過去の記録 ~05/25本日 05/26 | 今後の予定 05/27~


13:00-14:10   数理科学研究科棟(駒場) 052号室
Selma Chaker 氏 (Bank of Canada)
On High Frequency Estimation of the Frictionless Price: The Use of Observed Liquidity Variables (ENGLISH)
[ 講演概要 ]
Observed high-frequency prices are always contaminated with liquidity costs or market microstructure noise. Inspired by the market microstructure literature, I explicitly model this noise and remove it from observed prices to obtain an estimate of the frictionless price. I then formally test whether the prices adjusted for the estimated liquidity costs are either totally or partially free from noise. If the liquidity costs are only partially removed, the residual noise is smaller and closer to an exogenous white noise than the original noise is. To illustrate my approach, I use the adjusted prices to improve volatility estimation in the presence of noise. If the noise is totally absorbed, I show that the sum of squared returns - which would be inconsistent for return variance when based on observed returns - becomes consistent when based on adjusted returns.
[ 講演参考URL ]


16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
足助 太郎 氏 (東京大学大学院数理科学研究科)
Transverse projective structures of foliations and deformations of the Godbillon-Vey class (JAPANESE)
[ 講演概要 ]
Given a smooth family of foliations, we can define the derivative of the Godbillon-Vey class
with respect to the family. The derivative is known to be represented in terms of the projective
Schwarzians of holonomy maps. In this talk, we will study transverse projective structures
and connections, and show that the derivative is in fact determined by the projective structure
and the family.


16:30-18:00   数理科学研究科棟(駒場) 126号室
Ivan Cherednik 氏 (The University of North Carolina at Chapel Hill, RIMS
Global q,t-hypergeometric and q-Whittaker functions (ENGLISH)
[ 講演概要 ]
The lectures will be devoted to the new theory of global
difference hypergeometric and Whittaker functions, one of
the major applications of the double affine Hecke algebras
and a breakthrough in the classical harmonic analysis. They
integrate the Ruijsenaars-Macdonald difference QMBP and
"Q-Toda" (any root systems), and are analytic everywhere
("global") with superb asymptotic behavior.

The definition of the global functions was suggested about
14 years ago; it is conceptually different from the definition
Heine gave in 1846, which remained unchanged and unchallenged
since then. Algebraically, the new functions are closer to
Bessel functions than to the classical hypergeometric and
Whittaker functions. The analytic theory of these functions was
completed only recently (the speaker and Jasper Stokman).

The construction is based on DAHA. The global functions are defined
as reproducing kernels of Fourier-DAHA transforms. Their
specializations are Macdonald polynomials, which is a powerful
generalization of the Shintani and Casselman-Shalika p-adic formulas.
If time permits, the connection of the Harish-Chandra theory of global
q-Whittaker functions will be discussed with the Givental-Lee formula
(Gromov-Witten invariants of flag varieties) and its generalizations due

to Braverman and Finkelberg (algebraic theory of affine flag varieties).



10:30-12:00   数理科学研究科棟(駒場) 126号室
神本 丈 氏 (九州大学)
Resolution of singularities via Newton polyhedra and its application to analysis (JAPANESE)
[ 講演概要 ]
In the 1970s, A. N. Varchenko precisely investigated the leading term of the asymptotic expansion of an oscillatory integral with real analytic phase by using the geometry of the Newton polyhedron of the phase. Since his study, the importance of the resolution of singularities by means of Newton polyhedra has been strongly recognized. The purpose of this talk is to consider studies around this theme and to explain their relationship with some problems in several complex variables.


15:30-17:00   数理科学研究科棟(駒場) 122号室
Andrés Daniel Duarte 氏 (Institut de Mathématiques de Toulouse)
Higher Nash blowup on normal toric varieties and a higher order version of Nobile's theorem (ENGLISH)
[ 講演概要 ]
The higher Nash blowup of an algebraic variety replaces singular points with limits of certain vector spaces carrying first or higher order data associated to the variety at non-singular points. In the case of normal toric varieties, the higher Nash blowup has a combinatorial description in terms of the Gröbner fan. This description will allows us to prove a higher version of Nobile's theorem in this context: for a normal toric variety, the higher Nash blowup is an isomorphism if and only if the variety is non-singular. We will also present some further observations coming from computational experiments.


16:30-18:00   数理科学研究科棟(駒場) 002号室
Chien-Hong Cho 氏 (National Chung Cheng University)
On the finite difference approximation for blow-up solutions of the nonlinear wave equation (JAPANESE)
[ 講演概要 ]
We consider in this paper the 1-dim nonlinear wave equation $u_{tt}=u_{xx}+u^{1+\\alpha}$ $(\\alpha > 0)$ and its finite difference analogue. It is known that the solutions of the current equation becomes unbounded in finite time, a phenomenon which is often called blow-up. Numerical approaches on such kind of problems are widely investigated in the last decade. However, those results are mainly about parabolic blow-up problems. Compared with the parabolic ones, there is a remarkable property for the solution of the nonlinear wave equation -- the existence of the blow-up curve. That is, even though the solution has become unbounded at certain points, the solution continues to exist at other points and blows up at later times. We are concerned in this paper as to how a finite difference scheme can reproduce such a phenomenon.
[ 講演参考URL ]



10:00-11:30   数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
小野 肇 氏 (埼玉大学)
非ハミルトン体積最小なハミルトン安定ラグランジュトーラスについて (JAPANESE)
[ 講演概要 ]
Y. –G. Oh はケーラー多様体内のラグランジュ部分多様体について、ハミルトン変形のもとでの体積の極小性(ハミルトン安定性)や最小性(ハミルトン体積最小性)について考察した。これは等周問題の1つの一般化と考えられ、例えば、複素ユークリッド空間内の標準的トーラスや複素射影空間たちの直積のトーラス軌道などはハミルトン安定であることが知られていた。本講演では次の2つの結果について紹介する:
1. 3次元以上の複素ベクトル空間のほとんどの標準的トーラスはハミルトン体積最小ではない。
2. 3次元以上の任意のコンパクトトーリックケーラー多様体のトーラス軌道にはハミルトン体積最小ではないものが数多く存在する。



14:50-16:20   数理科学研究科棟(駒場) 128号室
江夏洋一 氏 (東京大学大学院数理科学研究科)
感染個体の齢構造を持つ微分方程式系の漸近挙動とその周辺 (JAPANESE)
[ 講演概要 ]
数理モデリングを用いた定性的な理論構築は広く行われてきた. 本講演では, 感
受性個体, 感染個体, 回復個体等の数を変数とする感染症モデルの正値解の漸近
挙動に関する成果を報告し, 基本再生産数を用いた感染症の終局的流行規模の変
化を議論する. 特に, Magal, McCluskey, Webb (2010) によって定式化された感
染個体の齢構造 (感染齢) を含む SIR 感染症モデルにおいて, 感染伝達パラメ
ータが感染齢について単調増加である場合, 感染齢を持つ方程式系から離散的・
い. Lyapunov 汎関数法, 単調反復法や感染平衡解の周りでの線形化方程式系に
例についても, 感染症モデルや糖尿病モデルなどと共に報告する.탞



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

A.P. Veselov 氏 (Loughborough, UK and Tokyo, Japan)
From hyperplane arrangements to Deligne-Mumford moduli spaces: Kohno-Drinfeld way (ENGLISH)
[ 講演概要 ]
Gaudin subalgebras are abelian Lie subalgebras of maximal
dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n,
associated to A-type hyperplane arrangement.
It turns out that Gaudin subalgebras form a smooth algebraic variety
isomorphic to the Deligne-Mumford moduli space \\bar M_{0,n+1} of
stable genus zero curves with n+1 marked points.
A real version of this result allows to describe the
moduli space of integrable n-dimensional tops and
separation coordinates on the unit sphere
in terms of the geometry of Stasheff polytope.

The talk is based on joint works with L. Aguirre and G. Felder and with K.



16:40-17:40   数理科学研究科棟(駒場) 056号室
丸山拓也 氏 (東京大学数理科学研究科)
An effective upper bound for the number of principally polarized Abelian schemes (JAPANESE)


16:30-18:00   数理科学研究科棟(駒場) 122号室
小沢登高 氏 (京大数理研)
Noncommutative real algebraic geometry of Kazhdan's property (T) (ENGLISH)



10:30-12:00   数理科学研究科棟(駒場) 128号室
斎藤俊輔 氏 (東大数理)
On the existence problem of Kähler-Ricci solitons (JAPANESE)


15:30-17:00   数理科学研究科棟(駒場) 122号室
Alexandru Dimca 氏 (Institut Universitaire de France )
Syzygies of jacobian ideals and Torelli properties (ENGLISH)
[ 講演概要 ]
Let $C$ be a reduced complex projective plane curve defined by a homogeneous equation $f(x,y,z)=0$. We consider syzygies of the type $af_x+bf_y+cf_z=0$, where $a,b,c$ are homogeneous polynomials and $f_x,f_y,f_z$ stand for the partial derivatives of $f$. In our talk we relate such syzygies with stable or splittable rank two vector bundles on the projective plane, and to Torelli properties of plane curves in the sense of Dolgachev-Kapranov.



13:30-16:00   数理科学研究科棟(駒場) 123号室
岡崎龍太郎 氏 (元・同志社大学) 13:30-14:30
実数上既約な、整数係数斉次4次形式$F(X,Y)$ に対する、$F(X,Y)=1$の解の個数の評価
岡崎龍太郎 氏 (元・同志社大学) 15:00-16:00
種数2の代数曲線と、その不分岐7次拡大の組のモジュライ (JAPANESE)



10:00-11:30   数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
野澤 啓 氏 (立命館大学)
Lie葉層構造の剛性について (JAPANESE)
[ 講演概要 ]
Lie葉層の葉たちが高実階非コンパクト型対称空間と計量同型であるとき、そのLie葉層のホロノミー群は超剛性や数論性などの高実階半単純群Lie群の一様格子と似た剛性を持つことが、Zimmerの定理により知られている。本講演では、Mostow剛性の変種の応用による、実階数1の場合を含むZimmerの定理の拡張について述べる。(Ga¥"el Meigniezとの共同研究。)



16:30-18:00   数理科学研究科棟(駒場) 122号室
武石拓也 氏 (東大数理)
Bost-Connes system for local fields of characteristic zero (ENGLISH)


16:40-17:40   数理科学研究科棟(駒場) 002号室
三枝洋一 氏 (東京大学数理科学研究科)
Non-tempered A-packets and the Rapoport-Zink spaces (JAPANESE)


14:50-16:20   数理科学研究科棟(駒場) 128号室
中田行彦 氏 (東京大学大学院数理科学研究科)
Age-structured epidemic model with infection during transportation (JAPANESE)
[ 講演概要 ]
現代、航空路を手段とした大陸間移動が身近であるがゆえに、多くの感染症が世界中に蔓延することが容易となっている。本発表では、Volterra型積分方程式と遅延微分方程式を用いて、感染者個体の感染齢(age since infection)を連続的なパラメータとして組み込みながら、複数領域に広がる感染病の伝染ダイナミクスを記述する数理モデルを紹介する。領域間の個体群移動を記述するために、非自励な遅延微分方程式の解が陰的に用いられる。最後に、領域間の移動においては、それぞれの感染個体の発生状態がその交通機関内での滞在時間に連続的に依存することから、無限次元のVolterra型積分方程式が得られることを示したい。本研究はD.H.KniplおよびG. Röstとの共同研究となっている。



16:30-18:00   数理科学研究科棟(駒場) 128号室
筒井 容平 氏 (東大 数理)
拡散性を有しない誘因因子に対する走化性方程式の小さな有界な解 (JAPANESE)
[ 講演概要 ]
We consider a chemotaxis system with a logarithmic
sensitivity and a non-diffusive chemical substance. For some chemotactic
sensitivity constants, Ahn and Kang proved the existence of bounded
global solutions to the system. An entropy functional was used in their
argument to control the cell density by the density of the chemical
substance. Our purpose is to show the existence of bounded global
solutions for all the chemotactic sensitivity constants. Assuming the
smallness on the initial data in some sense, we can get uniform
estimates for time. These estimates are used to extend local solutions.
This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu
Univ.) and Juan J. L. Vel\\'azquez (Univ. of Bonn).



16:30-18:00   数理科学研究科棟(駒場) 056号室
中澤嵩 氏 (東北大学大学院理学研究科)
人工血管の最適設計を目的としたNavier-Stokes方程式の周期解に対する形状最化問題 (JAPANESE)
[ 講演概要 ]
Stokes方程式やNavier-Stokes方程式の定常解に対する形状最適化問題は,これまで多く行われてきた.しかし, Navier-Stokes方程式の周期解に対しては十分に行われていない.本講演では,安定性理論を活用することで,Navier-Stokes方程式の周期解に対する形状最適化問題を人工血管の最適設計という現実の問題を通して考察する.
[ 講演参考URL ]


10:30-12:00   数理科学研究科棟(駒場) 126号室
山本 光 氏 (東大数理)
ラグランジュ平均曲率流とその具体例について (JAPANESE)



13:30-17:00   数理科学研究科棟(駒場) 128号室
高田 了 氏 (東北大学) 13:30-15:00
Strichartz estimates for incompressible rotating fluids (JAPANESE)
[ 講演概要 ]
3次元全空間において,回転による Coriolis 力の影響を考慮した
非圧縮性 Euler 方程式または Navier-Stokes 方程式を考察する.
Coriolis 力から生成される時間発展作用素に対して,
またその応用として,Euler 方程式の長時間可解性を考察する.
上記の Strichartz 評価と Beale-Kato-Majda 型爆発判定法を
尚,本講演の前半部分は,Seoul National University の
Youngwoo Koh 氏と Sanghyuk Lee 氏との共同研究に基づくものである.
岡田 正巳 氏 (首都大学東京) 15:30-16:30
不規則配置点で観測された関数値の補間近似サンプリング定理について (JAPANESE)
[ 講演概要 ]
(参考:H. Wendland, Scattered Data Approximation,
Cambridge U.P., 2005)



17:30-18:30   数理科学研究科棟(駒場) 056号室
Olivier Wittenberg 氏 (ENS and CNRS)
On the cycle class map for zero-cycles over local fields (ENGLISH)
[ 講演概要 ]
The Chow group of zero-cycles of a smooth and projective variety defined over a field k is an invariant of an arithmetic and geometric nature which is well understood only when k is a finite field (by higher-dimensional class field theory). In this talk, we will discuss the case of local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus over p-adic fields. The same statement holds for semistable K3 surfaces over C((t)), but does not hold in general for surfaces over C((t)) or over the maximal unramified extension of a p-adic field. This is a joint work with Hélène Esnault.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)



16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
内藤 貴仁 氏 (東京大学大学院数理科学研究科)
On the rational string operations of classifying spaces and the
Hochschild cohomology (JAPANESE)
[ 講演概要 ]
Chataur and Menichi initiated the theory of string topology of
classifying spaces.
In particular, the cohomology of the free loop space of a classifying
space is endowed with a product
called the dual loop coproduct. In this talk, I will discuss the
algebraic structure and relate the rational dual loop coproduct to the
cup product on the Hochschild cohomology via the Van den Bergh isomorphism.


10:30-11:30   数理科学研究科棟(駒場) 056号室
筒井 容平 氏 (東京大学)
An application of weighted Hardy spaces to the Navier-Stokes equations (JAPANESE)
[ 講演概要 ]
The purpose of this talk is to investigate decay orders of the L^2 energy of solutions to the incompressible homogeneous Navier-Stokes equations on the whole spaces by the aid of the theory of weighted Hardy spaces. The main estimates are two weighted inequalities for heat semigroup on weighted Hardy spaces and a weighted version of the div-curl lemma due to Coifman-Lions-Meyer-Semmes. It turns out that because of the use of weighted Hardy spaces, our decay orders of the energy can be close to the critical one of Wiegner.

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