## Seminar information archive

### 2008/09/08

#### Lie Groups and Representation Theory

11:00-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Federico Incitti (ローマ第 1 大学)
Dyck partitions, quasi-minuscule quotients and Kazhdan-Lusztig polynomials
[ Abstract ]
Kazhdan-Lusztig polynomials were first defined by Kazhdan and Lusztig in [Invent. Math., 53 (1979), 165-184]. Since then, numerous applications have been found, especially to representation theory and to the geometry of Schubert varieties. In 1987 Deodhar introduced parabolic analogues of these polynomials. These are related to their ordinary counterparts in several ways, and also play a direct role in other areas, including geometry of partial flag manifolds and the theory of Macdonald polynomials.

In this talk I study the parabolic Kazhdan-Lusztig polynomials of the quasi-minuscule quotients of the symmetric group. More precisely, I will first show how these quotients are closely related to rooted partitions'' and then I will give explicit, closed combinatorial formulas for the polynomials. These are based on a special class of rooted partitions the rooted-Dyck'' partitions, and imply that they are always (either zero or) a power of $q$.

I will conclude with some enumerative results on Dyck and rooted-Dyck partitions, showing a connection with random walks on regular trees.

This is partly based on a joint work with Francesco Brenti and Mario Marietti.
[ Reference URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2008/09/03

#### Lectures

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Fred Weissler (University of Paris 13)
Finite time blowup of oscillating solutions to the nonlinear heat equation
[ Abstract ]
(This is joint work with T. Cazenave and F. Dickstein.)

We study finite time blowup properties of solutions of the nonlinear heat equation, both on $R^N$, and on a ball in $R^N$ with Dirichlet boundary conditions. We show, among other results, that the set of initial values producing global solutions is not always star-shaped around the 0 solution. This contrasts with the case where only non-negative solutions are considered.

### 2008/08/27

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Don Zagier (Max Planck研究所)
$q$-series and modularity

### 2008/08/25

#### Lectures

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Ronald C. King (Emeritus Professor, University of Southampton)
Affine Weyl groups, grids, coloured tableaux and characters of affine algebras
[ Abstract ]
It is shown that certain coloured Young diagrams serve to specify not
only all the elements of the affine Weyl groups of the classical
affine Lie algebras but also their action on an arbitrary weight
vector. Through a judicious choice of coset representatives with
respect to the finite Weyl groups of the corresponding maximal rank
simple Lie algebras, both denominator and numerator formulae are
derived and exemplified, along with the explicit calculation of
characters of irreducible representations of the affine Lie algebras.

### 2008/08/21

#### thesis presentations

15:00-15:40   Room #126 (Graduate School of Math. Sci. Bldg.)

On some asymptotic properties of the Expectation-Maximization Algorithm and the Metropolis-Hastings Algorithm (EMアルゴリズムとメトロポリス-ヘイスティングスアルゴリズムの漸近的性質)

### 2008/08/06

#### Seminar on Mathematics for various disciplines

10:30-14:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Kazufumi Ito (North Carolina State University) 10:30-11:30
Adaptive Tikhonov Regularization for Inverse Problems
[ Abstract ]
Tikhonov regularization method plays a critical role in ill-posed inverse problems, arising in applications including computerized tomography, inverse scattering and image processing. The goodness of the inverse solution heavily depends on selection of the regularization parameter. Commonly used methods rely on a priori knowledge of the noise level. A method that automatically estimates the noise level and selects the regularization parameter automatically is presented.
Yimin Wei (Fudan University) 13:00-14:00
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems
[ Abstract ]
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this talk, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for the computation of the Moore-Penrose inverse as well as for the computation of solutions and residues of linear least squares problems. In both cases the data matrices have full column (row) rank.

#### Mathematical Finance

17:30-19:00   Room #122 (Graduate School of Math. Sci. Bldg.)

オペレーショナルリスクと fat tail を持つ iid 確率変数の和に対する極限定理

### 2008/08/01

#### Number Theory Seminar

13:00-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Olivier Brinon (Paris北大学) 13:00-14:00
B_dR-representations and Higgs bundles
Henrik Russell (Duisburg-Essen大学) 14:15-15:15
Generalized Albanese and duality
Thomas Geisser (南California大学) 15:45-16:45
Negative K-theory, homotopy invariance and regularity
[ Abstract ]
The topic of my talk are two classical conjectures in K-theory:
Weibel's conjecture states that a scheme of dimension d
has no K-groups below degree -d, and Vorst's conjecture
states that homotopy invariance of the K-theory of rings
implies that the ring must be regular.
I will give an easy introduction to the conjectures, and discuss
recent progress.
Fabien Trihan (Nottingham大学) 17:00-18:00
On Iwasawa theory for abelian varieties over function fields of positive characteristic

### 2008/07/29

#### Lie Groups and Representation Theory

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

Clifford代数の表現から作られる局所関数等式を満たす多項式とそれに付随する空間について(佐藤文広氏との共同研究)
[ Abstract ]

この講演では、概均質ベクトル空間の相対不変式ではないにもかかわらず、その複素ベキが同種の局所関数等式を満たすような多項式が、Clifford代数の表現より構成できることを報告する。

### 2008/07/28

#### Kavli IPMU Komaba Seminar

17:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Lin Weng (Kyushu University)
Symmetries and the Riemann Hypothesis
[ Abstract ]
Associated to each pair of a reductive group
and its maximal parabolic, we will introduce an abelian zeta function.
This zeta, defined using Weyl symmetries, is expected
to satisfy a standard functional equation and the Riemann Hypothesis.
Its relation with the so-called high rank zeta,
a very different but closely related non-abelian zeta,
defined using stable lattices and a new geo-arithmetical cohomology,
will be explained.
Examples for $SL, SO, Sp$ and $G_2$ and confirmations of
(Lagarias and) Masatoshi Suzuki on the RH for zetas
associated to rank 1 and 2 groups will be presented
as well.
[ Reference URL ]
http://xxx.lanl.gov/abs/0803.1269

### 2008/07/26

#### Infinite Analysis Seminar Tokyo

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

[ Abstract ]
A型変形W代数の自由場表示を用いてA型Macdomald多項式のtableau表示を構成する。さらにD型変形W代数の自由場表示を用いて、第一基本ウェイトの正数倍のウェイトを持つD型Macdomald多項式のtableau表示を構成する。尚、本研究は白石潤一氏(東京大学)との共同研究である。

Entanglement Entropy in Conventional and Topological Orders
[ Abstract ]

(1)量子ダイマー模型におけるトポロジカル・エントロピー
トポロジカル秩序を持つ系においては、エンタングルメント・エントロピーに、背景のゲージ理論を特徴づける、負の定数項が含まれることが、Kitaevらによって予想された。我々は、Z2トポロジカル秩序を示すと考えられる量子ダイマー模型において、予想の数値的検証を行い、予想が精度よく成り立つことを示した。
Ref. S. Furukawa & G. Misguich, Phys. Rev. B 75, 214407 (2007).
(2)自発的対称性の破れとマクロスコピック・エンタングルメント

### 2008/07/24

#### Lectures

16:00-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Noriko Yui (Queen's University)
On the modularity of Calabi-Yau varieties over $\\mathbf{Q}$

### 2008/07/23

#### Seminar on Mathematics for various disciplines

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Andrei Constantinescu (Ecole Polytechnique)
Identification of residual stresses: problem settings and results.
[ Abstract ]
Identiﬁcation of residual stresses is an important task in many engineering ﬁelds such as fatigue or fracture mechanics, where their presence can signiﬁcantly increase or decrease the apparent strength of mechanical components.

The present talk will try to make a review of existing problem settings identification results.
More precisely we shall:

1. discuss the linearization procedure strain and materials behaviour in finite elasticity around a stressed state in order to define in a mathematical precise way the problem settings for the identification of residual stresses.

2. present a series of measurement techniques currently used in industry and research for the measurement of residual stresses like the X-ray technique and strain measurements.

3. present existing results in the identification of residual stresses for the different

#### Seminar on Mathematics for various disciplines

10:30-14:00   Room #056 (Graduate School of Math. Sci. Bldg.)

Adaptive Tikhonov Regularization for Inverse Problems
[ Abstract ]
Tikhonov regularization method plays a critical role in ill-posed inverse problems, arising in applications including computerized tomography, inverse scattering and image processing. The goodness of the inverse solution heavily depends on selection of the regularization parameter. Commonly used methods rely on a priori knowledge of the noise level. A method that automatically estimates the noise level and selects the regularization parameter automatically is presented.
Yimin Wei (Fudan University) 13:00-14:00
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems
[ Abstract ]
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this talk, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for the computation of the Moore-Penrose inverse as well as for the computation of solutions and residues of linear least squares problems. In both cases the data matrices have full column (row) rank.

### 2008/07/17

#### Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
George Elliott (Univ. Toronto)
A canonical AF-algebra construction for rank two subgroups of R
(A new description of the Pimsner-Voiculescu embedding)

### 2008/07/16

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Valentina Di Proietto (Padova大学)
On p-adic differential equation on semi-stable varieties

### 2008/07/15

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

One-step Markov Theorem on exchange classes
[ Abstract ]
The main theorem in this talk claims the following.
Let L_A and L_B denote a closed a-braid and a closed b-braid,
respectively, that represent one link type.
After at most (a^2 b^2)/4 exchange moves on L_A,
we can 'see' the pair of closed braids."
In this talk, we explain the main theorem in details, and
we present some applications.
In particular, we propose a strategy to construct an algorithm
that determines whether two links are ambient isotopic.

#### Lie Groups and Representation Theory

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

GL(4,R)の退化主系列表現の一般Whittaker関数
[ Abstract ]
$GL(n,R)$の退化球主系列表現の一般Whittaker模型の空間は,対称空間$GL(n,R)/O(n)$上の$C^\\infty$級関数の中で,ある微分作用素達のkernelとして特徴付けられる.この微分作用素達は,大島利雄氏による退化主系列表現に対するPoisson変換の像の特徴付けに用いられたものであり,その明示的な表示が氏によって得られている.また,こうしたkernel定理は山下博氏のユニタリ最低ウエイト加群の一般Whittaker模型に対する定理の類似にあたる.こういった背景の下,$GL(4,R)$の退化主系列表現に対し、いくつかの具体例を考えたい.そこでは一般Whittaker模型は一変数変形Bessel関数、Hornの二変数合流型超幾何関数によって実現される.
[ Reference URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2008/07/12

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)

) 13:30-14:30
On certain types and the Hecke algebras for unramified p-adic unitary groups

The $(\\mathfrak{g},K)$-module structures of the principal series resentations for $SL(4,R)$

[ Abstract ]
$SL(4,R)$ の主系列表現 $H$ の $(\\mathfrak{g},K)$-module としての構造を

### 2008/07/10

#### Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

The Structure of a Hyponormal Operator (a joint work with Kotaro
Tanahashi)

#### Applied Analysis

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

Two positive solutions for an inhomogeneous scalar field equation
[ Abstract ]
We consider the following nonlinear elliptic equation:
$$-\\Delta u+u=g(u)+f(x), x \\in R^N,$$
where $N\\ge 3$. When $f(x)\\equiv 0$, it is known that there is a nontrivial solution for a wide class of nonlinearities. Even though $f(x) \\not\\equiv 0$, we can expect the existence of a nontrivial solution if $f(x)$ is small in a suitable sense. Our purpose is to show the existence of two positive solutions via the variational approach when $\\| f\\|_{L^2}$ is small. The first solution is characterized as a local minimizer. The second solution will be obtained by the Mountain Pass Method. Since we do not impose any global condition on the nonlinearity, we will need a presice interaction estimate.

#### Seminar on Probability and Statistics

16:20-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)

Bayesian learning of biological pathways on genomic data assimilation
[ Abstract ]
States of living cells are controlled by networks of biochemical reactions, referred to as biological pathways, which comprise of, for instance, phosphorylation and binding of protein molecules, gene expressions mediated by transcription factor activities. In systems biology, mathematical modeling and simulation, based on biochemical rate equations, have proved to be a popular approach for unraveling complex machinery of cellular mechanisms. To proceed to simulations, however, it is vital to find the effective values of kinetic rate constants that are difficult to measure directly from in vivo and in vitro experiments. Furthermore, once a set of hypothetical models is given, a proper statistical criterion is needed to test the reliability of the constructed models in terms of predictability and biological robustness. The aim of this research is to present a new statistical technology, called Genomic Data Assimilation, for handling data-driven model construction of biological pathways. The method starts with a knowledge-based pathway modeling with hybrid functional Petri net. It then proceeds to the Bayesian learning of model parameters for which experimental data are available. This process uses time course measurements of biochemical reactants, e.g. gene expression profiles. Another important issue that we consider is statistical evaluation and comparison of the constructed hypothetical models. For this purpose, we developed a new Bayesian information-theoretic measure that assesses the predictability and the biological robustness of models. In this talk, I will detail mathematical aspects of the proposed method, and then, show some statistical issues to be addressed.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/06.html

### 2008/07/08

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Otto van Koert (北海道大学大学院理学研究科, JSPS)
Contact homology of left-handed stabilizations and connected sums
[ Abstract ]
In this talk, we will give a brief introduction to contact homology, an invariant of contact manifolds defined by counting holomorphic curves in the symplectization of a contact manifold. We shall show that certain left-handed stabilizations of contact open books have vanishing contact homology.
This is done by finding restrictions on the behavior of holomorphic curves in connected sums. An additional application of this behavior of holomorphic curves is a long exact sequence for linearized contact homology.

#### Lie Groups and Representation Theory

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

construction of extended affine Lie algebras from multiloop Lie algebras
[ Abstract ]
affine Lie algebra の Kac-Moody Lie algebra とは異なる一般化として、extended affine Lie algebra と呼ばれる Lie algebra の class を考える。
ほとんどの extended affine Lie algebra は、有限次元 simple Lie algebra と、有限個の互いに可換な有限位数自己同型を用いて構成できることがすでに知られている。
この講演では、上の構成によって得られる extended affine Lie algebra がどのような場合に(適当な意味で)同型となるか、という問題に関する結果をお話ししたい。
[ Reference URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2008/07/07

#### Seminar on Geometric Complex Analysis

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

Henon 写像の複素力学系