## 過去の記録

### 2010年05月24日(月)

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室

A counterexample of the birational Torelli problem via Fourier--Mukai transforms (JAPANESE)
[ 講演概要 ]
We study the Fourier--Mukai numbers of rational elliptic surfaces. As
its application, we give an example of a pair of minimal 3-folds $X$
with Kodaira dimensions 1, $h^1(O_X)=h^2(O_X)=0$ such that they are
mutually derived equivalent, deformation equivalent, but not
birationally equivalent. It also supplies a counterexample of the
birational Torelli problem.

### 2010年05月19日(水)

#### 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

[ 講演概要 ]

れている現象が数多く存在する。その例として、(1)造影剤の濃度カーブを用い
た腎臓癌の転移危険性及び肝臓における血液灌流の評価、(2)大動脈瘤に対する
ステント治療の予後予測、について紹介する。前者は、血管からの造影剤の浸出

のである。後者は、個人差の大きい大動脈形状による血流の違いを数値シミュ
レーションによって求め、統計学的なクラスタリングと併せて予後を予測するも
のである。どちらも、モデリングにあたっては臨床医療の現場との緊密な連携が

の手順や困難な点、今後の展望などについて報告したい。

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/01.html

### 2010年05月18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 roots of Dehn twists (JAPANESE)
[ 講演概要 ]
Let $t_{c}$ be the Dehn twist about a nonseparating simple closed curve
$c$ in a closed orientable surface. If a mapping class $f$ satisfies
$t_{c}=f^{n}$ in mapping class group, we call $f$ a root of $t_{c}$ of
degree $n$. In 2009, Margalit and Schleimer constructed roots of $t_{c}$.
In this talk, I will explain the data set which determine a root of
$t_{c}$ up to conjugacy. Moreover, I will explain the minimal and the
maximal degree.

#### 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
B. Speh 氏 (Cornel University)
On the eigenvalues of the Laplacian on locally symmetric hyperbolic spaces (ENGLISH)
[ 講演概要 ]
A famous Theorem of Selberg says that the non-zero eigenvalues of the Laplacian acting on functions on quotients of the upper half plane H by congruence subgroups of the integral modular group, are bounded away from zero, as the congruence subgroup varies. Analogous questions on Laplacians acting on differential forms of higher degree on locally symmetric spaces (functions may be thought of as differential forms of degree zero) have geometric implications for the cohomology of the locally symmetric space.

Let $X$ be the real hyperbolic n-space and $\\Gamma \\subset$ SO(n, 1) a congruence arithmetic subgroup. Bergeron conjectured that the eigenvalues of the Laplacian acting on the differential forms on $X / \\Gamma$ are bounded from the below by a constant independent of the congruence subgroup. In the lecture I will show how one can use representation theory to show that this conjecture is true provided that it is true in the middle degree.

This is joint work with T.N. Venkataramana

### 2010年05月17日(月)

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室

On the GIT stability of Polarized Varieties (JAPANESE)
[ 講演概要 ]
Background:
Original GIT-stability notion for polarized variety is
"asymptotic stability", studied by Mumford, Gieseker etc around 1970s.
Recently a version appeared, so-called "K-stability", introduced by
Tian(1997) and reformulated by Donaldson(2002), by the way of seeking
the analogue of Kobayashi-Hitchin correspondence, which gives
"differential geometric" interpretation of "stability". These two have
subtle but interesting differences in dimension higher than 1.

Contents:
(1*) Any semistable (in any sense) polarized variety should have only
"semi-log-canonical" singularities. (Partly observed around 1970s)
(2) On the other hand, we proved some stabilities, which corresponds to
"Calabi conjecture", also with admitting mild singularities.

As applications these yield
(3*) Compact moduli spaces with GIT interpretations.
(4) Many counterexamples (as orbifolds) to folklore conjecture:
"K-stability implies asymptotic stability".

(*: Some technical points are yet to be settled.
Some parts for (1)(2) are available on arXiv:0910.1794.)

#### 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

On the norm defined on the holomorphic maps of compact Riemann surfaces (JAPANESE)

### 2010年05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

Strict positivity of the central values of some Rankin-Selberg
L-functions (JAPANESE)
[ 講演概要 ]
この講演では、荒川リフトというGSp(2)の内部形式上の保型形式に対する、
ある次数8のRankin-Selberg型のL関数の中心値が正となる例について紹介
する。このL関数は岡崎武生氏がGO(2,2)からのテータリフトにより

GSp(2)のRankin-Selberg型のL関数の中心値が正となる例も与える。

[ 講演概要 ]

### 2010年05月12日(水)

#### 講演会

15:30-17:00   数理科学研究科棟(駒場) 123号室
3回連続の最終回です。前2回より開始時間が早いのでご注意ください。

Luc Illusie 氏 (東京大学/Paris南大学)
Independence of families of $\\ell$-adic representations and uniform constructibility (ENGLISH)
[ 講演概要 ]
Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

#### 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

Differences between
Galois representations in outer-automorphisms
of the fundamental groups and those in automorphisms, implied by
topology of moduli spaces (ENGLISH)
[ 講演概要 ]
Fix a prime l. Let C be a proper smooth geometrically connected curve over a number ﬁeld K, and x be its closed point. Let Π denote the pro-l completion of the geometric fundamental group of C with geometric base point over x. We have two non-abelian Galois representations:

ρA : Galk(x) → Aut(Π),ρO : GalK → Out(Π).

Our question is: in the natural inclusion Ker(ρA) ⊂ Ker(ρO) ∩ Galk(x), whether the equality holds or not. Theorem: Assume that g ≥ 3, l divides 2g -2. Then, there are inﬁnitely many pairs (C, K) with the following property. If l does not divide the extension degree [k(x): K], then Ker(ρA) = (Ker(ρO) ∩ Galk(x)) holds.

This is in contrast to the case of the projective line minus three points and its canonical tangential base points, where the equality holds (a result of Deligne and Ihara).

There are two ingredients in the proof: (1) Galois representations often contain the image of the geometric monodromy (namely, the mapping class group) [M-Tamagawa 2000] (2) A topological result [S. Morita 98] [Hain-Reed 2000] on the cohomological obstruction of lifting the outer action of the mapping class group to automorphisms.

(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted to IHES by the internet.)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Jean-Pierre Puel 氏 (Graduate School of Mathematical Sciences
The University of Tokyo)
Exact controllability for incompressible fluids (ENGLISH)
[ 講演概要 ]
After a short presentation of J.-M. Coron's results for Euler equation, we will give the good notions of controllability for Navier-Stokes equations, namely the exact controllability to trajectories.
We will outline the strategy for obtaining local results, based on a fixed point argument following the study of null controllability for the linearized problem. This is equivalent to an observability inequality for the adjoint system, which requires a global Carleman estimate for linearized Navier-Stokes equations. We will explain this estimate and the different steps for obtaining it along the lines of the articles by E.Fernadez-Cara, S.Guerrero, O.Imanuvilov and J.-P.Puel (JMPA, 2004) and M.Gonzalez-Burgos, S.Guerrero and J.-P.Puel (CPAA, 2009).
We will end up with some important open problems.

#### 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

[ 講演概要 ]

[ 講演参考URL ]
http://www.infsup.jp/utnas/

#### GCOEセミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

[ 講演参考URL ]
http://www.infsup.jp/utnas/

### 2010年05月11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

The logarithms of Dehn twists (JAPANESE)
[ 講演概要 ]
We establish an explicit formula for the action of (non-separating and
separating) Dehn twists on the complete group ring of the fundamental group of a
surface. It generalizes the classical transvection formula on the first homology.
The proof is involved with a homological interpretation of the Goldman
Lie algebra. This talk is based on a jointwork with Yusuke Kuno (Hiroshima U./JSPS).

#### 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

On a finite $W$-algebra module structure on the space of
continuous Whittaker vectors for an irreducible Harish-Chandra module (ENGLISH)
[ 講演概要 ]
Let $G$ be a real reductive Lie group. The space of continuous Whittaker vectors for an irreducible Harish-Chandra module has a structure of a module over a finite $W$-algebra. We have seen such modules are irreducible for groups of type A. However, there is a counterexample to the naive conjecture. We discuss a refined version of the conjecture and further examples in this talk.

### 2010年05月10日(月)

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室

Grassmann多様体のトーリック退化とミラー対称性 (JAPANESE)
[ 講演概要 ]
Grassmann多様体のトーリック退化と、
それを用いたGrassmann多様体の完全交叉カラビ・ヤウ多様体に対するミラー構

とくに、項順序によるトーリック退化に着目すれば、

A型Grassmann多様体やスピノル多様体などの例に関してこの条件を考察する。

#### 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

ACH-Einstein計量の漸近展開と半可積分概CR多様体上のある不変テンソル場 (JAPANESE)
[ 講演概要 ]

### 2010年05月07日(金)

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 056号室
3回連続の第2回です。最終回は、5月12日(水)3時半から5時で、部屋は同じく056です。

Luc Illusie 氏 (東京大学/Paris南大学)
Independence of families of $\\ell$-adic representations and uniform constructibility
[ 講演概要 ]
Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

#### 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
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
Jean-Pierre Puel 氏 (The University of Tokyo, Universite de Versailles Saint-Quentin)
Why to study controllability problems and the mathematical tools involved (ENGLISH)
[ 講演概要 ]
We will give some examples of controllability problems and the underlying applications to practical situations. This includes vibrations of membranes or plates, motion of incompressible fluids or quantum systems occuring in quantum chemistry or in quantum logic information theory. These examples correspond to different types of partial differential equations for which specific analysis has to be done. Of course, at the moment, very few results are known and the domain is widely open. We will describe very briefly the mathematical tools used for each type of PDE, in particular microlocal analysis, global Carleman estimates or some specific real analysis estimates.These methods appear to be also useful to study some inverse problems and, if time permits, we will give a few elements on some examples.

### 2010年05月06日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Connes-Landi Deformation of Spectral Triples (ENGLISH)
[ 講演概要 ]
We describe a way to deform spectral triples with a 2-torus action and a real deformation parameter, motivated by deformation of manifolds after Connes-Landi. Such deformations are shown to have naturally isomorphic K-theoretic invariants independent of the deformation parameter.

### 2010年04月28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

Marcus Wunsch 氏 (Kyoto University
)
GLOBAL AND SINGULAR SOLUTIONS TO SOME
HYDRODYNAMIC EVOLUTION EQUATIONS
[ 講演概要 ]
The two-component Hunter-Saxton system is a recently derived system of evolution equations modeling, e.g., the nonlinear dynamics of nondissipative dark matter and the propagation of orientation waves in nematic liquid crystals. It is imbedded into a parameterized family of systems called the generalized Hunter-Saxton (2HS) system [2] reducing, if one component is omitted, to the generalized Proudman-Johnson(gPJ) equation [1] modeling three-dimensional vortex dynamics.
After demonstrating, by means of Kato's semigroup theory, the local-in-time existence of classical solutions, the blow-up scenarios for the 2HS system and the gPJ equation are described. The explicit construction of weak dissipative solutions for both models is discussed in detail.
Finally, global existence in time of these weak solutions is proved.

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 056号室
3回連続の第1回です。2回目と3回目は、5月7日(金)4時から5時半と
5月12日(水)3時半から5時です。部屋はどちらも056です。

Luc Illusie 氏 (東京大学/Paris南大学)
Independence of families of $\\ell$-adic representations and uniform constructibility
[ 講演概要 ]
Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 002号室

A Markov process for circular data (JAPANESE)
[ 講演概要 ]
We propose a discrete-time Markov process which takes values on the unit circle. Some properties of the process, including the limiting behaviour and ergodicity, are investigated. Many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers. The proposed model is compared with an existing Markov process for circular data. A simulation study is made to illustrate the mathematical properties of the model. Statistical inference for the process is briefly considered.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/00.html

### 2010年04月27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 the complex volume of hyperbolic knots (JAPANESE)
[ 講演概要 ]
In this talk, we give a formula of the volume and the Chern-Simons invariant of hyperbolic knot complements, which is closely related to the volume conjecture of hyperbolic knots.
We also discuss the volumes and the Chern-Simons invariants of closed 3-manifolds
obtained by Dehn surgeries on hyperbolic knots.

#### 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

Vogan-Zuckerman加群の対称部分群に関する制限 (JAPANESE)
[ 講演概要 ]
We study the restriction of Vogan-Zuckerman derived functor modules $A_\\frak{q}(\\lambda)$ to symmetric subgroups.
An algebraic condition for the discrete decomposability of
$A_\\frak{q}(\\lambda)$ was given by Kobayashi, which offers a framework for the detailed study of branching law.
In this talk, when $A_\\frak{q}(\\lambda)$ is discretely decomposable,
we construct some of irreducible components occurring in the branching law and determine their associated variety.