## 過去の記録

### 2008年03月13日(木)

#### 解析学火曜セミナー

15:00-17:30   数理科学研究科棟(駒場) 117号室
「解析学(臨時)セミナー」と名称変更し,曜日,部屋も臨時に変更.

Schr/"odinger equations on scattering manifolds and microlocal singularities
Maciej ZWORSKI 氏 (カリフォルニア大学バークレイ校) 16:30-17:30
Local smoothing in the presence of lots of trapping
[ 講演参考URL ]
http://agusta.ms.u-tokyo.ac.jp/seminerphotos2/Zworski-abstract.pdf

### 2008年02月23日(土)

#### 東京無限可積分系セミナー

13:00-16:30   数理科学研究科棟(駒場) 270号室

Solutions of hungry periodic discrete Toda equation and its ultradiscretization
[ 講演概要 ]
The hungry discrete Toda equation is a generalization of the discrete Toda
equation. Through the method of ultradiscretization, the generalized
Box-ball system (gBBS) with finitely many kinds of balls is obtained from
hungry discrete Toda eq.. It is to be expected that the general solution of
gBBS should be obtained from the solution of hungry discrete Toda eq.
through ultradiscretization. In this talk, we derive the solutions of hungry
periodic discrete Toda eq. (hpd Toda eq.), by using inverse scattering
method. Although the hpd Toda equation does not linearlized in the usual
sense on the Picard group of the spectral curve, it is possible to determine
its behavior on the Picard group.

A tropical analogue of Fay's trisecant identity and its application to the ultra-discrete periodic Toda equation.
[ 講演概要 ]
The ultra-discrete Toda equation is essentially equivalent to the integrable
Box and Ball system, and considered to be a fundamental object in
ultra-discrete integrable systems. In this talk, we construct the general
solution of ultra-discrete Toda equation with periodic boundary condition,
by using the tropical theta function and the bilinear form. The tropical
theta function is associated with the tropical curve defined through the Lax
matrix of (not ultra-) discrete periodic Toda equation. For the proof, we
introduce a tropical analogue of Fay's trisecant identity. (This talk is
based on the joint work with R. Inoue.)

### 2008年02月20日(水)

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 122号室

A Test for Cross-sectional Dependence of Microstructure Noises and their Cross-Covariance Estimator
[ 講演概要 ]

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/21.html

#### 講演会

13:30-17:45   数理科学研究科棟(駒場) 123号室

Divergence formulae on the space of continuous functions and Malliavin calculus

Ginibre random point field and a notion of convergence of Dirichlet forms
Lorenzo Zambotti 氏 (パリ第6大学) 15:30-16:30
Stochastic PDEs and infinite dimensional integration by parts formulae

ランダム環境下の確率モデルに関連する問題
(A problem arising in stochastic models in random environments)

### 2008年02月19日(火)

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 118号室
An overview on archimedean L-factors for G_1xG_2
[ 講演概要 ]
When G_1xG_2 is one of pairs GL(n)xGL(n), GL(n)xGL(n+1), GL(n)xSO(2n+1), and GL(n+1)xSO(2n+1), we have evaluation of the archimedian L-factors of automorphic L-functions obtained by Rankin-Selberg convolution.
The last two cases are joint works with Taku Ishii (Chiba Inst. of Tech) which are in progress.

### 2008年02月13日(水)

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 123号室

Realized multipower variationの統計推測への応用について
[ 講演概要 ]

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/20.html

### 2008年02月12日(火)

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 056号室
Katrin Wendland 氏 (University of Augrburg)
How to lift a construction by Hiroshi Inose to conformal field theory
[ 講演概要 ]
The moduli space of Einstein metrics is well known to algebraic and differential geometers. Physicists have introduced the notion of conformal field theories (CFTs) associated to K3, and the moduli space of these objects is well understood as well. It can be interpreted as a generalisation of the moduli space of Einstein metrics on K3, which allows us to introduce this space without having to use background knowledge from conformal field theory. However, just as no smooth Einstein metrics on K3 are known explicitly, the explicit construction of CFTs associated to K3 in general remains an open problem. The only known constructions which allow to deal with families of CFTs give CFTs associated to K3 surfaces with orbifold singularities.

We use a classical construction by Hiroshi Inose to explicitly construct a family of CFTs which are associated to a family of smooth algebraic K3 surfaces. Although these CFTs were known before, it is remarkable that they allow a description in terms of a family of smooth surfaces whose complex structure is deformed while all other geometric data remain fixed.

We also discuss possible extensions of this result to higher dimensional Calabi-Yau threefolds.

### 2008年02月07日(木)

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 002号室

Luc Illusie 氏 (パリ南大学)
On Gabber's refined uniformization theorem and applications
[ 講演概要 ]
Gabber has announced the following theorem : if X is a noetherian quasi-excellent scheme, Z a nowhere dense closed subset, and l a prime number invertible on X, then, locally for the topology on schemes of finite type over X generated, up to thickenings, by proper surjective maps which are generically finite of degree prime to l and by Nisnevich covers, the pair (X,Z) can be uniformized, i. e. replaced by a pair (Y,D), where Y is regular and D a strict normal crossings divisor. The whole proof is not yet written. I will give an overview. The plan is :
1. Statement and reduction to the complete local case (techniques of approximation)
2. Refined partial algebraization of complete local noetherian rings
3. Reduction to the equivariant log regular case (de Jong's techniques)
4. Making actions very tame, end of proof.
If time permits, I will show how the above theorem provides a short proof of Gabber's finiteness theorem for higher direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between quasi-excellent noetherian schemes.

### 2008年02月06日(水)

#### 統計数学セミナー

13:30-14:40   数理科学研究科棟(駒場) 056号室
Jean JACOD 氏 (Universite Paris 6)
Estimation of the integrated volatility in presence of microstructure noise
[ 講演概要 ]
The aim is to estimate the integrated volatility of a process observed discretely, in the setting of high frequency data, and when there is a microstructure noise. We use a kind of pre-averaging approach, which is rate-optimal when the noise is i.i.d., and may probably be even variance-optimal for a good choice of the kernel involved. However, the main innovative aspect is that it accommodates other types of noise, and in particular the case where the observations are rounded values of the underlying process plus an additive noise.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/17.html

#### 統計数学セミナー

14:50-16:00   数理科学研究科棟(駒場) 056号室
Jean JACOD 氏 (Universite Paris 6)
Estimating the Degree of Activity of jumps in High Frequency Data
[ 講演概要 ]
Suppose that a continuous-time process X = (X_t )_{t >= 0} is observed at finitely many times, regularly spaced, on the fixed time interval [0, T ]. We suppose that this process is an It\\^o semimartingale, with a non-vanishing diffusion coefficient, and with jumps. The aim is to estimate the so-called ”Blumenthal-Getoor” index of the (partially observed) path on [0, T ], which is the (random) infimum of all reals r such that the sum \\sum_{s\\le T} |\\Delta X_s|^r is finite (\\Delta X_s denotes the jump size at time s). When X is a L'evy process, this infimum is non-random, and also independent of T , and has been introduced by Blumenthal and Getoor. Under appropriate assumptions, unfortunately rather restrictive, we provide an estimator, which is consistent when the step size between observations goes to 0, and satisfies in addition a Central Limit Theorem. We also show the (surprising) values that this estimator takes, when applied to real financial data.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/18.html

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 056号室

A Hybrid Asymptotic Expansion Scheme: an Application to Long-term Currency Options
[ 講演概要 ]
In this session we develop a general approximation scheme, henceforth called a hybrid asymptotic expansion scheme for the valuation of multi-factor European path-independent derivatives. Specifically, we apply it to pricing long-term currency options under a market model of interest rates and a general diffusion stochastic volatility model with jumps of spot exchange rates.

Our scheme is very effective for a type of models in which there exist correlations among all the factors whose dynamics are not necessarily affine nor even Markovian so long as the randomness is generated by Brownian motions. It can also handle models that include jump components under an assumption of their independence of the other random variables when the characteristic functions for the jump parts can be analytically obtained.

Moreover, the hybrid scheme develops Fourier transform method with an asymptotic expansion to utilize closed-form characteristic functions obtainable in parts of a model.

Our scheme also introduces a characteristic-function-based Monte Carlo simulation method with the asymptotic expansion as a control variable in order to make full use of analytical approximations by the asymptotic expansion and of closed-form characteristic functions.

Finally, a series of numerical examples shows the validity of our scheme.

(This is a collaborative research with Professor Akihiko Takahashi(Graduate School of Economics, The University of Tokyo).)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/19.html

#### 数理ファイナンスセミナー

18:00-19:30   数理科学研究科棟(駒場) 128号室
Daniel Bloch 氏 ( )
Fast calibration of some Affine and Quadratic models with applications to derivatives on variance swaps

### 2008年01月31日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室

A generalization of property (T) of SL(n,R)

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 118号室

Luc Illusie 氏 (パリ南大学)
On Gabber's refined uniformization theorem and applications
[ 講演概要 ]
Gabber has announced the following theorem : if X is a noetherian quasi-excellent scheme, Z a nowhere dense closed subset, and l a prime number invertible on X, then, locally for the topology on schemes of finite type over X generated, up to thickenings, by proper surjective maps which are generically finite of degree prime to l and by Nisnevich covers, the pair (X,Z) can be uniformized, i. e. replaced by a pair (Y,D), where Y is regular and D a strict normal crossings divisor. The whole proof is not yet written. I will give an overview. The plan is :
1. Statement and reduction to the complete local case (techniques of approximation)
2. Refined partial algebraization of complete local noetherian rings
3. Reduction to the equivariant log regular case (de Jong's techniques)
4. Making actions very tame, end of proof.
If time permits, I will show how the above theorem provides a short proof of Gabber's finiteness theorem for higher direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between quasi-excellent noetherian schemes.

### 2008年01月30日(水)

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室
Luc Illusie 氏 (Universite Paris-Sud 11)
Odds and ends on finite group actions and traces
[ 講演概要 ]
Suppose a finite group G acts on a scheme X separated and of finite type over a field k. This raises several questions about the traces of elements s of G (or more generally products sg, for g in the Galois group of k) on cohomology groups of various types associated with X/k (with compact support or no support, Betti if k = C, l-adic, rigid). Some were considered and solved long ago, others only recently. I will in particular discuss an equivariant generalization of a theorem of Laumon on Euler-Poincar¥'e characteristics.

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Oleg Yu. Emanouilov 氏 (Colorado State University)
Carleman estimates for parabolic equations, a Stokes system and the Navier-Stokes equations and applications to the control problem
[ 講演概要 ]
We prove a new Carleman estimate for general linear second order parabolic equation with nonhomogeneous boundary conditions. On basis of this estimate we obtain an improved Carleman estimate for the Stokes system and a system of parabolic equations with a parameter which can be viewed as an approximation of the Stokes system. We will discuss the applications to the control problem for these systems.

### 2008年01月29日(火)

#### 代数幾何学セミナー

10:00-12:00   数理科学研究科棟(駒場) 128号室
Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homological methods in non-commutative geometry, part 11 (last lecture)
[ 講演参考URL ]
http://imperium.lenin.ru/~kaledin/math/tokyo/

#### トポロジー火曜セミナー

16:30-18:30   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 rotation number function on groups of circle diffeomorphisms
[ 講演概要 ]
ポアンカレは、円周の向きを保つ同相写像に対して、回転数の有理性と有限軌道の存在が

る種の群に対して一般化できることを説明する。特に、円周の向きを保つ実解析的微分同

あることを示す。

A Diagrammatic Construction of Third Homology Classes of Knot Quandles
[ 講演概要 ]
There exists a family of third (quandle / rack) homology classes,
called the shadow (fundamental / diagram) classes,
of the knot quandle, which are obtained from
the shadow colourings of knot diagrams.
We will show the construction of these homology classes,
and also show their relation to the shadow quandle cocycle
invariants of knots and that to other third homology classes.

### 2008年01月28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) 128号室

### 2008年01月25日(金)

#### 談話会・数理科学講演会

17:00-18:00   数理科学研究科棟(駒場) 123号室
お茶&Coffee&お菓子: 16:30～17:00 (コモンルーム)

Keller-Segel系に対する保存的上流有限要素法
[ 講演概要 ]

### 2008年01月24日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室
A compactness result in micromagnetics
[ 講演概要 ]
We study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem, depending on two parameters, for maps with values into the unit sphere. There is a physical prediction for the optimal configuration of the magnetization called the Landau state. Our goal is to prove compactness of the Landau state. This is a joint work with Felix Otto.

### 2008年01月23日(水)

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室
Weizhe Zheng 氏 (Universite Paris-Sud 11)
Integrality, Rationality, and Independence of l in l-adic Cohomology over Local Fields
[ 講演概要 ]
I will discuss two problems on traces in l-adic cohomology over local fields with finite residue field. In the first part, I will describe the behavior of integral complexes of l-adic sheaves under Grothendieck's six operations and the nearby cycle functor. In the second part, I will talk about rationality and independence of l. More precisely, I will introduce a notion of compatibility for systems of l-adic complexes and explain the proof of its stability by the above operations, in a slightly more general context (equivariant under finite groups). The main tool in this talk is a theorem of de Jong on
alterations.

#### 数理ファイナンスセミナー

17:30-19:00   数理科学研究科棟(駒場) 128号室

### 2008年01月22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
Serge Richard 氏 (Univ. Lyon 1)
Magnetic Schroedinger operators and twisted crossed product
[ 講演概要 ]
During this seminar, we shall study spectral properties of generalized
magnetic Schroedinger operators H(B,V) with anisotropic magnetic field B
and scalar potential V. The essential spectrum of such operators is
expressed as a union of spectra of some asymptotic operators supported by
the quasi-orbits of a suitable dynamical system. A localization property
of the functional calculus of H(B,V) will also be presented. It directly
implies a non-propagation result for the unitary group generated by this
operator. The proofs rely on the use of twisted crossed product
C*-algebras. Twisted dynamical systems and their corresponding algebras
will be introduced and the natural link with magnetic Schroedinger
operators will be clearly established.

#### 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

Connecion problems for Fuchsian differential equations free from accessory parameters
[ 講演概要 ]
The classification of Fuchsian equations without accessory parameters was formulated as Deligne-Simpson problem, which was solved by Katz and they are studied by Haraoka and Yokoyama.
If the number of singular points of such equations is three, they have no geometric moduli.
We give a unified connection formula for such differential equations as a conjecture and show that it is true for the equations whose local monodromy at a singular point has distinct eigenvalues.
Other Fuchsian differential equations with accessory parameters and hypergeometric functions with multi-variables are also discussed.
[ 講演参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html