## 過去の記録

### 2012年10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 コモンルーム

Geometric flows and their self-similar solutions
(JAPANESE)
[ 講演概要 ]
In the first half of this expository talk we consider the Ricci flow and its self-similar solutions,
namely the Ricci solitons. We then specialize in the K\\"ahler case and discuss on the K\\"ahler-Einstein
problem. In the second half of this talk we consider the mean curvature flow and its self-similar
solutions, and see common aspects of the two geometric flows.

### 2012年10月01日(月)

#### 代数幾何学セミナー

13:30-15:00   数理科学研究科棟(駒場) 122号室
Robert Laterveer 氏 (CNRS, IRMA, Université de Strasbourg)
Weak Lefschetz for divisors (ENGLISH)
[ 講演概要 ]
Let $X$ be a complex projective variety (possibly singular), and $Y\\subset X$ a generic hyperplane section. We prove several weak Lefschetz results concerning the restriction $A^1(X)_{\\qq}\\to A^1(Y)_{\\qq}$, where $A^1$ denotes Fulton--MacPherson's operational Chow cohomology group. In addition, we reprove (and slightly extend) a weak Lefschetz result concerning the Chow group of Weil divisors first proven by Ravindra and Srinivas. As an application of these weak Lefschetz results, we can say something about when the natural map from the Picard group to $A^1$ is an isomorphism.

#### 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

Frobenius morphisms and derived categories on two dimensional toric Deligne--Mumford stacks (JAPANESE)
[ 講演概要 ]
For a toric Deligne-Mumford (DM) stack over the complex number field, we can consider a certain generalization of the Frobenius endomorphism. For such an endomorphism of a two-dimensional toric DM stack, we show that the push-forward of the structure sheaf generates the bounded derived category of coherent sheaves on the stack. This is joint work with Hokuto Uehara.

### 2012年09月20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
Bernold Fiedler 氏 (Free University of Berlin)
Fusco-Rocha meanders: from Temperley-Lieb algebras to black holes
(ENGLISH)
[ 講演概要 ]
Fusco and Rocha studied Neumann boundary value problems for ODEs of second order via a shooting approach. They introduced the notion of what we now call Sturm permutation. These permutation relate, on the one hand, to a special class of meandering curves as introduced by Arnol'd in a singularity context. On the other hand, their special class became central in the study of global attractors of parabolic PDEs of Sturm type.

We discuss relations of Fusco-Rocha meanders with further areas: the multiplicative and trace structure in Temperley-Lieb algebras, discrete versions of Cartesian billiards, and the problem of constructing initial conditions for black hole dynamics which satisfy the Einstein constraints. We also risk a brief glimpse at the long and meandric history of meander patterns themselves.

This is joint work with Juliette Hell, Brian Smith, Carlos Rocha, Pablo Castaneda, and Matthias Wolfrum.

### 2012年09月15日(土)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

SU(2,1)とSU(3,1)の大きい離散系列表現の行列係数 (JAPANESE)
[ 講演概要 ]
この講演では,$SU(2,1)$と$SU(3,1)$の大きい離散系列表現の行列係数の動径成分に対して,(一般化)超幾何級数を用いた表示を与える.また,この表示に対してVidunas氏の結果を適用する事で得られる行列係数の漸近挙動に関する結果についても紹介する.(織田孝幸氏,古関春隆氏,早田孝博氏との共同研究)

GSp(1,1)のRankin型のL関数の中心値の正値性と超幾何級数の特殊値 (JAPANESE)
[ 講演概要 ]
We discuss the strict positivity of the central values of
certain convolution type L-functions for several theta lifts to GSp(1,1). Such strict positivity is closely related to special values of some hypergeometric functions.

### 2012年09月04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) 002号室
Tea: 16:30 - 17:00 コモンルーム
Piotr Nowak 氏 (the Institute of Mathematics, Polish Academy of Sciences)
Poincare inequalities, rigid groups and applications (ENGLISH)
[ 講演概要 ]
Kazhdan’s property (T) for a group G can be expressed as a
fixed point property for affine isometric actions of G on a Hilbert
space. This definition generalizes naturally to other normed spaces. In
this talk we will focus on the spectral (aka geometric) method for
proving property (T), based on the work of Garland and studied earlier
by Pansu, Zuk, Ballmann-Swiatkowski, Dymara-Januszkiewicz
(“lambda_1>1/2” conditions) and we generalize it to to the setting of
all reflexive Banach spaces.
As applications we will show estimates of the conformal dimension of the
boundary of random hyperbolic groups in the Gromov density model and
present progress on Shalom’s conjecture on vanishing of 1-cohomology
with coefficients in uniformly bounded representations on Hilbert spaces.

### 2012年08月29日(水)

#### 博士論文発表会

10:30-11:45   数理科学研究科棟(駒場) 123号室

Studies on the asymptotic invariants of cohomology groups and the positivity in complex geometry （コホモロジー群の漸近的な不変量と複素幾何学における正値性の研究） (JAPANESE)

### 2012年08月20日(月)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 128号室

The variational formulation of the fully parabolic Keller-Segel system with degenerate diffusion （退化拡散項を持つ完全放物型Keller-Segel系に対する変分的定式化） (JAPANESE)

### 2012年07月30日(月)

#### 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
Gianluca Pacienza 氏 (Université de Strasbourg)
Log Bend-and-Break on Deligne-Mumford stacks (ENGLISH)
[ 講演概要 ]
We prove a logarithmic Bend-and-Break lemma on a LCI Deligne-Mumford stacks with projective moduli space and integral boundary divisor. As a by-product we obtain a logarithmic version of the Miyaoka-Mori numerical criterion of uniruledness for DM stacks (under additional conditions on the boundary and on the non-schematic locus) and a Cone Theorem for Deligne-Mumford stacks with boundary. These results hold on an algebraically closed field of any characteristic. This is joint work with Michael McQuillan.

### 2012年07月27日(金)

#### 統計数学セミナー

14:00-17:00   数理科学研究科棟(駒場) 006号室

[ 講演概要 ]

[ 講演参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/06.html

### 2012年07月25日(水)

#### GCOEレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 118号室
George Elliott 氏 (University of Toronto)
A survey of recent results on the classification of C*-algebras (ENGLISH)

### 2012年07月24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
Greg McShane 氏 (Institut Fourier, Grenoble)
Orthospectra and identities (ENGLISH)
[ 講演概要 ]
The orthospectra of a hyperbolic manifold with geodesic
boundary consists of the lengths of all geodesics perpendicular to the
boundary.
We discuss the properties of the orthospectra, asymptotics, multiplicity
and identities due to Basmajian, Bridgeman and Calegari. We will give
a proof that the identities of Bridgeman and Calegari are the same.

#### 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

The Dynkin index and conformally invariant systems of Heisenberg parabolic type (ENGLISH)
[ 講演概要 ]
Heisenberg parabolic subalgebraから構築されたconformally invariant
systemに関する二つの定数について考察する。それらの定数はそのconformally
invariant systemを構築する際に重要な役割を果たしたが、ある二つの式の比率
として定義されただけで具体的な式などは表されなかった。本講演ではそれらの

### 2012年07月23日(月)

#### 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

Derived category of smooth proper Deligne-Mumford stack with p_g>0 (JAPANESE)
[ 講演概要 ]
Semiorthogonal decomposition (SOD) of the derived category of coherent sheaves reflects interesting geometry of varieties (more generally stacks), such as minimal model program. We show that the global sections of the canonical line bundle (if exists) give restrictions on the possible form of SODs. As a special case, we see that the global generation of the canonical line bundle implies the non-existence of SODs. (joint work with Kotaro Kawatani)

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 126号室
Thomas W. Roby 氏 (University of Connecticut)
Combinatorial Ergodicity (ENGLISH)
[ 講演概要 ]
Many cyclic actions $\\tau$ on a finite set $S$ of
combinatorial objects, along with many natural
statistics $\\phi$ on $S$, exhibitcombinatorial ergodicity'':
the average of $\\phi$ over each $\\tau$-orbit in $S$ is
the same as the average of $\\phi$ over the whole set $S$.
One example is the case where $S$ is the set of
length $n$ binary strings $a_{1}\\dots a_{n}$
with exactly $k$ 1's,
$\\tau$ is the map that cyclically rotates them,
and $\\phi$ is the number of \\textit{inversions}
(i.e, pairs $(a_{i},a_{j})=(1,0)$ for $iJ$ less than $j$).

This phenomenon was first noticed by Panyushev
in 2007 in the context of antichains in root posets;
Armstrong, Stump, and Thomas proved his
conjecture in 2011.
We describe a theoretical framework for results of this kind,
and discuss old and new results for products of two chains.

This is joint work with Jim Propp.

### 2012年07月21日(土)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

degree n の Siegel-Eisenstein 級数の Fourier 係数について (JAPANESE)
[ 講演概要 ]
この話では,まず,あるdegree nのSiegel-Eisenstein級数G_{k,\\chi}を定義し,そのFourier係数の明示公式について述べます.このEisenstein級数G_{k,\\chi}は通常のSiegel-Eisenstein級数E_{k,\\chi}とは定義が違うのですが,G_{k,\\chi}のFourier係数の明示公式から,\\chiが特別な場合のE_{k,\\chi}のFourier係数の明示が得られます.

[ 講演概要 ]

### 2012年07月19日(木)

#### GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 370号室
Oleg Emanouilov 氏 (Colorado State Univ.)
Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)
[ 講演概要 ]
We consider the Dirichlet-to-Neumann map for determining potential in two-dimensional Schroedinger equation. We relax the regularity condition on potentials and establish the uniqueness within L^p class with p > 2.

### 2012年07月18日(水)

#### 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
Shane Kelly 氏 (Australian National University)
Voevodsky motives and a theorem of Gabber (ENGLISH)
[ 講演概要 ]
The assumption that the base field satisfies resolution of singularities litters Voevodsky's work on motives. While we don't have resolution of singularities in positive characteristic p, there is a theorem of Gabber on alterations which may be used as a substitute if we are willing to work with Z[1/p] coefficients. We will discuss how this theorem of Gabber may be applied in the context of Voevodsky's work and mention some consequences.

#### 古典解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室

Free divisors, holonomic systems and algebraic Painlev\\'{e} sixth solutions (ENGLISH)
[ 講演概要 ]
In this talk, I will report an attempt to treat algebraic solutions of Painlev\\'{e} VI equation in a unified manner.
A classification of algebraic solutions of Painlev\\'{e} VI equation was accomplished by O. Lisovyy and Y. Tykhyy after efforts on the construction of such solutions by many authors, K. Iwasaki N. J. Hitchin, P. Boalch, B. Dubrovin, M. Mazzocco, A. V. Kitaev, R. Vidunas and others.
The outline of my approach is as follows.
Let $t$ be a variable and let $w$ be its algebraic function such that $w$ is a solution of Painlev\\'{e} sixth equation. Suppose that both $t$ and $w$ are rational functions of a parameter. Namely $(t,w)$ defines a rational curve.
(1) Find a polynomial $P(u)$ such that $t=\\frac{P(-u)}{P(u)}$.
(2) From $P(u)$, define a weighted homogeneous polynomial $f(x_1,x_2,x_3)=x_3f_1(x_1,x_2,x_3)$ of three variables $x_1,x_2,x_3$, where $(1,2,n)$ is the weight system of $(x_1,x_2,x_3)$ with $n=\\deg P(u)$. The hypersurface $D:f(x)=0$ is a free divisor in ${\\bf C}^3$. Note that $\\deg_{x_3}f_1=2$.
(3) Construct a holonomic system ${\\sl M}$ on ${\\bf C}^3$ of rank two with singularities along $D$.
(4) Construct an ordinary differential equation from the holonomic system ${\\sl M}$ with respect to $x_3$. This differential equation has three singular points $z_0,z_1,a_s$ in $x_3$-line.
(5) Putting $t=\\frac{z_1}{z_0},\\lambda=\\frac{a_s}{z_0}$, we conclude that $(t,\\lambda)$ is equivalent to the pair $(t,w)$.
Our study starts with showing the existence of $P(u)$ in (1). From the classification by Losovyy and Tykhyy, I find that the existence of $P(u)$ is guaranteed for Solutions III, IV, Solutions $k$ ($1\\le k\\le 21$, $k\\not= 4,13,14,20$) and Solution 30. We checked whether (1)-(5) are true or not in these cases separately and as a consequence (1)-(5) hold for the all these cases except Solutions 19, 21.

### 2012年07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

Contact structure of mixed links (JAPANESE)
[ 講演概要 ]
A strongly non-degenerate mixed function has a Milnor open book
structures on a sufficiently small sphere. We introduce the notion of
{\\em a holomorphic-like} mixed function
and we will show that a link defined by such a mixed function has a
canonical contact structure.
Then we will show that this contact structure for a certain
holomorphic-like mixed function
is carried by the Milnor open book.

#### GCOEレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 118号室
George Elliott 氏 (University of Toronto)
An introduction to C*-algebra classification theory (ENGLISH)

#### 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

2次元円環領域におけるLiouville-Gel\\'fand方程式の非球対称解の構造 (JAPANESE)
[ 講演概要 ]

#### Lie群論・表現論セミナー

17:00-18:30   数理科学研究科棟(駒場) 126号室
Eric Opdam 氏 (Universiteit van Amsterdam)
Dirac induction for graded affine Hecke algebras (ENGLISH)
[ 講演概要 ]
In recent joint work with Dan Ciubotaru and Peter Trapa we
constructed a model for the discrete series representations of graded affine Hecke algebras as the index of a Dirac operator.
We discuss the K-theoretic meaning of this result, and the remarkable relation between elliptic character theory of a Weyl group and the ordinary character theory of its Pin cover.

### 2012年07月14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
このセミナーは,月に1度程度,不定期に開催されます.

(岐阜大学) 13:30-15:00

(JAPANESE)
[ 講演概要 ]

その結果、対応するTrudigner-Moser型不等式、対数型Hardyの不等式及び対数型Young関数による一般化されたMorrey空間への埋込み定理を導出する。

) 15:30-17:00
Boundedness of operators on Hardy spaces with variable exponents
(JAPANESE)
[ 講演概要 ]
In this talk, as an off-spring, we will discuss the boundedness of various operators. Our plan of the talk is as follows:
First we recall the definition of Hardy spaces with variable exponents and then we describe the atomic decomposition.
Based upon the atomic decomposition, I define linear operators such as singular integral operators and commutators.
After the definition, I will state the boundedness results and outline the proof of the boundedness of these operators.

### 2012年07月12日(木)

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 370号室
M. Lavrentiev 氏 (Sobolev Institute of Mathematics)
Real time tsunami parameters evaluation (ENGLISH)
[ 講演概要 ]
We would like to propose several improvements to the existing software tools for tsunami modeling. Combination of optimaly located system of sensors with advantages of modern hardware architectures will make it possible to deliver calculated parameters of tsunami wave in 12-15 minutes after seismic event.