## Seminar information archive

### 2008/11/28

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #128 (Graduate School of Math. Sci. Bldg.)

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

[ Reference URL ]
[開催日にご注意下さい]

#### GCOE lecture series

14:40-16:10   Room #002 (Graduate School of Math. Sci. Bldg.)
Andrei Pajitnov (Univ. de Nantes)
Circle-valued Morse theory
, Lecture 2

### 2008/11/26

#### Algebraic Geometry Seminar

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Piotr Pragacz
(Banach Institute)
Diagonal subschemes and vector bundles

#### GCOE lecture series

14:40-16:10   Room #002 (Graduate School of Math. Sci. Bldg.)
Andrei Pajitnov (Univ. de Nantes)
Circle-valued Morse theory, Lecture 1
[ Abstract ]
Morse theory of circle-valued functions, initiated by S. P. Novikov in 1980-1982 is now a rapidly developing domain with applications and connections to many other fields of geometry and topology such as dynamical systems, Lagrangian intersections,
knots and links in three-dimensional sphere.

We will start with the basics of the theory, discuss the construction of the Novikov complex, relations with the dynamical zeta functions, and the knot theory. We will conclude with a list of the open problems of the theory.

#### Number Theory Seminar

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)

Lang's Observation in Diophantine Problems
[ Abstract ]
In 1964, Serge Lang suggested the following problem, which reads now as follows:
Let $E$ be an elliptic curve defined over a number field $K$, and $\\varphi$ be a rational function on $E$. Then, for every point $P\\in E(K)$ where $\\varphi$ does not vanish at $P$, the logarithms of a norm of $\\varphi(P)$ is at worst linear in the logarithms of the Neron-Tate height of the point $P$.
We give a simultaneous Diophantine approximation for linear forms in elliptic logarithms which actually implies this conjecture. We also present Lang's observations in Diophantine problems.

### 2008/11/25

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Ovidiu Calin (Eastern Michigan University)
Heat kernels for subelliptic operators
[ Abstract ]
Subelliptic operators are differential operators with missing
directions. Their behavior is very different than the behavior or
elliptic operators. Among the most well known subelliptic operators
are the Grusin operator, the Heisenberg operator, and the Kolmogorov
operator. There are several methods of finding the heat kernels of
subelliptic operators. The heat kernels of subelliptic operators are
usually represented in integral form, but in the case of the
Kolmogorov operator we shall show that the heat kernel is of function
type. We shall spend some time on other subelliptic operators too.

#### Algebraic Geometry Seminar

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Xavier Roulleau (東大)
Cotangent maps of surfaces of general type
[ Abstract ]
Surfaces are usualy studied and classified via the properties of the pluricanonical maps. For surfaces of general type whose cotangent sheaf is generated by global sections, we propose to study an other map, called the cotangent map, in order to obtain geometric informations on the surface. In this way, we obtain informations on the ampleness of the cotangent sheaf of such a surface. We will illustate this talk with the example of the Fano surface of lines of cubic threefolds.

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)

$\\mathbb R^n$への$\\mathbb R^2$の固有な作用と周期性
[ Abstract ]
Consider $\\R^2$ actions on $\\R^n$ which is free, affine and unipotent. Our concern here is to answer the following question:

"Does the quotient topology admits a manifold structure?"

Under some weak assumption, we classify all actions up to conjugate, and give a complete answer to the question.

If Lipsman's conjecture were true, all of the answer should be affirmative.

But, we shall find a unique action which gives a negative answer for each $n\\geq 5$. And, we also find a periodicity on such counterexamples.

As a key lemma, we use "proper analogue" of the five lemma on
exact sequence.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Andrei Pajitnov (Univ. de Nantes)
Circle-valued Morse theory for knots and links
[ Abstract ]
We will discuss several recent developments in
this theory. In the first part of the talk we prove that the Morse-Novikov number of a knot is less than or equal to twice the tunnel number of the knot, and present consequences of this result. In the second part we report on our joint project with Hiroshi Goda on the half-transversal Morse-Novikov theory for 3-manifolds.

### 2008/11/22

#### Infinite Analysis Seminar Tokyo

13:30-16:00   Room #117 (Graduate School of Math. Sci. Bldg.)

Quantum Entanglement in Exactly Solvable Models
[ Abstract ]

は、この新しく導入された指標が量子多体系の基本性質を正しく反映しているか
をテストする一種の実験室として重要な役割を果たしてきた。セミナーでは、

1. Affleck-Kennedy-Lieb-Tasaki modelのvalence bond solid基底状態におけるenta
nglementと端状態
2. Calogero-Sutherland modelにおける粒子間entanglementと排他的分数統計
3. Bethe ansatz波動関数の行列積表示

づくものである。

[ Abstract ]
KRクリスタルとはアフィンリー環gのディンキン図の0以外の頂点と

の場合には昨年確認された。今年になって、それらの結晶グラフの

についてgが$A_{2n-1}^{(2)}$と$C_n^{(1)}$の場合にお話したい。
また、組合せ論的に与えた結晶グラフが、なぜ表現論的に存在が
わかった結晶基底のグラフと一致するかについての証明の概略に
ついても触れたい。

### 2008/11/21

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #128 (Graduate School of Math. Sci. Bldg.)

デリバティブ・プロダクツの価格付け II

#### Colloquium

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)

What is Q-curvature?
[ Abstract ]

[ Reference URL ]

### 2008/11/20

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
(Vienna University of Technology(オーストリア))
Stochastic Particle Approximation for Measure Valued Solutions of the 2D Keller-Segel System
[ Abstract ]
We construct an approximation to the measure valued, global in time solutions to the Keller-Segel model in 2D, based on systems of stochastic interacting particles. The advantage of our approach is that it reproduces the well-known dichtomy in the qualitative behavior of the system and, moreover, captures the solution even after the possible blow-up events. We present a numerical method based on this approach and show some numerical results. Moreover, we make a first step toward the convergence analysis of our scheme by proving the convergence of the stochastic particle approximation for the Keller-Segel model with a regularized interaction potential. The proof is based on a BBGKY-like approach for the corresponding particle distribution function.

### 2008/11/19

#### Number Theory Seminar

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Olivier Fouquet (大阪大学)
Dihedral Iwasawa theory of ordinary modular forms
[ Abstract ]
According to Hida theory, the Galois representation attached to a nearly-ordinary Hilbert eigencuspform belongs to a p-adic analytic family of Galois representations parametrized by varying weights. After restricting it to the absolute Galois group of a quadratic totally complex extension, it also belongs to a p-adic family coming from classical dihedral Iwasawa theory. We will explain the proofs of part of the main conjecture in Iwasawa theory in these situations, i.e divisibilities of characteristic ideals when equalities are actually expected.

### 2008/11/18

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Jorge Vargas (FAMAF-CIEM, C\'ordoba)
Liouville measures and multiplicity formulae for admissible restriction of Discrete Series
[ Abstract ]
Let $H \\subset G$ be reductive matrix Lie groups. We fix a square integrable irreducible representation $\\pi$ of $G.$
Let $\\Omega$ denote the coadjoint orbit of the Harish-Chandra parameter of $\\pi.$

Assume $\\pi$ restricted to $H$ is admissible. In joint work with Michel Duflo, by means of "discrete" and "continuos" Heaviside functions we relate the multiplicity of each irreducible $H-$factor of $\\pi$ restricted to $H$ and push forward to $\\mathfrak h^\\star$ of the Liouville measure for $\\Omega.$ This generalizes work of Duflo-Heckman-Vergne.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

ある種の力学系においては、相空間やパラメータ空間の

ある意味で剛性の問題とつながっている。この現象の説明には、
ある部分集合への再帰写像の構成から得られる、あるクラスの

くりこみ作用素の考え方が重要である。これに関して、

### 2008/11/17

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

Deformation of Sasakian metrics

### 2008/11/14

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #128 (Graduate School of Math. Sci. Bldg.)

### 2008/11/13

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)

Aronson-Benilan type estimate and the optimal Hoelder continuity of weak solutions for the 1D degenerate Keller-Segel systems
[ Abstract ]
We consider the Cauchy problem for the 1D Keller-Segel system of degenerate
type (KS)_m with $m>1$:
u_t= \\partial_x^2 u^m - \\partial_x (u^{q-2} \\partial_x v),
-\\partial_x^2 v + v - u=0.
We establish a uniform estimate from below of $\\partial_x^2 u^{m-1}$.
The corresponding estimate to the porous medium equation is well-known
as an Aronson-Benilan type.
As an application of our Aronson-Benilan type estimate,
we prove the optimal Hoelder continuity of the weak solution $u$ of (KS)_m.
In addition, we find that the positive region $D(t):=\\{x \\in \\R; u(x,t)>0\\}$
of $u$ is monotonically non-decreasing with respect to the time $t$.

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (IPMU)
Groups of friezes and property RD

### 2008/11/11

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)

Rotation number approach to spectral analysis of the generalized Kronig-Penney Hamiltonians

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Thomas Andrew Putman (MIT)
The second rational homology group of the moduli space of curves
with level structures
[ Abstract ]
Let $\\Gamma$ be a finite-index subgroup of the mapping class
group of a closed genus $g$ surface that contains the Torelli group. For
instance, $\\Gamma$ can be the level $L$ subgroup or the spin mapping class
group. We show that $H_2(\\Gamma;\\Q) \\cong \\Q$ for $g \\geq 5$. A corollary
of this is that the rational Picard groups of the associated finite covers
of the moduli space of curves are equal to $\\Q$. We also prove analogous
results for surface with punctures and boundary components.

### 2008/11/10

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

### 2008/11/07

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #128 (Graduate School of Math. Sci. Bldg.)

デリバティブ・プロダクツの価格付け I