## 過去の記録

### 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.
[ 参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

#### 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 10
[ 参考URL ]
http://imperium.lenin.ru/~kaledin/math/tokyo/

#### 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21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

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 126号室
Torbjorn Lundh 氏 (Chalmers & Göteborg University)
Potential theory of funnels and wounds
[ 講演概要 ]
We will talk about a result concerning Green functions, namely the so called 3G-inequality, which I studied together with H. Aikawa. The focus of the talk will be on the description of the way to that result, where we among other tools used numerical methods to get a better intuitive understanding the situation. We will also discuss a possible potential theoretic view-point of an ancient wound healing question.

### 2008年01月17日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

Cup product on the Periodic Cyclic Cohomology

#### Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 123号室

Proper actions of SL(2,R) on irreducible complex symmetric spaces
[ 講演概要 ]
We determine the irreducible complex symmetric spaces on which SL(2,R) acts properly. We use the T. Kobayashi's criterion for the proper actions. Also we use the symmetry or unsymmetry of the weighted Dynkin diagram of the theory of nilpotent orbits.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### 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16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

Implementation of a jump-detection method and applications to real markets
[ 講演概要 ]

[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/15.html

#### 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
Antoine Chambert-Loir 氏 (Universite de Rennes 1)
Equidistribution theorems in Arakelov geometry
[ 講演概要 ]
The proof of Bogomolov's conjecture by Zhang made a crucial use
of an equidistribution property for the Galois orbits of points of small
heights in Abelian varieties defined over number fields.
Such an equidistribution property is proved using a method invented
by Szpiro, Ullmo and Zhang, and makes use of Arakelov theory.
This equidistribution theorem takes place in the complex torus
associated to the Abelian variety. I will show how a similar
equidistribution theorem can be proven for the p-adic topology ;
we have to use Berkovich space. Thanks to recent results of Yuan
about `big line bundles' in Arakelov geometry, the situation
is now very well understood.

#### 統計数学セミナー

14:50-16:00   数理科学研究科棟(駒場) 122号室
Marc HOFFMANN 氏 (Universite Paris-est Marne la vallee)
Statistical analysis of fragmentation chains
[ 講演概要 ]
We address statistical inference in self-similar conservative fragmentation chains, when only observations on the size of the fragments below a given threshold are available. (Possibly, the measurement of the fragments themselves are subject to further systematic experimental noise.) This framework, introduced by Bertoin and Martinez is motivated by mineral crushing in mining industry. We compute upper and lower rates of estimation for several functionals of the dislocation measure, both in a semi-parametric and a non-parametric framework. The underlying estimated object is the step distribution of the random walk associated to a randomly tagged fragment that evolves along the genealogical tree representation of the fragmentation process. We establish a formal link with the statistical problem of estimating the overshoot of the distribution as the crossing level goes to infinity with the size of the dataset; in particular the difficulty of the estimation problem in the non-parametric case is comparable to ill-posed linear inverse problems of order 1 in signal denoising.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/15.html

### 2008年01月15日(火)

#### トポロジー火曜セミナー

16:30-17:30   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

Adiabatic limits of eta-invariants and the Meyer functions
[ 講演概要 ]
The Meyer function is the function defined on the hyperelliptic
mapping class group, which gives a signature formula for surface
bundles over surfaces.
In this talk, we introduce certain generalizations of the Meyer
function by using eta-invariants and we discuss the uniqueness of this
function and compute the values for Dehn twists.

#### 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
Fulton Gonzalez 氏 (Tufts University)
Group contractions, invariant differential operators and the matrix Radon transform

[ 講演概要 ]
Let $M_{n,k}$ denote the vector space of real $n\\times k$ matrices.
The matrix motion group is the semidirect product $(\\text O(n)\\times \\text O(k))\\ltimes M_{n,k}$, and is the Cartan motion group
associated with the real Grassmannian $G_{n,n+k}$.
The matrix Radon transform is an
integral transform associated with a double fibration involving
homogeneous spaces of this group. We provide a set of
algebraically independent generators of the subalgebra of its
universal enveloping algebra invariant under the Adjoint
representation. One of the elements of this set characterizes the range of the matrix Radon transform.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### 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 9
[ 参考URL ]
http://imperium.lenin.ru/~kaledin/math/tokyo/

### 2008年01月09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

Parameter estimated standardized U-statistics with degenerate kernel for weakly dependent random variables
[ 講演概要 ]
In this paper, extending the results of Gombay and Horv'{a}th (1998), we prove limit theorems for the maximum of standardized degenerate U-statistics defined by some absolutely regular sequences or functionals of them.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/14.html

### 2008年01月08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
Nikolay Tzvetkov 氏 (Lille大学)
On the restrictions of Laplace-Beltrami eigenfunctions to curves

#### 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 8

### 2008年01月07日(月)

#### 諸分野のための数学研究会

13:30-14:30   数理科学研究科棟(駒場) 056号室

An Optimal Feedback Solution to Quantum Control Problems.
[ 講演概要 ]
Control of quantum systems described by Schrodinger equation is considered. Feedback control laws are developed for the orbit tracking via a controled Hamiltonian. Asymptotic tracking properties of the feedback laws are analyzed. Numerical integrations via time-splitting are also analyzed and used to demonstrate the feasibility of the proposed feedback laws.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2008年01月06日(日)

#### 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

[ 講演概要 ]

### 2007年12月26日(水)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Pinhas Grossman 氏 (Vanderbilt University)
Pairs of intermediate subfactors

### 2007年12月25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
Gregory Eskin 氏 (UCLA)
Inverse boundary value problems for the Schrodinger equation with time-dependent electromagnetic potentials and the Aharonov-Bohm effect
[ 講演概要 ]
We consider the determination of the time-dependent magnetic and electric potentials (modulo gauge transforamtions) by the boundary measurements in domains with obstacles. We use the geometric optics and the tomography of broken rays. The presence of the obstacles leads to the Aharonov-Bohm effect caused by the magnetic and electric fluxes.

### 2007年12月22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) 117号室

Double Schubert polynomials for the classical Lie groups
[ 講演概要 ]
For each infinite series of the classical Lie groups of type $B$,
$C$ or $D$, we introduce a family of polynomials parametrized by the
elements of the corresponding Weyl group of infinite rank. These
polynomials
represent the Schubert classes in the equivariant cohomology of the
corresponding
flag variety. When indexed by maximal Grassmannian elements of the Weyl
group,
these polynomials are equal to the factorial analogues of Schur $Q$- or
$P$-functions defined earlier by Ivanov. This talk is based on joint work
with L. Mihalcea and H. Naruse.

Nichols-Woronowicz model of the K-ring of flag vaieties G/B
[ 講演概要 ]
We give a model of the equivariant $K$-ring $K_T(G/B)$ for
generalized flag varieties $G/B$ in the braided Hopf algebra
called Nichols-Woronowicz algebra. Our model is based on
the Chevalley-type formula for $K_T(G/B)$ due to Lenart
and Postnikov, which is described in terms of alcove paths.
We also discuss a conjecture on the model of the quantum
$K$-ring $QK(G/B)$.

### 2007年12月21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)
D. Eisenbud 氏 (Univ. of California, Berkeley)
Plato's Cave: what we still don't know about generic projections
[ 講演概要 ]
Riemann Surfaces were first studied algebraically by first projecting them into the complex projective plan; later the same idea was applied to surfaces and higher dimensional varieties, projecting them to hypersurfaces. How much damage is done in this process? For example, what can the fibers of a generic linear projection look like? This is pretty easy for smooth curves and surfaces (though there are still open questions), not so easy in the higher-dimensional case. I'll explain some of what's known, including recent work of mine with Roya Beheshti, Joe Harris, and Craig Huneke.

### 2007年12月20日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

Gauge-invariant ideal structure of ultragraph $C^*$-algebras