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過去の記録 ～05/01｜本日 05/02 | 今後の予定 05/03～
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
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.
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
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.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100202kassel
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.
https://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
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
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.
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
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.
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
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.
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
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.
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
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
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
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
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
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 $C^m(\\mathbf{R}^n)$?
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
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 $C^m(\\mathbf{R}^n)$?
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)
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
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.
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
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.
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
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 $C^m(\\mathbf{R}^n)$?
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 $C^m(\\mathbf{R}^n)$?
講演会
16:30-18:00 数理科学研究科棟(駒場) 056号室
伊東一文 氏 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 4
伊東一文 氏 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 4
[ 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.
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.
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
Colin Guillarmou 氏 (Ecole Normale Superieure)
Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic manifolds
Colin Guillarmou 氏 (Ecole Normale Superieure)
Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic 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
權業 善範 氏 (東大数理)
On weak Fano varieties with log canonical singularities
權業 善範 氏 (東大数理)
On weak Fano varieties with log canonical singularities
[ 講演概要 ]
We prove that the anti-canonical divisors of weak Fano
3-folds with log canonical singularities are semiample. Moreover, we consider
semiampleness of the anti-log canonical divisor of any weak log Fano pair
with log canonical singularities. We show semiampleness dose not hold in
general by constructing several examples. Based on those examples, we propose
sufficient conditions which seem to be the best possible and we prove
semiampleness under such conditions. In particular we derive semiampleness of the
anti-canonical divisors of log canonical weak Fano 4-folds whose lc centers
are at most 1-dimensional. We also investigate the Kleiman-Mori cones of
weak log Fano pairs with log canonical singularities.
We prove that the anti-canonical divisors of weak Fano
3-folds with log canonical singularities are semiample. Moreover, we consider
semiampleness of the anti-log canonical divisor of any weak log Fano pair
with log canonical singularities. We show semiampleness dose not hold in
general by constructing several examples. Based on those examples, we propose
sufficient conditions which seem to be the best possible and we prove
semiampleness under such conditions. In particular we derive semiampleness of the
anti-canonical divisors of log canonical weak Fano 4-folds whose lc centers
are at most 1-dimensional. We also investigate the Kleiman-Mori cones of
weak log Fano pairs with log canonical singularities.
2010年01月22日(金)
GCOE社会数理講演シリーズ
16:20-17:50 数理科学研究科棟(駒場) 117号室
中川淳一 氏 (新日本製鐵(株)技術開発本部)
数学者と企業研究者との連携
中川淳一 氏 (新日本製鐵(株)技術開発本部)
数学者と企業研究者との連携
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 3
伊東一文 氏 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 3
[ 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.
Nonlinear evolution equations, Crandall-Ligget theory,
Locally quasi-dissipative operators approach
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.
Nonlinear evolution equations, Crandall-Ligget theory,
Locally quasi-dissipative operators approach
2010年01月21日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
山下真 氏 (東大数理)
On Subfactors Arising from Asymptotic Representations of Symmetric Groups
山下真 氏 (東大数理)
On Subfactors Arising from Asymptotic Representations of Symmetric Groups
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 122号室
Danielle Hilhorst 氏 (パリ南大学 / CNRS)
A finite volume method on general meshes for a degenerate parabolic convection-reaction-diffusion equation
Danielle Hilhorst 氏 (パリ南大学 / CNRS)
A finite volume method on general meshes for a degenerate parabolic convection-reaction-diffusion equation
[ 講演概要 ]
We propose a finite volume method on general meshes for degenerate parabolic convection-reaction-diffusion equations. Such equations arise for instance in the modeling of contaminant transport in groundwater. After giving a convergence proof, we present the results of numerical tests.
We propose a finite volume method on general meshes for degenerate parabolic convection-reaction-diffusion equations. Such equations arise for instance in the modeling of contaminant transport in groundwater. After giving a convergence proof, we present the results of numerical tests.
2010年01月20日(水)
東京幾何セミナー
17:00-18:30 数理科学研究科棟(駒場) 122号室
場所は東大数理(駒場)、東京工業大学(大岡山)のいずれかで行います。
詳細については、上記セミナーURLよりご確認下さい。
「今後の予定」欄には、東工大で行われるセミナーは表��
Craig Van Coevering 氏 (MIT)
Asymptotically conical manifolds and the Monge-Ampere equation
場所は東大数理(駒場)、東京工業大学(大岡山)のいずれかで行います。
詳細については、上記セミナーURLよりご確認下さい。
「今後の予定」欄には、東工大で行われるセミナーは表��
Craig Van Coevering 氏 (MIT)
Asymptotically conical manifolds and the Monge-Ampere equation
[ 講演概要 ]
Some analysis is considered on manifolds with a conical end. Then we show that in the Kahler case the complex Monge-Ampere equation can be solved with the same regularity as is known in the ALE case. By considering resolutions of toric singularities and hypersurface singularities this can easily be used to produce many Calabi-Yau manifolds with a conical end.
Some analysis is considered on manifolds with a conical end. Then we show that in the Kahler case the complex Monge-Ampere equation can be solved with the same regularity as is known in the ALE case. By considering resolutions of toric singularities and hypersurface singularities this can easily be used to produce many Calabi-Yau manifolds with a conical end.
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 2
伊東一文 氏 (大学院数理科学研究科)
Fractional Evolution Equations and Applications 2
[ 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.
Existence and Uniqueness by C_0 semigroup theory, dissipative linear
operator
and Hille-Yoshida, Trotter-Kato theory.
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.
Existence and Uniqueness by C_0 semigroup theory, dissipative linear
operator
and Hille-Yoshida, Trotter-Kato theory.
数理人口学・数理生物学セミナー
14:40-16:10 数理科学研究科棟(駒場) 052号室
江島啓介 氏 (東京大学情報理工学研究科数理情報専攻修士課程)
東京都市圏パーソントリップ調査に基づく新型インフルエンザ感染拡大シミュレーション
江島啓介 氏 (東京大学情報理工学研究科数理情報専攻修士課程)
東京都市圏パーソントリップ調査に基づく新型インフルエンザ感染拡大シミュレーション
[ 講演概要 ]
新型インフルエンザの感染拡大に対する対応策として,学校施設等の閉鎖など外
出時の感染機会を減らすための措置が考えられるが,その効果は十分に明らかで
はない.そこで本研究では,individual based modelに東京都市圏パーソント
リップ調査を組み合わせることにより感染拡大モデルを構築し,数値シミュレー
ションによって外出規制および施設閉鎖の効果を検討した.外出規制に関して
は,規制日数が12日以上と長い場合には効果が大きいことがわかった.また,施
設閉鎖に関しては,閉鎖期間・閉鎖基準を厳しくすると,ピークまでの日数は変
わらないものの,累積罹患率は低下することがわかった.
新型インフルエンザの感染拡大に対する対応策として,学校施設等の閉鎖など外
出時の感染機会を減らすための措置が考えられるが,その効果は十分に明らかで
はない.そこで本研究では,individual based modelに東京都市圏パーソント
リップ調査を組み合わせることにより感染拡大モデルを構築し,数値シミュレー
ションによって外出規制および施設閉鎖の効果を検討した.外出規制に関して
は,規制日数が12日以上と長い場合には効果が大きいことがわかった.また,施
設閉鎖に関しては,閉鎖期間・閉鎖基準を厳しくすると,ピークまでの日数は変
わらないものの,累積罹患率は低下することがわかった.
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