過去の記録

過去の記録 ~02/23本日 02/24 | 今後の予定 02/25~

博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 128号室
西山 了允 氏 (東京大学大学院数理科学研究科)
CONSTRUCTION OF ISOTROPIC CELLULAR AUTOMATON AND ITS APPLICATION (等方セル・オートマトンの構成とその応用)

2010年02月04日(木)

博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 122号室
久野 雄介 氏 (東京大学大学院数理科学研究科)
The Meyer functions for projective varieties and their applications to local signatures for fibered 4-manifolds (射影多様体に対するMeyer函数と,その局所符号数への応用)

博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 122号室
服部 広大 氏 (東京大学大学院数理科学研究科)
On hyperkähler manifolds of type A∞ (A∞型超ケーラー多様体について)

博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 122号室
篠原 克寿 氏 (東京大学大学院数理科学研究科)
On the index problem for C1-generic wild homoclinic classes (C1通有的に野性的なホモクリニック類の指数問題について)

博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 122号室
佐藤 正寿 氏 (東京大学大学院数理科学研究科)
The abelianization of the level d mapping class group (レベルd写像類群のアーベル化)

博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 126号室
毛 仕寛 氏 (東京大学大学院数理科学研究科)
Singularities for Solutions to Schrödinger Equations (シュレーディンガー方程式の解の特異性)

博士論文発表会

15:45-17:00   数理科学研究科棟(駒場) 126号室
Si, Duc Quang 氏 (東京大学大学院数理科学研究科)
Nevanlinna theory for holomorphic mappings and related problems (正則写像のネヴァンリンナ理論と関連する問題)

博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 128号室
高岡 洋介 氏 (東京大学大学院数理科学研究科)
On existence of models for the logical system MPCL (単相格論理系におけるモデルの存在について)

博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 128号室
岩尾 慎介 氏 (東京大学大学院数理科学研究科)
Exact Solutions of Ultradiscrete Integrable Systems (超離散可積分系の厳密解)

博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 128号室
中田 庸一 氏 (東京大学大学院数理科学研究科)
Vertex operators and background solutions for ultradiscrete soliton equations (超離散ソリトン方程式における頂点作用素と背景解)

2010年02月02日(火)

Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーとの合同で行います。いつもと場所が違います。
Fanny Kassel 氏 (Orsay)
Deformation of compact quotients of homogeneous spaces
[ 講演概要 ]
Let G/H be a reductive homogeneous space. In all known examples, if
G/H admits compact Clifford-Klein forms, then it admits "standard"
ones, by uniform lattices of some reductive subgroup L of G acting
properly on G/H. In order to obtain more generic Clifford-Klein forms,
we prove that for L of real rank 1, if one slightly deforms in G a
uniform lattice of L, then its action on G/H remains properly
discontinuous. As an application, we obtain compact quotients of SO(2,2n)/U(1,n) by Zariski-dense discrete subgroups of SO(2,2n) acting properly discontinuously.

トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Lie群論・表現論セミナーと合同, Tea: 16:00 - 16:30 コモンルーム
Fanny Kassel 氏 (Univ. Paris-Sud, Orsay)
Deformation of compact quotients of homogeneous spaces
[ 講演概要 ]
Let G/H be a reductive homogeneous space. In all known examples, if
G/H admits compact Clifford-Klein forms, then it admits "standard"
ones, by uniform lattices of some reductive subgroup L of G acting
properly on G/H. In order to obtain more generic Clifford-Klein forms,
we prove that for L of real rank 1, if one slightly deforms in G a
uniform lattice of L, then its action on G/H remains properly
discontinuous. As an application, we obtain compact quotients of
SO(2,2n)/U(1,n) by Zariski-dense discrete subgroups of SO(2,2n) acting
properly discontinuously.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100202kassel

2010年02月01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
大沢健夫 氏 (名古屋大学多元数理科学研究科)
Connectedness of Levi nonflat pseudoconvex hypersurfaces in Kaehler manifolds

代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室
大川 新之介 氏 (東大数理)
Extensions of two Chow stability criteria to positive characteristics
[ 講演概要 ]
I will talk about two results on Chow (semi-)stability of cycles in positive characteristics, which were originally known in characteristic 0. One is on the stability of non-singular projective hypersurfaces of degree greater than 2, and the other is the criterion by Y. Lee in terms of the log canonical threshold of Chow divisor. A couple of examples will be discussed in detail.

Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Timur Sadykov 氏 (Siberian Federal University)
Bases in the solution space of the Mellin system
[ 講演概要 ]
I will present a joint work with Alicia Dickenstein.
We consider algebraic functions $z$ satisfying equations of the
form
\\begin{equation}
a_0 z^m + a_1z^{m_1} + a_2 z^{m_2} + \\ldots + a_n z^{m_n} +
a_{n+1} =0.
\\end{equation}
Here $m > m_1 > \\ldots > m_n>0,$ $m,m_i \\in \\N,$ and
$z=z(a_0,\\ldots,a_{n+1})$ is a function of the complex variables
$a_0, \\ldots, a_{n+1}.$ Solutions to such equations are
classically known to satisfy holonomic systems of linear partial
differential equations with polynomial coefficients. In the talk
I will investigate one of such systems of differential equations which
was introduced by Mellin. We compute the holonomic rank of the
Mellin system as well as the dimension of the space of its
algebraic solutions. Moreover, we construct explicit bases of
solutions in terms of the roots of initial algebraic equation and their
logarithms. We show that the monodromy of the Mellin system is
always reducible and give some factorization results in the
univariate case.

2010年01月29日(金)

談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 002号室
お茶&Coffee&お菓子: 16:00~16:30 (コモンルーム)
Charles Fefferman 氏 (Princeton University)
Extension of Functions and Interpolation of Data
[ 講演概要 ]
Let $f$ be a given real-valued function defined on a subset of $\\mathbb{R}^n$. We explain how to decide whether $f$ extends to a function $F$ in $C^m(\\mathbb{R}^n)$. If such an $F$ exists, we show how to construct one.

2010年01月28日(木)

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室
清水扇丈 氏 (静岡大学理学部)
相転移を伴う非圧縮性2相流の線形化問題について
[ 講演概要 ]
氷が常圧で0度以上になると水になるなどの相転移を伴う非圧縮性2相流に対し,質量保存則, 運動量保存則, エネルギー保存則を界面を含む系全体に適用し, 線形化した方程式系について考察する. 本講演では, 線形化方程式系のL_p-L_q 最大正則性定理について述べる.

密度が異なる場合は, 法線方向の高さ関数は表面張力つき2相Stokes問題の高さ関数と同じ正則性をもち, 系は流速が支配するのに対し,密度が等しい場合は, Gibbs-Thomson補正された表面張力つき2相Stefan問題の高さ関数と同じ正則性をもち, 系は温度が支配する.

講演会

10:40-12:10   数理科学研究科棟(駒場) 123号室
Olivier Alvarez 氏 (Head of quantitative research, IRFX options Asia, BNP Paribas)
Partial differential equations in Finance I
[ 講演概要 ]
1. Markov processes and Partial differential equations (PDE)
- Markov processes, stochastic differential equations and infinitesimal generator

- The Feynman Kac formula and the backward Kolmogorov equation

- The maximum principle

- Exit time problems and Dirichlet boundary conditions

- Optimal time problems and obstacle problems

2. Application to the pricing of exotic options
- The model equation

- The Black-Scholes equation : absence of arbitrage and dynamical hedging

- Recovering the Black-Scholes formula

- Pricing exotic options : Knock-out / knock-in, american, Asian, lookback

- Overview of affine models and semi-closed formulae

- Heston model : valuing European options

- The Hull White model for IR exotics : valuing zero-coupons, caplets and swaptions.


3. Finite difference methods in Finance
- Basic concepts for numerical schemes : consistency, stability, accuracy and

convergence; the Lax equivalence theorem

- Finite difference methods in dimension 1 : Explicit, implicit, Crank-Nicholson methods for the heat equation : overview, accuracy and convergence

Incorporating first-order derivatives : upwind derivative, stability

- Finite difference methods in dimension 2 : presentation of various schemes :explicit, implicit, alternating direction implicit (ADI), Hopscotch method

- Solving high dimensional linear systems :

LU decomposition, iterative methods

- Finite difference and Monte Carlo methods

4. Optimal control in finance
- Introduction to optimal control

- The dynamic programming principle and the Hamilton-Jacobi-Bellman equation

- The verification theorem and the determination of the optimal control policy

- Utility maximization and Merton's problem

- Pricing with uncertain parameters

- Pricing with transaction costs

- Finite difference methods for optimal control

講演会

13:00-14:10   数理科学研究科棟(駒場) 122号室
Olivier Alvarez 氏 (Head of quantitative research, IRFX options Asia, BNP Paribas)
Partial differential equations in Finance II
[ 講演概要 ]
1. Markov processes and Partial differential equations (PDE)
- Markov processes, stochastic differential equations and infinitesimal generator

- The Feynman Kac formula and the backward Kolmogorov equation

- The maximum principle

- Exit time problems and Dirichlet boundary conditions

- Optimal time problems and obstacle problems

2. Application to the pricing of exotic options
- The model equation

- The Black-Scholes equation : absence of arbitrage and dynamical hedging

- Recovering the Black-Scholes formula

- Pricing exotic options : Knock-out / knock-in, american, Asian, lookback

- Overview of affine models and semi-closed formulae

- Heston model : valuing European options

- The Hull White model for IR exotics : valuing zero-coupons, caplets and swaptions.


3. Finite difference methods in Finance
- Basic concepts for numerical schemes : consistency, stability, accuracy and

convergence; the Lax equivalence theorem

- Finite difference methods in dimension 1 : Explicit, implicit, Crank-Nicholson methods for the heat equation : overview, accuracy and convergence

Incorporating first-order derivatives : upwind derivative, stability

- Finite difference methods in dimension 2 : presentation of various schemes :explicit, implicit, alternating direction implicit (ADI), Hopscotch method

- Solving high dimensional linear systems :

LU decomposition, iterative methods

- Finite difference and Monte Carlo methods

4. Optimal control in finance
- Introduction to optimal control

- The dynamic programming principle and the Hamilton-Jacobi-Bellman equation

- The verification theorem and the determination of the optimal control policy

- Utility maximization and Merton's problem

- Pricing with uncertain parameters

- Pricing with transaction costs

- Finite difference methods for optimal control

GCOEレクチャーズ

16:30-17:30   数理科学研究科棟(駒場) 999号室
Charles Fefferman 氏 (Princeton University)
Extension of Functions and Interpolation of Data
[ 講演概要 ]
This series of three lectures will discuss the following questions. No special background will be assumed, and the third lecture will not assume familiarity with the first two.

Fix positive integers $m, n$. Let $f$ be a real-valued function on a subset $E$ of $\\mathbf{R}^n$. How can we tell whether $f$ extends to a $C^m$ function $F$ on the whole $\\mathbf{R}^n$?
If $F$ exists, how small can we take its $C^m$ norm? Can we take $F$ to depend linearly on $f$? What can we say about the derivatives of $F$ at a given point of $E$?

Suppose $E$ is finite. Can we then compute an $F$ with $C^m$ norm close to least-possible? How many operations does it take? What if we ask merely that $F$ and $f$ agree approximately on $E$? What if we are allowed to delete a few points of $E$?

What can be said about the above problems for function spaces other than $C^m(\\mathbf{R}^n)$?

2010年01月27日(水)

GCOEレクチャーズ

14:40-16:10   数理科学研究科棟(駒場) 002号室
Charles Fefferman 氏 (Princeton University)
Extension of Functions and Interpolation of Data
[ 講演概要 ]
This series of three lectures will discuss the following questions. No special background will be assumed, and the third lecture will not assume familiarity with the first two.

Fix positive integers $m, n$. Let $f$ be a real-valued function on a subset $E$ of $\\mathbf{R}^n$. How can we tell whether $f$ extends to a $C^m$ function $F$ on the whole $\\mathbf{R}^n$?
If $F$ exists, how small can we take its $C^m$ norm? Can we take $F$ to depend linearly on $f$? What can we say about the derivatives of $F$ at a given point of $E$?

Suppose $E$ is finite. Can we then compute an $F$ with $C^m$ norm close to least-possible? How many operations does it take? What if we ask merely that $F$ and $f$ agree approximately on $E$? What if we are allowed to delete a few points of $E$?

What can be said about the above problems for function spaces other than $C^m(\\mathbf{R}^n)$?

2010年01月26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
Jacob S. Christiansen 氏 (コペンハーゲン大学)
Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)

トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム
栗林 勝彦 氏 (信州大学)
On the (co)chain type levels of spaces
[ 講演概要 ]
Avramov, Buchweitz, Iyengar and Miller have introduced
the notion of the level for an object of a triangulated category.
The invariant measures the number of steps to build the given object
out of some fixed object with triangles.
Using this notion in the derived category of modules over a (co)chain
algebra,
we define a new topological invariant, which is called
the (co)chain type level of a space.
In this talk, after explaining fundamental properties of the invariant,
I describe the chain type level of the Borel construction
of a homogeneous space as a computational example.

I will also relate the chain type level of a space to algebraic
approximations of the L.-S. category due to Kahl and to
the original L.-S. category of a map.

講演会

16:30-18:00   数理科学研究科棟(駒場) 118号室
伊東一文 氏 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 5
[ 講演概要 ]
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.

2010年01月25日(月)

GCOEレクチャーズ

14:40-16:10   数理科学研究科棟(駒場) 002号室
Charles Fefferman 氏 (Princeton University)
Extension of Functions and Interpolation of Data
[ 講演概要 ]
This series of three lectures will discuss the following questions. No special background will be assumed, and the third lecture will not assume familiarity with the first two.

Fix positive integers $m, n$. Let $f$ be a real-valued function on a subset $E$ of $\\mathbf{R}^n$. How can we tell whether $f$ extends to a $C^m$ function $F$ on the whole $\\mathbf{R}^n$?
If $F$ exists, how small can we take its $C^m$ norm? Can we take $F$ to depend linearly on $f$? What can we say about the derivatives of $F$ at a given point of $E$?

Suppose $E$ is finite. Can we then compute an $F$ with $C^m$ norm close to least-possible? How many operations does it take? What if we ask merely that $F$ and $f$ agree approximately on $E$? What if we are allowed to delete a few points of $E$?

What can be said about the above problems for function spaces other than $C^m(\\mathbf{R}^n)$?

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