Seminar information archive

Seminar information archive ~08/17Today's seminar 08/18 | Future seminars 08/19~


Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
金 英子 (東京工業大学情報理工学研究科)
Two invariants of pseudo--Anosov mapping classes: hyperbolic volume vs dilatation
(joint work with Mitsuhiko Takasawa)
[ Abstract ]
We concern two invariants of pseudo-Anosov mapping classes.
One is the dilatation of pseudo--Anosov maps and the other is the volume
of mapping tori. To study how two invariants are related, fixing a surface
we represent a mapping class by using the standard generator set and compute
these two for all pseudo--Anosov mapping classes with up to some word length.
In the talk, we observe two properties:

(1) The ratio of the topological entropy (i.e. logarithm of the dilatation) to
the volume is bounded from below by some positive constant which only
depends on the surface.

(2) The conjugacy class having the minimal dilatation reaches the minimal volume.

On the observation (1), in case of the mapping class group of a once--punctured
torus, we give a concrete lower bound of the ratio.


Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
飯田修一 (東大数理)
On the Meyer function for theta divisors


Lie Groups and Representation Theory

15:30-17:45   Room #122 (Graduate School of Math. Sci. Bldg.)
Salem Ben Said (Nancy大)
On the theory of Bessel functions associated with root systems
[ Abstract ]
The theory of spherical functions on Riemannian symmetric spaces G/K and on non-compactly causal symmetric spaces G/H has a long and rich history. In this talk we will show how one can use a limit transition approach to obtain generalized Bessel functions on flat symmetric spaces via the spherical functions. A similar approach can be applied to the theory of Heckman-Opdam hypergeometric functions to investigate generalized Bessel functions related to arbitrary root system. We conclude the talk by giving a conjecture about the nature and order of the singularities of the Bessel functions related to non-compactly causal symmetric spaces.
[ Reference URL ]


Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
谷本溶 (東大数理)
A new construction of causal nets of operator algebras


Seminar on Probability and Statistics

16:20-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)
小方 浩明 (早稲田大学, 国際教養学部)
Empirical likelihood method for time series analysis
[ Abstract ]
For a class of vector-valued non-Gaussian stationary processes with unkown parameters, we develop the empirical likelihood approach which was proposed in the i.i.d. setting. In the time series analysis it is known that Whittle likelihood is one of fundamental tools to get a good estimator of unknown parameters and that the score functions are asymptotically normal. Motivated by the Whittle likelihood, we take its score as an estimating function and obtain the asymptotic distribution of our test statistic. Since the fitted spectral model may be different from true spectral structure, the results enable us to construct confidence rigions for various important time series parameters without knowing true spectral structure. We also consider the approach to a minimum contrast estimation and Cressie-Read power-divergence statistic. Numerical studies are introduced and illuminate some interesting features of the empirical approach.
[ Reference URL ]

Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Stephen Lichtenbaum (Brown University)
The conjecture of Birch and Swinnerton-Dyer is misleading
[ Abstract ]
All values of zeta and L-functions at integral points should be given in terms of products and quotients of Euler characteristics, and the order of the zeroes and poles at these
points should be given by the sum and difference of the ranks of
corresponding finitely generated abelian groups.

Mathematical Finance

17:30-19:00   Room #128 (Graduate School of Math. Sci. Bldg.)
山本 匡 (東京大)
Selection and Performance Analysis of Asia-Pacific Hedge Funds


Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
小櫃邦夫 (鹿児島大学)
Weil-Petersson 計量とTakhtajan-Zograf 計量の漸近挙動


Algebraic Geometry Seminar

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Qi Zhang (Missouri大学)
Projective varieties with nef anti-canonical divisors
[ Abstract ]
Projective varieties with nef anti-canonical divisors appear naturally in the minimal model program and the theory of classification of higher-dimensional algebraic varieties. In this talk we describe a comprehensive approach to birational geometry of log canonical pair (X, D) with nef anti-canonical class -(K_X+D). In particular, We present two theorems on the birational structure of the varieties. We will also discuss some recent results and new aspects of the subject.


Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Richard D. Burstein (UC Berkeley)
Subfactors Arising from Symmetric Commuting Squares (following Jones/Sunder)


Geometry Seminar

14:40-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
中田文憲 (東京大学大学院数理科学研究科) 14:40-16:10
LeBrun-Mason 対応とその簡約について
[ Abstract ]
LeBrun と Mason は近年,正則円板の族に関するツイスター型の対応を発見した.彼らは次元の異なる二つのタイプの対応を示しているが,どちらも Penrose や Hitchin による解析的・局所的な理論の,非解析的・大域的な version とみなすことができる.一方 Penrose らの枠組みにおいては,次元の異なるツイスター型対応を関連づける次元簡約という現象が生じることが,Dunajski などによって最近研究されている.この講演では,LeBrun らの大域的な状況で簡約理論を展開しようとするときに生じる問題点を示し,ある種の特異性を導入することでこれを解決できることを説明したい.論文:math.DG/0701116
後藤竜司 (大阪大学大学院理学研究科) 16:30-18:00
Deformations of generalized Kahler and Calabi-Yau structures
[ Abstract ]
一般化された複素構造,ケーラー 構造は Hitchin,Gualtieri により,導入された複素構造とシンプレクティック構造と統一する幾何構造である.講演では,最近得られた一般化されたケーラー構造の安定性定理を解説する.これは,Kodaira-Spencer によるケーラー構造の複素構造の(small) 変形のもとでの安定性の拡張であり,証明には Calabi-Yau の変形の非障害性定理でのテクニックを用いる.応用として,射影空間や Fano 曲面上に一般化されたケーラー構造が豊富に存在することを示す.また,ケーラー多様体上の正則ポアソン構造から一般化されたケーラー構造が構成されることを見る.


15:00-16:00   Room #470 (Graduate School of Math. Sci. Bldg.)
Y.S. Chow (台湾中央研究院数学研究所)
On evolution games with local interaction and mutation


Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
堤 誉志雄 (京都大学理学研究科)
Unconditional uniqueness of solution for the Cauchy problem of the nonlinear Schr\\"odinger equation

Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
原岡喜重氏 (熊本大学)
Rigid local systemとその切断の積分表示,および接続係数
[ Abstract ]
A local system on $CP^1-\\{finite points\\}$ is called physically rigid if it is uniquely determined up to isomorphisms by the local monodromies. We explain two algorithms to construct every physically rigid local systems. By applying the algorithms we obtain integral representations of solutions of the corresponding Fuchsian differential equation. Moreover we can express connection coefficients of the equation in terms of the integrals. These results will be applied to several differential equations arising from the representation theory.


Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
清水 悟 (東北大学)
An intrinsic characterization of the unit polydisc


Infinite Analysis Seminar Tokyo

13:30-16:00   Room #117 (Graduate School of Math. Sci. Bldg.)
土岡俊介 (京都大学数理解析研究所) 13:30-14:30
Lie theoretic structures for the generalized symmetric groups
[ Abstract ]
近年、Ariki, Brundan, Grojnowski, Kleshchev, Vazirani等によって、
modular表現論とKac-Moody Lie環/量子群といったLie theoreticな対象との関係が研究

(1) 標数p>0において、対称群\\mathfrak{S}_nの(有限次元)表現のGrothendieck群の
(nを走らせた)直和には、Kac-Moody Lie環g(A^{1}_{p-1})のレベル1基本既約最高

(2) 対称群の既約表現の同型類の直和には、量子群U_q(g(A^{1}_{p-1}))の


研究において、(A^{(1)}_{p-1})^{\\otimes r}(ここでrはpとmから決まる自然数)

なお、G(m,1,n)の群環のq-変形と考えられているcyclotomic Hecke algebraにおいて、
渡辺文彦 (北見工業大学) 15:00-16:00
Wirtinger 積分の構造について
[ Abstract ]
Wirtinger はガウスの超幾何函数 $_2F_1$ を一意化する目的でこれを
テータ函数の冪積の積分で表わす表示を1902年に得た.Wirtinger の発見以降,
この積分を講演者は前述に因んで Wirtinger 積分と呼んでいる.
公式のみを用いて Wirtinger 積分のみたすさまざまな関係式を導出することが
理由は,超幾何函数の新しい一般化の可能性が Wirtinger 積分に見えているという
本講演では Wirtinger 積分と超幾何函数との関係および一般化の可能性について,
小生は世間の情報にうといので,講演中などにWirtinger 積分の関連で



16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
井原茂男 (東京大学先端科学技術研究センター, システム生物医学ラボラトリー(LSBM), ダイナミカルバイオインフォーマティクス)
[ Abstract ]


PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Walter Strauss (Brown University)
Steady Water Waves with Vorticity
[ Abstract ]
Consider a classical 2D water wave under the influence of gravity with an arbitrary vorticity function. Assume such a wave is traveling at a constant speed over a flat bed. Then there exist many families of such waves of large amplitude. The proof is based on elliptic PDEs, bifurcation and degree theory. I will also exhibit some recent numerical computations. If the vorticity is sufficiently large, the first stagnation point occurs not at the crest (as with irrotational flows) but on the bed directly below the crest. For variable vorticity the first stagnation point can occur in the interior of the fluid.
[ Reference URL ]

Mathematical Biology Seminar

14:40-15:40   Room #123 (Graduate School of Math. Sci. Bldg.)
Alex Cook (Actuarial Mathematics and Statistics,
School of Mathematical and Computer Sciences,
Heriot-Watt University)
Return of the Giant Hogweed: modelling the invasion of Britain by a dangerous alien plant
[ Abstract ]
As a result of changing climate and land use, as well as due to human intervention, increasingly species are moving to new abitats. We wish to understand the risk of invasive species entering new areas, and as an example consider the spread of Giant Hogweed (Heracleum mantegazzianum) from SW Asia in Great Britain, a species that has been damaging Britain's biodiversity since it was introduced in the 19th C and which is dangerous to human health. We construct a spatio-temporal stochastic model for its spread (both local and at distance) that takes account of covariates such as the heterogeneous land-cover and climate of the island. We then fit the model directly to observed data. Fitting the model was non-trivial and involved the use of Markov chain Monte Carlo techniques. The approach taken allows spatio-temporal predictions of the future spread of the weed can be made, consistent with the invasion history; it also allows the effect of varying habitats and climate to be understood. The approach we have taken can be generalised to other biological systems exhibiting stochastic variability, and there are clear parallels to epidemic models for the spread of disease within heterogeneous host populations.
[ Reference URL ]


Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Tian-Jun Li (University of Minnesota)
The Kodaira dimension of symplectic 4-manifolds
[ Abstract ]
Various results and questions about symplectic4-manifolds can be
formulated in terms of the notion of the Kodaira dimension. In particular,
we will discuss the classification and the geography problems. It is interesting
to understand how it behaves undersome basic constructions.Time permitting
we will discuss the symplectic birational aspect of this notion and speculate
how to extend it to higher dimensional manifolds.


Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
山下真 (東大数理)
Affine holonomy foliations


Seminar on Probability and Statistics

16:20-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)
小池 健一 (筑波大学大学院数理物質科学研究科)
[ Abstract ]
有界な台をもつ非正則な位置尺度母数分布族に対して,その位置母数の逐次点推定を考える.ここでは,平均二乗誤差に費用も加えてリスクを考える.レンジに基づく停止則を提案し,これが漸近有効であることを示す.また,良く知られているRobbinsの逐次推定方式との比較を行い,密度関数の台の端点で密度関数が急激に変化する場合には,提案する逐次推定方式が標本数やリスクの意味で優れていることを示す.この結果は,逐次区間推定に関するKoike (2007)のものと同様であることが分かる
[ Reference URL ]


Tuesday Seminar on Topology

17:00-18:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Emmanuel Giroux (ENS Lyon)
Symplectic mapping classes and fillings
[ Abstract ]
We will describe a joint work in progress with Paul Biran in
which contact geometry is combined with properties of Lagrangian manifolds
in subcritical Stein domains to obtain nontrivaility results for symplectic
mapping classes.


Seminar on Geometric Complex Analysis

10:45-12:15   Room #128 (Graduate School of Math. Sci. Bldg.)
坂井秀隆 (東京大学)


Mathematical Finance

17:30-19:00   Room #128 (Graduate School of Math. Sci. Bldg.)
楠岡 成雄 (東京大)
分布が Fat tail を持つ i.i.d. 確率変数の和に関して

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