special Hermitian
metrics with semi-positive curvatures, diverges in the following two situations;
a line bundle admitting no Zariski decomposition even after any
modifications (Nakayama example)
and a nef line bundle $L$ on $X$ satisfying $D \\subset |mL|$ and $|mL-D| = \\emptyset$ for some divisor $D \\subset X$ and for all $m \\geq 1$ (
Zariski example).

### 2013年11月22日(金)

#### FMSPレクチャーズ

10:40-11:40   数理科学研究科棟(駒場) 123号室
Alfred RAMANI 氏 (École polytechnique)
Integrable discrete systems, an introduction Pt. 2 (ENGLISH)
[ 講演概要 ]
The second part will mostly be devoted to the various integrability detectors (singularity confinement, algebraic entropy) for integrability of discrete systems, in one or more dimensions. The most important systems identified through these detectors, namely the discrete Painlev¥'e equations, will be presented in detail, through a geometric approach.

### 2013年11月21日(木)

#### GCOEセミナー

15:30-17:00   数理科学研究科棟(駒場) 056号室
この講義はMini workshop on birational geometryの一環として行われます
Florin Ambro 氏 (IMAR)
Cyclic covers and toroidal embeddings (ENGLISH)
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/documents/miniworkshop.pdf